Actimath à l'infini 1 - 2e édition - le cahier d'activités by VAN IN

CAHIER D’ACTIVITÉS

Cahier d’activités Actimath à l’infini - 2 e édition

Ph. Ancia M. Bams M. Colin P. Dewaele F. Huin J.-L. Lozet A. Want

1 2 e édition

ISBN 978-90-306-9297-3 590881

9 789030 692973

vanin.be

1 Philippe Ancia Maryse Bams Marlène Colin Pascal Dewaele Fabrice Huin Jean-Luc Lozet Aline Want

CAHIER D'ACTIVITÉS 2 e édition

Udiddit͕ ůĂ ƉůĂƚĞͲĨŽƌŵĞ Ě͛ĂƉƉƌĞŶƟƐƐĂŐĞ ĞŶ ůŝŐŶĞ ƉŽƵƌ ůĞƐ ĠůğǀĞƐ Ğƚ ůĞƐ ĞŶƐĞŝŐŶĂŶƚƐ >Ă ƉůĂƚĞͲĨŽƌŵĞ Udiddit ƚĞ ĚŽŶŶĞ͕ ƉĂƌ ĞǆĞŵƉůĞΎ͕ ĂĐĐğƐ ă ͗ Ͳ ĚĞƐ ĞǆĞƌĐŝĐĞƐ ĞŶ ůŝŐŶĞ ƉŽƵƌ ƚ͛ĞŶƚƌĂŠŶĞƌ͕ Ͳ ƵŶ ĂƉĞƌĕƵ ĚĞ ƚĞƐ ƉƌŽŐƌğƐ Ğƚ ĚĞ ƚĞƐ ƌĠƐƵůƚĂƚƐ͕ Ͳ ĚƵ ŵĂƚĠƌŝĞů ĚĞ ĐŽƵƌƐ͕ Ͳ ĚĞƐ ũĞƵǆ ĐĂƉƟǀĂŶƚƐ͕ Ͳ Ğƚ ďŝĞŶ ƉůƵƐ ĞŶĐŽƌĞ͘͘͘ Ύ Ŷ ĨŽŶĐƟŽŶ ĚĞ ůĂ ŵĠƚŚŽĚĞ

ƌĠĞͲƚŽŝ ƵŶ ĐŽŵƉƚĞ ƐƵƌ ǁǁǁ͘ƵĚŝĚĚŝƚ͘ďĞ Ğƚ ĂĐͲ ĐğĚĞ ă ƚŽŶ ĐŽŶƚĞŶƵ ă ů͛ĂŝĚĞ ĚƵ ĐŽĚĞ Ě͛ĂĐƟǀĂƟŽŶ ĐŝͲĚĞƐƐŽƵƐ ͗

ĞƩĞ ůŝĐĞŶĐĞ ĞƐƚ ǀĂůĂďůĞ ƉĞŶĚĂŶƚ ϭ ĂŶ ă ƉĂƌƟƌ ĚĞ ůĂ ĚĂƚĞ Ě͛ĂĐƟǀĂƟŽŶ͘

ŽŵƉŽƐŝƟŽŶ Ě͛ ĐƟŵĂƚŚ ă ů͛ŝŶĮŶŝ ϭ WŽƵƌ ů͛ĠůğǀĞ

ĂŚŝĞƌ ĚΖĂĐƟǀŝƚĠƐ ;н ĂĐĐğƐ hĚŝĚĚŝƚ ĂƵǆ ĞǆĞƌĐŝĐĞƐ ŶƵŵĠƌŝƋƵĞƐͿ ZĠĨĠƌĞŶƟĞů ĚĞ ƚŚĠŽƌŝĞ ƉŽƵƌ ůĂ ϭre ĂŶŶĠĞ

WŽƵƌ ůĞ ƉƌŽĨĞƐƐĞƵƌ 'ƵŝĚĞ ŵĠƚŚŽĚŽůŽŐŝƋƵĞ ;н ĂĐĐğƐ hĚŝĚĚŝƚ ĂƵ ŵĂƚĠƌŝĞů ĚĞ ĐŽƵƌƐͿ >ŝǀƌĞ ŶƵŵĠƌŝƋƵĞ ĐƟŵĂƚŚ ă ů͛ŝŶĮŶŝ ϭ ʹ ĂŚŝĞƌ ĚΖĂĐƟǀŝƚĠƐ ƵƚĞƵƌƐ ͗

DĂƌǇƐĞ ĂŵƐ͕ DĂƌůğŶĞ ŽůŝŶ͕ WĂƐĐĂů ĞǁĂĞůĞ͕ &ĂďƌŝĐĞ ,ƵŝŶ͕ :ĞĂŶͲ>ƵĐ >ŽǌĞƚ Ğƚ ůŝŶĞ tĂŶƚ ƐŽƵƐ ůĂ ĚŝƌĞĐƟŽŶ ĚĞ Ğƚ ĂǀĞĐ WŚŝůŝƉƉĞ ŶĐŝĂ

ŽƵǀĞƌƚƵƌĞ ͗ DŝƐĞ ĞŶ ƉĂŐĞ ͗

ĂĐŐ ƚĞůŝĞƌ ƌĠĂƟŽŶ 'ƌĂƉŚŝƋƵĞ ůŝŶĞĂ 'ƌĂƉŚŝĐƐ

>ĞƐ ƉŚŽƚŽĐŽƉŝĞƵƐĞƐ ƐŽŶƚ Ě͛ƵŶ ƵƐĂŐĞ ƚƌğƐ ƌĠƉĂŶĚƵ Ğƚ ďĞĂƵĐŽƵƉ Ǉ ƌĞĐŽƵƌĞŶƚ ĚĞ ĨĂĕŽŶ ĐŽŶƐƚĂŶƚĞ Ğƚ ŵĂĐŚŝŶĂůĞ͘ DĂŝƐ ůĂ ƉƌŽĚƵĐƟŽŶ ĚĞ ůŝǀƌĞƐ ŶĞ ƐĞ ƌĠĂůŝƐĞ ƉĂƐ ĂƵƐƐŝ ĨĂĐŝůĞŵĞŶƚ ƋƵ͛ƵŶĞ ƐŝŵƉůĞ ƉŚŽƚŽĐŽƉŝĞ͘ ůůĞ ĚĞŵĂŶĚĞ ďŝĞŶ ƉůƵƐ Ě͛ĠŶĞƌŐŝĞ͕ ĚĞ ƚĞŵƉƐ Ğƚ Ě͛ĂƌŐĞŶƚ͘ >Ă ƌĠŵƵŶĠƌĂƟŽŶ ĚĞƐ ĂƵƚĞƵƌƐ͕ Ğƚ ĚĞ ƚŽƵƚĞƐ ůĞƐ ƉĞƌƐŽŶŶĞƐ ŝŵƉůŝƋƵĠĞƐ ĚĂŶƐ ůĞ ƉƌŽĐĞƐƐƵƐ ĚĞ ĐƌĠĂƟŽŶ Ğƚ ĚĞ ĚŝƐƚƌŝďƵƟŽŶ ĚĞƐ ůŝǀƌĞƐ͕ ƉƌŽǀŝĞŶƚ ĞǆĐůƵƐŝǀĞŵĞŶƚ ĚĞ ůĂ ǀĞŶƚĞ ĚĞ ĐĞƐ ŽƵǀƌĂŐĞƐ͘ Ŷ ĞůŐŝƋƵĞ͕ ůĂ ůŽŝ ƐƵƌ ůĞ ĚƌŽŝƚ Ě͛ĂƵƚĞƵƌ ƉƌŽƚğŐĞ ů͛ĂĐƟǀŝƚĠ ĚĞ ĐĞƐ ĚŝīĠƌĞŶƚĞƐ ƉĞƌƐŽŶŶĞƐ͘ >ŽƌƐƋƵ͛ŝů ĐŽƉŝĞ ĚĞƐ ůŝǀƌĞƐ͕ ĞŶ ĞŶƟĞƌ ŽƵ ĞŶ ƉĂƌƟĞ͕ ĞŶ ĚĞŚŽƌƐ ĚĞƐ ĞǆĐĞƉƟŽŶƐ ĚĠĮŶŝĞƐ ƉĂƌ ůĂ ůŽŝ͕ ů͛ƵƐĂŐĞƌ ƉƌŝǀĞ ĐĞƐ ĚŝīĠƌĞŶƚĞƐ ƉĞƌƐŽŶŶĞƐ Ě͛ƵŶĞ ƉĂƌƚ ĚĞ ůĂ ƌĠŵƵŶĠƌĂƟŽŶ ƋƵŝ ůĞƵƌ ĞƐƚ ĚƵĞ͘ ͛ĞƐƚ ƉŽƵƌƋƵŽŝ ůĞƐ ĂƵƚĞƵƌƐ Ğƚ ůĞƐ ĠĚŝƚĞƵƌƐ ĚĞŵĂŶĚĞŶƚ ƋƵ͛ĂƵĐƵŶ ƚĞǆƚĞ ƉƌŽƚĠŐĠ ŶĞ ƐŽŝƚ ĐŽƉŝĠ ƐĂŶƐ ƵŶĞ ĂƵƚŽƌŝƐĂƟŽŶ ĠĐƌŝƚĞ ƉƌĠĂůĂďůĞ͕ ĞŶ ĚĞŚŽƌƐ ĚĞƐ ĞǆĐĞƉƟŽŶƐ ĚĠĮŶŝĞƐ ƉĂƌ ůĂ ůŽŝ͘ >͛ĠĚŝƚĞƵƌ Ɛ͛ĞƐƚ ĞīŽƌĐĠ Ě͛ŝĚĞŶƟĮĞƌ ƚŽƵƐ ůĞƐ ĚĠƚĞŶƚĞƵƌƐ ĚĞ ĚƌŽŝƚƐ͘ ^ŝ͕ ŵĂůŐƌĠ ĐĞůĂ͕ ƋƵĞůƋƵ͛ƵŶ ĞƐƟŵĞ ĞŶƚƌĞƌ ĞŶ ůŝŐŶĞ ĚĞ ĐŽŵƉƚĞ ĞŶ ƚĂŶƚ ƋƵ͛ĂǇĂŶƚ ĚƌŽŝƚ͕ ŝů ĞƐƚ ŝŶǀŝƚĠ ă Ɛ͛ĂĚƌĞƐƐĞƌ ă ů͛ĠĚŝƚĞƵƌ͘

Ξ ĚŝƟŽŶƐ s E /E͕ DŽŶƚͲ^ĂŝŶƚͲ'ƵŝďĞƌƚ ʹ tŽŵŵĞůŐĞŵ͕ ϮϬϭϵ dŽƵƐ ĚƌŽŝƚƐ ƌĠƐĞƌǀĠƐ͘ Ŷ ĚĞŚŽƌƐ ĚĞƐ ĞǆĐĞƉƟŽŶƐ ĚĠĮŶŝĞƐ ƉĂƌ ůĂ ůŽŝ͕ ĐĞƚ ŽƵǀƌĂŐĞ ŶĞ ƉĞƵƚ ġƚƌĞ ƌĞƉƌŽĚƵŝƚ͕ ĞŶƌĞŐŝƐƚƌĠ ĚĂŶƐ ƵŶ ĮĐŚŝĞƌ ŝŶĨŽƌŵĂƟƐĠ ŽƵ ƌĞŶĚƵ ƉƵďůŝĐ͕ ŵġŵĞ ƉĂƌƟĞůůĞŵĞŶƚ͕ ƉĂƌ ƋƵĞůƋƵĞ ŵŽǇĞŶ ƋƵĞ ĐĞ ƐŽŝƚ͕ ƐĂŶƐ ů͛ĂƵƚŽƌŝƐĂƟŽŶ ĠĐƌŝƚĞ ĚĞ ů͛ĠĚŝƚĞƵƌ͘

Ϯe ĠĚŝƟŽŶ ͗ ϮϬϭϵ /^ E ϵϳϴͲϵϬͲϯϬϲͲϵϮϵϳͲϯ ͬϮϬϭϵͬϬϬϳϴͬϵϱ ƌƚ͘ ϱϵϬϴϴϭͬϬϭ പ

Introduction dƵ ǀŝĞŶƐ ĚĞ ƚĞƌŵŝŶĞƌ ů͛ ĐŽůĞ WƌŝŵĂŝƌĞ ƋƵŝ ƚ͛Ă ĨŽƵƌŶŝ ůĞƐ ďĂƐĞƐ ŶĠĐĞƐƐĂŝƌĞƐ ă ƵŶĞ ƌĠƵƐƐŝƚĞ ĞŶ ŵĂƚŚĠŵĂƟ ƋƵĞƐ ͗ ĐĂůĐƵů ŵĞŶƚĂů͕ ĐĂůĐƵů ĠĐƌŝƚ͕ ƉƌŽďůğŵĞƐ͕ ƐǇƐƚğŵĞ ŵĠƚƌŝƋƵĞ͕ ĨŽƌŵĞƐ ŐĠŽŵĠƚƌŝƋƵĞƐ͘ ƵũŽƵƌĚ͛ŚƵŝ͕ ƚƵ ĞŶƚƌĞƐ ĞŶ ƉƌĞŵŝğƌĞ ĂŶŶĠĞ ĚƵ ^ĞĐŽŶĚĂŝƌĞ ĚŽŶƚ ů͛ŽďũĞĐƟ Ĩ ƉƌŝŶĐŝƉĂů ĞƐƚ ĚĞ ĐŽŶƐŽůŝĚĞƌ ůĞ ƐĂǀŽŝƌ ĂĐƋƵŝƐ ĂŶƚĠƌŝĞƵƌĞŵĞŶƚ͕ ĞŶ ƉĂƌƟ ĐƵůŝĞƌ ĞŶ ĐĂůĐƵů Ğƚ ĞŶ ŐĠŽŵĠƚƌŝĞ͘ >ΖĂƉƉƌĞŶƟ ƐƐĂŐĞ ĚĞƐ ŵĂƚŚĠŵĂƟ ƋƵĞƐ ĚĂŶƐ ůΖĞŶƐĞŝŐŶĞŵĞŶƚ ƐĞĐŽŶĚĂŝƌĞ ǀĂ ĚĠǀĞůŽƉƉĞƌ ƚĞƐ ĐŽŵƉĠƚĞŶĐĞƐ ŵĂƚŚĠŵĂƟ ƋƵĞƐ͕ ƚĞ ĨĂŝƌĞ ĂĐƋƵĠƌŝƌ ƵŶ ĞƐƉƌŝƚ Ě͛ĂŶĂůǇƐĞ͕ ůŽŐŝƋƵĞ Ğƚ ĐƌĠĂƟ Ĩ͘ dƵ ǀĂƐ ĂƉƉƌĞŶĚƌĞ ă ĚĠĐƌŝƌĞ͕ ŝŶƚĞƌƉƌĠƚĞƌ͕ ũƵŐĞƌ Ğƚ ĂƉƉůŝƋƵĞƌ ƚĞƐ ĐŽŶŶĂŝƐƐĂŶĐĞƐ͘ Į Ŷ ƋƵĞ ƚƵ ƉƵŝƐƐĞƐ ĂƩ ĞŝŶĚƌĞ ƚŽƵƐ ĐĞƐ ŽďũĞĐƟ ĨƐ͕ ŶŽƵƐ ĂǀŽŶƐ ĐŽŶĕƵ ƵŶ ŵĂŶƵĞů Žƶ ƐĞ ĐƀƚŽŝĞŶƚ ĂĐƟ ǀŝƚĠƐ ĚĞ ĚĠĐŽƵǀĞƌƚĞ͕ ĞǆĞƌĐŝĐĞƐ Ě͛ĂƉƉůŝĐĂƟ ŽŶ͕ ƉƌŽďůğŵĞƐ ŵĂƚŚĠŵĂƟ ƋƵĞƐ Ğƚ ƉƌŽďůğŵĞƐ ĚĞ ůĂ ǀŝĞ ĐŽƵƌĂŶƚĞ͘ WŽƵƌ ƚΖĂŝĚĞƌ ă ĞǆƉůŽƌĞƌ Ğƚ ă ĐŽŵƉƌĞŶĚƌĞ ĐĞƐ ƐŝƚƵĂƟ ŽŶƐ ŶŽƵǀĞůůĞƐ͕ ŶŽƵƐ ĂǀŽŶƐ ƐƚƌƵĐƚƵƌĠ ĐŚĂƋƵĞ ĐŚĂƉŝƚƌĞ ĞŶ ĂĐƟ ǀŝƚĠƐ͘ ĞůůĞƐͲĐŝ ĚŽŝǀĞŶƚ ƚĞ ƉĞƌŵĞƩ ƌĞ ĚĞ ĨĂŝƌĞ ůĞ ƉŽŝŶƚ ƐƵƌ ĐĞ ƋƵĞ ƚƵ ƐĂŝƐ͕ ĚĞ ƌĠƐŽƵĚƌĞ ĚĞƐ ƉĞƟ ƚƐ ƉƌŽďůğŵĞƐ ĂǀĞĐ ůĞƐ ŵŽǇĞŶƐ ĚŽŶƚ ƚƵ ĚŝƐƉŽƐĞƐ͕ ĚĞ ĐŽŶĨƌŽŶƚĞƌ ƚĂ ƌĞĐŚĞƌĐŚĞ ĂǀĞĐ ĐĞůůĞ Ě͛ĂƵƚƌĞƐ ĠůğǀĞƐ Ğƚ ĚĞ ƚŽŶ ƉƌŽĨĞƐƐĞƵƌ͕ ĚΖĞǆƉůŝƋƵĞƌ ƚĂ ĚĠŵĂƌĐŚĞ͕ ĚĞ ǀĠƌŝĮ Ğƌ ƚĞƐ ƌĠƐƵůƚĂƚƐ͕ ĞŶ ƵŶ ŵŽƚ ĚĞ ĚĠĐŽƵǀƌŝƌ ůĞƐ ŵĂƚŚĠŵĂƟ ƋƵĞƐ͘ dŽŶ ƉƌŽĨĞƐƐĞƵƌ ƵƟ ůŝƐĞƌĂ ƉĞƵƚͲġƚƌĞ ĞŶ ĐůĂƐƐĞ ůĞ ŵĂŶƵĞů ŶƵŵĠƌŝƋƵĞ ĚĞ ƚŽŶ ĐƟ ŵĂƚŚ ă ů͛/ŶĮ Ŷŝ͘ dŽƵƐ ůĞƐ ĞǆĞƌĐŝĐĞƐ ĂŶŝŵĠƐ ƋƵĞ ƚƵ Ǉ ǀĞƌƌĂƐ ƐŽŶƚ ĚŝƐƉŽŶŝďůĞƐ ƐƵƌ ůĂ ƉůĂƚĞĨŽƌŵĞ hĚŝĚĚŝƚ͘ dƵ ƉŽƵƌƌĂƐ ĚŽŶĐ ůĞƐ ƌĞĨĂŝƌĞ ĐŚĞǌ ƚŽŝ͘ ĞƐ ĞǆĞƌĐŝĐĞƐ ƐĞƌŽŶƚ ƌĞŶƐĞŝŐŶĠƐ ĚĂŶƐ ƚŽŶ ĐĂŚŝĞƌ ƉĂƌ ƵŶ ůŽŐŽ ƐƉĠĐŝĮ ƋƵĞ͘ dƵ Ǉ ƚƌŽƵǀĞƌĂƐ ĠŐĂůĞŵĞŶƚ ĚĞƐ ĞǆĞƌĐŝĐĞƐ ŝŶƚĞƌĂĐƟ ĨƐ ĂƵǆƋƵĞůƐ ƚƵ ƉŽƵƌƌĂƐ ƚΖĂĚŽŶŶĞƌ ůŝďƌĞŵĞŶƚ Ğƚ ƉŽƵƌ ůĞƐƋƵĞůƐ ƚƵ ĚŝƐƉŽƐĞƌĂƐ ĚΖƵŶ ĨĞĞĚďĂĐŬ ƉĞƌƐŽŶŶĂůŝƐĠ͘ ͛ĞƐƚ ĠŐĂůĞŵĞŶƚ ĚĂŶƐ ƚŽŶ ĐĂŚŝĞƌ Ě͛ĂĐƟ ǀŝƚĠƐ ƋƵĞ ƚƵ ƚƌŽƵǀĞƌĂƐ ƚŽŶ ĐŽĚĞ Ě͛ĂĐĐğƐ ă ƚŽŶ ĐŽŵƉƚĞ hĚŝĚĚŝƚ͘ EŽƵƐ ĞƐƉĠƌŽŶƐ ƋƵĞ ĐĞ ŵĂŶƵĞů ƚΖĂŝĚĞƌĂ ĚĂŶƐ ůĂ ĐŽŶƐƚƌƵĐƟ ŽŶ ĚĞ ƚŽŶ ƐĂǀŽŝƌ ŵĂƚŚĠŵĂƟ ƋƵĞ Ğƚ ƋƵΖĂƵ ƚĞƌŵĞ ĚĞ ĐĞƩ Ğ ƉƌĞŵŝğƌĞ ĂŶŶĠĞ͕ ƚƵ ĚŝƐƉŽƐĞƌĂƐ ĚĞ ŶŽƵǀĞĂƵǆ ŽƵƟ ůƐ ƋƵŝ ƚĞ ƉĞƌŵĞƩ ƌŽŶƚ͕ ĚĂŶƐ ůΖĂǀĞŶŝƌ͕ ĚĞ ĨĂŝƌĞ ĚĞ ŐƌĂŶĚƐ ƉƌŽŐƌğƐ ĞŶ ŵĂƚŚĠŵĂƟ ƋƵĞƐ Ğƚ ƐƵƌƚŽƵƚ ĚĞ ůĞƐ ǀŽŝƌ ƐŽƵƐ ƵŶ ũŽƵƌ ŶŽƵǀĞĂƵ͘ >ĞƐ ĂƵƚĞƵƌƐ

Mode d’emploi dŽŶ ůŝǀƌĞ͕ ĐƟ ŵĂƚŚ ă ů͛ŝŶĮ Ŷŝ͕ ĞƐƚ ĚŝǀŝƐĠ ĞŶ ĚŽƵǌĞ ĐŚĂƉŝƚƌĞƐ͕ ĨĂĐŝůĞŵĞŶƚ ƌĞƉĠƌĂďůĞƐ ŐƌąĐĞ ĂƵǆ ŝŶĚŝĐĂƟ ŽŶƐ ƐŝƚƵĠĞƐ ƐƵƌ ůĞ ďŽƌĚ ĞǆƚĠƌŝĞƵƌ ŵĞŶƟ ŽŶŶĂŶƚ ůĞ ŶƵŵĠƌŽ ĚƵ ĐŚĂƉŝƚƌĞ͘ ĞƐ ĐŚĂƉŝƚƌĞƐ ƐŽŶƚ ĞƵǆͲŵġŵĞƐ ĚŝǀŝƐĠƐ ĞŶ ĂĐƟ ǀŝƚĠƐ͘ dŽŶ ƉƌŽĨĞƐƐĞƵƌ ĐŚŽŝƐŝƌĂ ĐĞůůĞƐ ƋƵŝ ƚĞ ƉĞƌŵĞƩ ƌŽŶƚ ĚΖĂƩ ĞŝŶĚƌĞ ůĞƐ ŽďũĞĐƟ ĨƐ Į ǆĠƐ Ğƚ ŝů ƚĞ ĚŽŶŶĞƌĂ ĚĞƐ ĐŽŶƐĞŝůƐ ƉŽƵƌ ĐŽŵƉůĠƚĞƌ ĐĞƐ Į ĐŚĞƐ ĚĞ ƚƌĂǀĂŝů͘ >Ă ƚŚĠŽƌŝĞ ƌĞůĂƟ ǀĞ ă ĐŚĂƋƵĞ ĐŚĂƉŝƚƌĞ ĞƐƚ ƌĞŐƌŽƵƉĠĞ ĚĂŶƐ ƵŶ ƌĠĨĠƌĞŶƟ Ğů ƋƵĞ ƚƵ ĚĞǀƌĂƐ ĂƉƉŽƌƚĞƌ ĂǀĞĐ ƚŽŝ ă ĐŚĂƋƵĞ ŚĞƵƌĞ ĚĞ ĐŽƵƌƐ͘ Ŷ Ğī Ğƚ͕ ĐŚĂƋƵĞ ĨŽŝƐ ƋƵ͛ƵŶĞ ŶŽƵǀĞůůĞ ŶŽƟ ŽŶ ƚŚĠŽƌŝƋƵĞ ƐĞƌĂ ŵŝƐĞ ĞŶ ƉůĂĐĞ͕ ƚŽŶ ƉƌŽĨĞƐƐĞƵƌ ƚĞ ƌĞŶǀĞƌƌĂ ă ĐĞ ŵĂŶƵĞů ĚĞ ƌĠĨĠƌĞŶĐĞ͘ dƵ ƌĞŵĂƌƋƵĞƌĂƐ ƚƌğƐ ǀŝƚĞ ƋƵĞ ƚƌŽŝƐ ůŽŐŽƐ ĂƉƉĂƌĂŝƐƐĞŶƚ ƌĠŐƵůŝğƌĞŵĞŶƚ ĂƵ Į ů ĚĞƐ ƉĂŐĞƐ͘ /ůƐ ŽŶƚ ĠǀŝĚĞŵŵĞŶƚ ƵŶĞ ƐŝŐŶŝĮ ĐĂƟ ŽŶ ƉĂƌƟ ĐƵůŝğƌĞ͘ WĞŶĚĂŶƚ ƵŶĞ ĂĐƟ ǀŝƚĠ͕ Ɛŝ ƵŶĞ ŶŽƟ ŽŶ ƉĞƵƚ ;ĚŽŝƚͿ ġƚƌĞ ƉƌĠĐŝƐĠĞ ŽƵ ĨŽƌŵƵůĠĞ͕ ĐĞ ůŽŐŽ ƚΖŝŶĚŝƋƵĞ ůĂ ƌĠĨĠƌĞŶĐĞ ƉĞƌŵĞƩ ĂŶƚ ĚĞ ůĂ ƌĞƚƌŽƵǀĞƌ ĚĂŶƐ ůĂ ƚŚĠŽƌŝĞ͘ Ğ ůŽŐŽ ƐŝŐŶĂůĞ ƋƵĞ ĚĞƐ ĞǆĞƌĐŝĐĞƐ ĚĞ ƚŽŶ ůŝǀƌĞ ƐŽŶƚ ĂŶŝŵĠƐ Ğƚ ƐĞ ƚƌŽƵǀĞŶƚ ƐƵƌ ůĂ ƉůĂƚĞĨŽƌŵĞ hĚŝĚĚŝƚ͘ ĞůĂ ƚĞ ƉĞƌŵĞƩ ƌĂ ĚĞ ƚ͛ĞǆĞƌĐĞƌ ă ĚŽŵŝĐŝůĞ͘ CE

1D 7 17

Ğ ůŽŐŽ ŝŶĚŝƋƵĞ ƋƵĞ ůΖĞǆĞƌĐŝĐĞ ĐŽŶĐĞƌŶĠ Ă ĠƚĠ ƌĞƉƌŝƐ ĚĞƐ ƋƵĞƐƟ ŽŶƐ ĚƵ ϭ Ğƚ ĞŶ ƉƌĠĐŝƐĞ ůΖĂŶŶĠĞ͘

ŚĂƋƵĞ ĐŚĂƉŝƚƌĞ ƐĞ ƚĞƌŵŝŶĞ ƉĂƌ ƋƵĞůƋƵĞƐ ĨĞƵŝůůĞƐ ůĠŐğƌĞŵĞŶƚ ĐŽůŽƌĠĞƐ ĐŽŶƚĞŶĂŶƚ ƵŶĞ ƐĠƌŝĞ ĚΖĞǆĞƌĐŝĐĞƐ ĐŽŵƉůĠŵĞŶƚĂŝƌĞƐ͘ ĞƵǆͲĐŝ ƐŽŶƚ ĐůĂƐƐĠƐ ĞŶ ƚƌŽŝƐ ĐĂƚĠŐŽƌŝĞƐ͘ ͻ KEE 2dZ ^ĞůŽŶ ůĞƐ ĐĂƐ͕ ƚƵ ĚĞǀƌĂƐ ŝůůƵƐƚƌĞƌ ƵŶ ĠŶŽŶĐĠ ƉĂƌ ƵŶ ĞǆĞŵƉůĞ ŽƵ ƵŶ ĚĞƐƐŝŶ͕ ũƵƐƟ Į Ğƌ ĐĞƌƚĂŝŶĞƐ ĠƚĂƉĞƐ Ě͛ƵŶ ĐĂůĐƵů͕ ͘͘͘ ͻ WW>/Yh Z ĞƐ ĞǆĞƌĐŝĐĞƐ ƚĞ ƉĞƌŵĞƩ ƌŽŶƚ Ě͛ƵƟ ůŝƐĞƌ͕ Ě͛ĂƉƉůŝƋƵĞƌ ĚĞ ŵĂŶŝğƌĞ ƌĠŇ ĠĐŚŝĞ ůĞƐ ƐĂǀŽŝƌƐ ĂĐƋƵŝƐ͘ ͻ dZ E^& Z Z dƵ ƐĞƌĂƐ ĐŽŶĨƌŽŶƚĠ;ĞͿ ă ĚĞƐ ƐŝƚƵĂƟ ŽŶƐ ŶŽƵǀĞůůĞƐ Ğƚ ŝŶĠĚŝƚĞƐ ƋƵŝ Ɛ͛ŝŶƐĐƌŝǀĞŶƚ ƚŽƵƚĞĨŽŝƐ ĚĂŶƐ ůĞ ƉƌŽůŽŶŐĞŵĞŶƚ ĚĞ ĐĞůůĞƐ ĞǆƉůŽŝƚĠĞƐ ůŽƌƐ ĚĞƐ ĂƉƉƌĞŶƟ ƐƐĂŐĞƐ͘ >Ğ ŵŽŵĞŶƚ ǀĞŶƵ͕ ƚŽŶ ƉƌŽĨĞƐƐĞƵƌ ƚĞ ĚŝƌĂ ƋƵĞůƐ ĞǆĞƌĐŝĐĞƐ ƌĠƐŽƵĚƌĞ͘ dŽŶ ůŝǀƌĞ ƐĞ ƚĞƌŵŝŶĞ ƉĂƌ ƋƵĞůƋƵĞƐ ƉĂŐĞƐ Ě͛ĞǆĞƌĐŝĐĞƐ ĚĞƐƟ ŶĠƐ ă ǀĠƌŝĮ Ğƌ ƋƵĞ ƚƵ ŵĂŠƚƌŝƐĞƐ ůĞƐ ĐŽŵƉĠƚĞŶĐĞƐ ĚĠǀĞůŽƉƉĠĞƐ͘ WŽƵƌ ůĞƐ ƌĠƐŽƵĚƌĞ͕ ƚƵ ĚĞǀƌĂƐ ŵĞƩ ƌĞ ĞŶ ƈƵǀƌĞ͕ ĞŶ ůĞƐ ŽƌŐĂŶŝƐĂŶƚ͕ ĚĞƐ ƐĂǀŽŝƌƐ͕ ĚĞƐ ƐĂǀŽŝƌͲĨĂŝƌĞ Ğƚ ĚĞƐ Ăƫ ƚƵĚĞƐ͘ /ůƐ ƚĞ ƉƌĠƉĂƌĞƌŽŶƚ ă ů͛ĠƉƌĞƵǀĞ ĚƵ ϭ ă ůĂƋƵĞůůĞ ƚƵ ƐĞƌĂƐ ƐŽƵŵŝƐ ă ůĂ Į Ŷ ĚƵ ƉƌĞŵŝĞƌ ĚĞŐƌĠ͘ dŽŶ ƉƌŽĨĞƐƐĞƵƌ ƵƟ ůŝƐĞƌĂ ƉĞƵƚͲġƚƌĞ ĞŶ ĐůĂƐƐĞ ůĞ ŵĂŶƵĞů ŶƵŵĠƌŝƋƵĞ ĚĞ ƚŽŶ ĐƟ ŵĂƚŚ ă ů͛/ŶĮ Ŷŝ͘ dŽƵƐ ůĞƐ ĞǆĞƌĐŝĐĞƐ ĂŶŝŵĠƐ ƋƵĞ ƚƵ Ǉ ǀĞƌƌĂƐ ƐŽŶƚ ĚŝƐƉŽŶŝďůĞƐ ƐƵƌ hĚŝĚĚŝƚ͘ dƵ Ǉ ƚƌŽƵǀĞƌĂƐ ĠŐĂůĞŵĞŶƚ ĚĞƐ ĞǆĞƌĐŝĐĞƐ ŝŶƚĞƌĂĐƟ ĨƐ ĂƵǆƋƵĞůƐ ƚƵ ƉŽƵƌƌĂƐ ƚΖĂĚŽŶŶĞƌ ůŝďƌĞŵĞŶƚ Ğƚ ƉŽƵƌ ůĞƐƋƵĞůƐ ƚƵ ĚŝƐƉŽƐĞƌĂƐ ĚΖƵŶ ĨĞĞĚďĂĐŬ ƉĞƌƐŽŶŶĂůŝƐĠ͘ dŽƵƚĞƐ ůĞƐ ǀŝĚĠŽƐ ƐŽŶƚ ĂĐĐĞƐƐŝďůĞƐ ĚŝƌĞĐƚĞŵĞŶƚ ǀŝĂ ƚŽŶ ƐŵĂƌƚƉŚŽŶĞ ŽƵ ƚĂ ƚĂďůĞƩ Ğ ͊ ϭ͘ dĠůĠĐŚĂƌŐĞ ůΖĂƉƉůŝĐĂƟ ŽŶ ^ĠƐĂŵĞ ĚĞƐ ĚŝƟ ŽŶƐ s E /E͘

Ϯ͘ ^ĐĂŶŶĞ ůĞ YZ ĐŽĚĞ ƐƵƌ ůĂ ƉĂŐĞ ͗ ƚƵ ĂƵƌĂƐ ĚŝƌĞĐƚĞŵĞŶƚ ĂĐĐğƐ ĂƵǆ ǀŝĚĠŽƐ ͊

ŽŶ ƚƌĂǀĂŝů ĂǀĞĐ ĐƟ ŵĂƚŚ ă ů͛ŝŶĮ Ŷŝ ͊ 4

Table des matières /ŶƚƌŽĚƵĐƟ ŽŶ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Mode d’emploi ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

dĂďůĞ ĚĞƐ ŵĂƟ ğƌĞƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Chapitre 1 • Calcul mental ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ĐƟ ǀŝƚĠ ϭ ĐƟ ǀŝƚĠ Ϯ ĐƟ ǀŝƚĠ ϯ ĐƟ ǀŝƚĠ ϰ ĐƟ ǀŝƚĠ ϱ ĐƟ ǀŝƚĠ ϲ ĐƟ ǀŝƚĠ ϳ

sŽĐĂďƵůĂŝƌĞ ĚĞƐ ŽƉĠƌĂƟ ŽŶƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ WƌŽƉƌŝĠƚĠƐ ĚĞ ů͛ĂĚĚŝƟ ŽŶ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ WƌŽƉƌŝĠƚĠƐ ĚĞ ůĂ ŵƵůƟ ƉůŝĐĂƟ ŽŶ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ŝƐƚƌŝďƵƟ ǀŝƚĠ ƐŝŵƉůĞ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ DŝƐĞ ĞŶ ĠǀŝĚĞŶĐĞ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ WƌŝŽƌŝƚĠƐ ĚĞƐ ŽƉĠƌĂƟ ŽŶƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ĠŶŽŵďƌĞŵĞŶƚ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϭϬ ϭϮ ϭϯ ϭϰ ϭϱ ϭϳ Ϯϭ

ǆĞƌĐŝĐĞƐ ĐŽŵƉůĠŵĞŶƚĂŝƌĞƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϮϮ

ŚĂƉŝƚƌĞ Ϯ ͻ ŝǀŝƐĞƵƌƐ Ğƚ ŵƵůƟ ƉůĞƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ĐƟ ǀŝƚĠ ϭ ĐƟ ǀŝƚĠ Ϯ ĐƟ ǀŝƚĠ ϯ ĐƟ ǀŝƚĠ ϰ ĐƟ ǀŝƚĠ ϱ ĐƟ ǀŝƚĠ ϲ ĐƟ ǀŝƚĠ ϳ ĐƟ ǀŝƚĠ ϴ ĐƟ ǀŝƚĠ ϵ ĐƟ ǀŝƚĠ ϭϬ ĐƟ ǀŝƚĠ ϭϭ ĐƟ ǀŝƚĠ ϭϮ

ŝǀŝƐĞƵƌƐ Ě͛ƵŶ ŶŽŵďƌĞ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ DƵůƟ ƉůĞƐ Ě͛ƵŶ ŶŽŵďƌĞ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ŝǀŝƐĞƵƌ ŽƵ ŵƵůƟ ƉůĞ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ĂƌĂĐƚğƌĞƐ ĚĞ ĚŝǀŝƐŝďŝůŝƚĠ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ŝǀŝƐŝďŝůŝƚĠ Ğƚ ƉƌŽƉƌŝĠƚĠƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ :ƵƐƟ Į ĐĂƟ ŽŶ ĚĞ ůĂ ĚŝǀŝƐŝďŝůŝƚĠ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ĠĐŽŵƉŽƐŝƟ ŽŶ Ě͛ƵŶ ŶŽŵďƌĞ ĞŶ ƵŶ ƉƌŽĚƵŝƚ ĚĞ ĨĂĐƚĞƵƌƐ ƉƌĞŵŝĞƌƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ WƵŝƐƐĂŶĐĞƐ Ě͛ƵŶ ŶŽŵďƌĞ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ WƵŝƐƐĂŶĐĞƐ ĚĞ ϭϬ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ WƌŝŽƌŝƚĠƐ ĚĞƐ ŽƉĠƌĂƟ ŽŶƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ &ĂĐƚŽƌŝƐĂƟ ŽŶ ƉƌĞŵŝğƌĞ Ě͛ƵŶ ŶŽŵďƌĞ ŶĂƚƵƌĞů Ğƚ ĚŝǀŝƐĞƵƌƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ĠŶŽŵďƌĞŵĞŶƚ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Ϯϳ ϯϬ ϯϮ ϯϯ ϯϲ ϰϬ ϰϭ ϰϮ ϰϰ ϰϱ ϰϲ ϱϬ

ϱϭ

Chapitre 3 • Traitement de données et pourcentages ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ĐƟ ǀŝƚĠ ϭ ĐƟ ǀŝƚĠ Ϯ ĐƟ ǀŝƚĠ ϯ ĐƟ ǀŝƚĠ ϰ ĐƟ ǀŝƚĠ ϱ ĐƟ ǀŝƚĠ ϲ

'ƌĂƉŚŝƋƵĞƐ ĚĞ ƚŽƵƚĞƐ ƐŽƌƚĞƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ĂůĐƵůƐ ĚĞ ƉŽƵƌĐĞŶƚĂŐĞƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ EŽƟ ŽŶ ĚĞ ƌĞƉĠƌĂŐĞ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ hƟ ůŝƐĂƟ ŽŶ ĚƵ ƌĂƉƉŽƌƚĞƵƌ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ZĞƉƌĠƐĞŶƚĂƟ ŽŶ ĚĞ ĚŽŶŶĠĞƐ ŶƵŵĠƌŝƋƵĞƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ŶĂůǇƐĞ ĚĞ ŐƌĂƉŚŝƋƵĞƐ Ğƚ ĚĞ ĚŝĂŐƌĂŵŵĞƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϱϵ ϲϭ ϲϰ ϲϳ ϲϴ ϳϬ

ϳϯ

ŚĂƉŝƚƌĞ ϰ ͻ ĚĚŝƟ ŽŶ Ğƚ ƐŽƵƐƚƌĂĐƟ ŽŶ ĂǀĞĐ ůĞƐ ŶŽŵďƌĞƐ ĞŶƟ ĞƌƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ĐƟ ǀŝƚĠ ϭ ĐƟ ǀŝƚĠ Ϯ ĐƟ ǀŝƚĠ ϯ ĐƟ ǀŝƚĠ ϰ ĐƟ ǀŝƚĠ ϱ ĐƟ ǀŝƚĠ ϲ ĐƟ ǀŝƚĠ ϳ ĐƟ ǀŝƚĠ ϴ ĐƟ ǀŝƚĠ ϵ

Ğ ŶŽƵǀĞĂƵǆ ŶŽŵďƌĞƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ŽŵƉĂƌĂŝƐŽŶ ĚĞ ĚĞƵǆ ŶŽŵďƌĞƐ ĞŶƟ ĞƌƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ^ŽŵŵĞ ĚĞ ĚĞƵǆ ŶŽŵďƌĞƐ ĞŶƟ ĞƌƐ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ŝī ĠƌĞŶĐĞ ĚĞ ĚĞƵǆ ŶŽŵďƌĞƐ ĞŶƟ ĞƌƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ^ŽŵŵĞ Ğƚ Ěŝī ĠƌĞŶĐĞ ĚĞ ĚĞƵǆ ŶŽŵďƌĞƐ ĞŶƟ ĞƌƐ ƐĂŶƐ ƉĂƌĞŶƚŚğƐĞƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ^ŽŵŵĞ Ğƚ Ěŝī ĠƌĞŶĐĞ ĚĞ ĚĞƵǆ ŶŽŵďƌĞƐ ĞŶƟ ĞƌƐ ;ƐǇŶƚŚğƐĞͿ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ WƌŽƉƌŝĠƚĠƐ ĚĞ ů͛ĂĚĚŝƟ ŽŶ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ZĞƉĠƌĂŐĞ Ě͛ƵŶ ƉŽŝŶƚ ĚƵ ƉůĂŶ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ WƌŽďůğŵĞƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϴϭ ϴϮ ϴϯ ϴϱ ϴϲ ϴϳ ϴϵ ϵϭ ϵϰ

ϵϲ

TABLE DES MATIÈRES

ŚĂƉŝƚƌĞ ϱ ͻ dƌĂŶƐĨŽƌŵĂƟ ŽŶƐ ĚƵ ƉůĂŶ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ 101 ĐƟ ǀŝƚĠ ϭ ĐƟ ǀŝƚĠ Ϯ ĐƟ ǀŝƚĠ ϯ ĐƟ ǀŝƚĠ ϰ ĐƟ ǀŝƚĠ ϱ

ĠĐŽƵǀĞƌƚĞ ĚĞƐ ƚƌĂŶƐĨŽƌŵĂƟ ŽŶƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ZĞĐŚĞƌĐŚĞ ĚĞ ƚƌĂŶƐĨŽƌŵĂƟ ŽŶƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ^ǇŵĠƚƌŝĞ ŽƌƚŚŽŐŽŶĂůĞ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ^ǇŵĠƚƌŝĞ ĐĞŶƚƌĂůĞ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ dƌĂŶƐůĂƟ ŽŶ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϭϬϯ ϭϬϱ ϭϬϳ ϭϬϴ ϭϬϵ

ǆĞƌĐŝĐĞƐ ĐŽŵƉůĠŵĞŶƚĂŝƌĞƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϭϭϬ Chapitre 6 • Figures planes ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϭϭϱ ĐƟ ǀŝƚĠ ϭ ĐƟ ǀŝƚĠ Ϯ ĐƟ ǀŝƚĠ ϯ ĐƟ ǀŝƚĠ ϰ ĐƟ ǀŝƚĠ ϱ ĐƟ ǀŝƚĠ ϲ ĐƟ ǀŝƚĠ ϳ ĐƟ ǀŝƚĠ ϴ ĐƟ ǀŝƚĠ ϵ ĐƟ ǀŝƚĠ ϭϬ ĐƟ ǀŝƚĠ ϭϭ ĐƟ ǀŝƚĠ ϭϮ

ĠĐŽƵǀĞƌƚĞ ĚĞƐ ƋƵĂĚƌŝůĂƚğƌĞƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ĠĮ ŶŝƟ ŽŶ ĚĞƐ ƋƵĂĚƌŝůĂƚğƌĞƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ hŶŝĐŝƚĠ ĚĞ ůĂ ƉĂƌĂůůğůĞ Ğƚ ĚĞ ůĂ ƉĞƌƉĞŶĚŝĐƵůĂŝƌĞ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ KƌŐĂŶŝŐƌĂŵŵĞ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ĂƌĂĐƚĠƌŝƐƟ ƋƵĞƐ ĚĞƐ ƋƵĂĚƌŝůĂƚğƌĞƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ŝĂŐŽŶĂůĞƐ ĚĞƐ ƋƵĂĚƌŝůĂƚğƌĞƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ĠĐŽƵǀĞƌƚĞ ĚĞƐ ƚƌŝĂŶŐůĞƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ŽŶƐƚƌƵĐƟ ŽŶƐ ĚĞ ƚƌŝĂŶŐůĞƐ ƐĂŶƐ ŵĞƐƵƌĞƐ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ŽŶƐƚƌƵĐƟ ŽŶƐ ĚĞ ƚƌŝĂŶŐůĞƐ ĂǀĞĐ ŵĞƐƵƌĞƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ƌŽŝƚĞƐ ƌĞŵĂƌƋƵĂďůĞƐ ĚĞƐ ƚƌŝĂŶŐůĞƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ &ŝŐƵƌĞƐ ŝŶƐĐƌŝƚĞƐ ĚĂŶƐ ƵŶ ĐĞƌĐůĞ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ WƌŽďůğŵĞƐ ĚĞ ƉĠƌŝŵğƚƌĞƐ Ğƚ Ě͛ĂŝƌĞƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϭϭϴ ϭϮϬ ϭϮϬ ϭϮϭ ϭϮϮ ϭϮϰ ϭϮϲ ϭϮϴ ϭϮϴ ϭϯϬ ϭϯϮ ϭϯϯ

ǆĞƌĐŝĐĞƐ ĐŽŵƉůĠŵĞŶƚĂŝƌĞƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϭϯϲ Chapitre 7 • Solides ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϭϰϯ ĐƟ ǀŝƚĠ ϭ ĐƟ ǀŝƚĠ Ϯ ĐƟ ǀŝƚĠ ϯ ĐƟ ǀŝƚĠ ϰ ĐƟ ǀŝƚĠ ϱ ĐƟ ǀŝƚĠ ϲ ĐƟ ǀŝƚĠ ϳ ĐƟ ǀŝƚĠ ϴ

^ŽůŝĚĞƐ ĂƵ ƋƵŽƟ ĚŝĞŶ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ZĞƉƌĠƐĞŶƚĂƟ ŽŶƐ ĚĞ ƐŽůŝĚĞƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ WůĂŶƐ͕ ĨĂĐĞƐ͕ ĚƌŽŝƚĞƐ Ğƚ ĂƌġƚĞƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ĠǀĞůŽƉƉĞŵĞŶƚƐ ĚĞ ƐŽůŝĚĞƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ĠǀĞůŽƉƉĞŵĞŶƚƐ ĚƵ ĐƵďĞ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ sƵĞƐ ĐŽŽƌĚŽŶŶĠĞƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ WƌŝƐŵĞƐ Ğƚ ĚĠŶŽŵďƌĞŵĞŶƚ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ WƌŽďůğŵĞƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϭϰϱ ϭϰϳ ϭϱϭ ϭϱϮ ϭϱϯ ϭϱϰ ϭϱϱ ϭϱϲ

ǆĞƌĐŝĐĞƐ ĐŽŵƉůĠŵĞŶƚĂŝƌĞƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϭϱϴ ŚĂƉŝƚƌĞ ϴ ͻ KƉĠƌĂƟ ŽŶƐ ĂǀĞĐ ůĞƐ ŶŽŵďƌĞƐ ĞŶƟ ĞƌƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ 163 ĐƟ ǀŝƚĠ ϭ ĐƟ ǀŝƚĠ Ϯ ĐƟ ǀŝƚĠ ϯ ĐƟ ǀŝƚĠ ϰ ĐƟ ǀŝƚĠ ϱ ĐƟ ǀŝƚĠ ϲ ĐƟ ǀŝƚĠ ϳ

WƌŽĚƵŝƚ ĚĞ ĚĞƵǆ ŶŽŵďƌĞƐ ĞŶƟ ĞƌƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ WƌŽƉƌŝĠƚĠƐ ĚĞ ůĂ ŵƵůƟ ƉůŝĐĂƟ ŽŶ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ KƉĠƌĂƟ ŽŶƐ ĠůĠŵĞŶƚĂŝƌĞƐ ĂǀĞĐ ůĞƐ ŶŽŵďƌĞƐ ĞŶƟ ĞƌƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ WƌŝŽƌŝƚĠƐ ĚĞƐ ŽƉĠƌĂƟ ŽŶƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ sĂůĞƵƌƐ ŶƵŵĠƌŝƋƵĞƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ WƌŽďůğŵĞƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ >ŝĞŶ ĞŶƚƌĞ ĐŽŽƌĚŽŶŶĠĞƐ Ğƚ ĚƌŽŝƚĞƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϭϲϱ ϭϲϳ ϭϲϴ ϭϳϬ ϭϳϮ ϭϳϯ ϭϳϱ

ǆĞƌĐŝĐĞƐ ĐŽŵƉůĠŵĞŶƚĂŝƌĞƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϭϳϳ

TABLE DES MATIÈRES ŚĂƉŝƚƌĞ ϵ ͻ ĂůĐƵů ůŝƩ ĠƌĂů ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ 181 ĐƟ ǀŝƚĠ ϭ ĐƟ ǀŝƚĠ Ϯ ĐƟ ǀŝƚĠ ϯ ĐƟ ǀŝƚĠ ϰ ĐƟ ǀŝƚĠ ϱ ĐƟ ǀŝƚĠ ϲ ĐƟ ǀŝƚĠ ϳ ĐƟ ǀŝƚĠ ϴ ĐƟ ǀŝƚĠ ϵ ĐƟ ǀŝƚĠ ϭϬ ĐƟ ǀŝƚĠ ϭϭ

ǆƉƌĞƐƐŝŽŶ ůŝƩ ĠƌĂůĞ Ğƚ ĐŽĚĂŐĞ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ZĠĚƵĐƟ ŽŶ ĚĞ ƐŽŵŵĞƐ ĂůŐĠďƌŝƋƵĞƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ZĠĚƵĐƟ ŽŶ ĚĞ ƉƌŽĚƵŝƚƐ ĂůŐĠďƌŝƋƵĞƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ǆƉƌĞƐƐŝŽŶƐ ůŝƩ ĠƌĂůĞƐ Ğƚ ŶŽŵďƌĞƐ ĞŶƟ ĞƌƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ WƌŝŽƌŝƚĠƐ ĚĞƐ ŽƉĠƌĂƟ ŽŶƐ Ğƚ ĐĂůĐƵů ůŝƩ ĠƌĂů ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ƋƵĂƟ ŽŶƐ ͗ ƉƌĞŵŝğƌĞ ĂƉƉƌŽĐŚĞ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ŝƐƚƌŝďƵƟ ǀŝƚĠ ƐŝŵƉůĞ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ DŝƐĞ ĞŶ ĠǀŝĚĞŶĐĞ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ^ƵƉƉƌĞƐƐŝŽŶ ĚĞ ƉĂƌĞŶƚŚğƐĞƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ &ĂŵŝůůĞƐ ĚĞ ŶŽŵďƌĞƐ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ĠŶŽŵďƌĞŵĞŶƚ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϭϴϯ ϭϴϰ ϭϴϲ ϭϴϴ ϭϵϬ ϭϵϭ ϭϵϱ ϭϵϳ ϭϵϵ ϮϬϭ ϮϬϯ

ǆĞƌĐŝĐĞƐ ĐŽŵƉůĠŵĞŶƚĂŝƌĞƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϮϬϲ ŚĂƉŝƚƌĞ ϭϬ ͻ ZĞƚŽƵƌ ĂƵǆ ƚƌĂŶƐĨŽƌŵĂƟ ŽŶƐ ĚƵ ƉůĂŶ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ 211 ĐƟ ǀŝƚĠ ϭ ĐƟ ǀŝƚĠ Ϯ ĐƟ ǀŝƚĠ ϯ ĐƟ ǀŝƚĠ ϰ ĐƟ ǀŝƚĠ ϱ ĐƟ ǀŝƚĠ ϲ

ZĞƚŽƵƌ ĂƵǆ ƚƌĂŶƐĨŽƌŵĂƟ ŽŶƐ ͊ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ^ǇŵĠƚƌŝĞ ŽƌƚŚŽŐŽŶĂůĞ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ^ǇŵĠƚƌŝĞ ĐĞŶƚƌĂůĞ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ dƌĂŶƐůĂƟ ŽŶ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ /ŶǀĂƌŝĂŶƚƐ ĚĞƐ ƚƌĂŶƐĨŽƌŵĂƟ ŽŶƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ŽŶƐƚƌƵĐƟ ŽŶƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϮϭϮ ϮϭϮ Ϯϭϰ Ϯϭϱ Ϯϭϳ Ϯϭϵ

ǆĞƌĐŝĐĞƐ ĐŽŵƉůĠŵĞŶƚĂŝƌĞƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϮϮϬ ŚĂƉŝƚƌĞ ϭϭ ͻ WƌŽƉŽƌƟ ŽŶŶĂůŝƚĠ ĐƟ ǀŝƚĠ ϭ ĐƟ ǀŝƚĠ Ϯ ĐƟ ǀŝƚĠ ϯ ĐƟ ǀŝƚĠ ϰ

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

223

'ƌĂŶĚĞƵƌƐ ĚŝƌĞĐƚĞŵĞŶƚ ƉƌŽƉŽƌƟ ŽŶŶĞůůĞƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ 'ƌĂŶĚĞƵƌƐ ĚŝƌĞĐƚĞŵĞŶƚ ƉƌŽƉŽƌƟ ŽŶŶĞůůĞƐ ŽƵ ŶŽŶ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ WƌŽďůğŵĞƐ ĚĞ ƌğŐůĞ ĚĞ ƚƌŽŝƐ Ğƚ ĚĞ ƉƌŽƉŽƌƟ ŽŶŶĂůŝƚĠ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ĐŚĞůůĞ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϮϮϰ ϮϮϲ ϮϮϵ Ϯϯϭ

ǆĞƌĐŝĐĞƐ ĐŽŵƉůĠŵĞŶƚĂŝƌĞƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ Ϯϯϰ ŚĂƉŝƚƌĞ ϭϮ ͻ &ƌĂĐƟ ŽŶƐ Ğƚ ŶŽŵďƌĞƐ ĚĠĐŝŵĂƵǆ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ 239 ĐƟ ǀŝƚĠ ϭ ĐƟ ǀŝƚĠ Ϯ ĐƟ ǀŝƚĠ ϯ ĐƟ ǀŝƚĠ ϰ ĐƟ ǀŝƚĠ ϱ ĐƟ ǀŝƚĠ ϲ ĐƟ ǀŝƚĠ ϳ ĐƟ ǀŝƚĠ ϴ ĐƟ ǀŝƚĠ ϵ

>Ă ĨƌĂĐƟ ŽŶ ƐŽƵƐ ƚŽƵƚĞƐ ƐĞƐ ĨŽƌŵĞƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ &ƌĂĐƟ ŽŶƐ ĠƋƵŝǀĂůĞŶƚĞƐ Ğƚ ƐŝŵƉůŝĮ ĐĂƟ ŽŶ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ &ƌĂĐƟ ŽŶ Ğƚ ŶŽŵďƌĞ ĚĠĐŝŵĂů ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ƌŽŝƚĞ ŐƌĂĚƵĠĞ Ğƚ ǀĂůĞƵƌƐ ĂƉƉƌŽĐŚĠĞƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ŽŵƉĂƌĂŝƐŽŶ ĚĞ ĨƌĂĐƟ ŽŶƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ WƌŽĚƵŝƚ ĚĞ ĨƌĂĐƟ ŽŶƐ Ğƚ ĚĞ ŶŽŵďƌĞƐ ĚĠĐŝŵĂƵǆ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ YƵŽƟ ĞŶƚ ĂǀĞĐ ĚĞƐ ĨƌĂĐƟ ŽŶƐ Ğƚ ĚĞƐ ŶŽŵďƌĞƐ ĚĠĐŝŵĂƵǆ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ^ŽŵŵĞ Ğƚ Ěŝī ĠƌĞŶĐĞ ĚĞ ĨƌĂĐƟ ŽŶƐ Ğƚ ĚĞ ŶŽŵďƌĞƐ ĚĠĐŝŵĂƵǆ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ WƌŽďůğŵĞƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Ϯϰϭ Ϯϰϰ Ϯϰϱ Ϯϰϳ Ϯϰϵ Ϯϱϭ Ϯϱϰ Ϯϱϱ Ϯϱϴ

ǆĞƌĐŝĐĞƐ ĐŽŵƉůĠŵĞŶƚĂŝƌĞƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ Ϯϲϭ Exercices de compétences ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ 265 Index ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ 271

Chapitre 1 Calcul mental Tableaux de compétences Libre EŽŵďƌĞƐ ƌĂƟ ŽŶŶĞůƐ 11

DĂŠƚƌŝƐĞƌ ůĞƐ ĐŽŶǀĞŶƟ ŽŶƐ Ě͛ĠĐƌŝƚƵƌĞ ŵĂƚŚĠŵĂƟ ƋƵĞ ĚĞƐ ŶŽŵďƌĞƐ ĚĠĐŝŵĂƵǆ ;ĨƌĂĐƟ ŽŶƐͿ͘

Compétences communes aux nombres 15

:ƵƐƟ Į Ğƌ ƵŶĞ ŵĠƚŚŽĚĞ ĚĞ ĐĂůĐƵů ĞŶ ƵƟ ůŝƐĂŶƚ ůĞƐ ƉƌŽƉƌŝĠƚĠƐ ĚĞƐ ŽƉĠƌĂƟ ŽŶƐ͘

ZĞĐŽŶŶĂŠƚƌĞ ůĞƐ ĐŝƌĐŽŶƐƚĂŶĐĞƐ Ě͛ƵƟ ůŝƐĂƟ ŽŶ ĚĞƐ ƚĞƌŵĞƐ ƵƐƵĞůƐ͕ ĚĞƐ ŶŽƚĂƟ ŽŶƐ Ğƚ ĚĞƐ ŽƉĠƌĂƟ ŽŶƐ ƉƌŽƉƌĞƐ ĂƵǆ ŶŽŵďƌĞƐ͘

sĠƌŝĮ Ğƌ ĂǀĞĐ ƵŶĞ ĐĂůĐƵůĂƚƌŝĐĞ ůĂ ƉůĂƵƐŝďŝůŝƚĠ Ě͛ƵŶ ƌĠƐƵůƚĂƚ͘

ZĞƐƉĞĐƚĞƌ ůĞƐ ƉƌŝŽƌŝƚĠƐ ĚĞƐ ŽƉĠƌĂƟ ŽŶƐ ƉŽƵƌ Ğī ĞĐƚƵĞƌ ĚĞƐ ŽƉĠƌĂƟ ŽŶƐ ĚĂŶƐ ĚĞƐ ƐŝƚƵĂƟ ŽŶƐ ǀĂƌŝĠĞƐ͘

ī ĞĐƚƵĞƌ ƵŶ ĐĂůĐƵů ĐŽŵƉŽƌƚĂŶƚ ƉůƵƐŝĞƵƌƐ ĠƚĂƉĞƐ ă ů͛ĂŝĚĞ Ě͛ƵŶĞ ĐĂůĐƵůĂƚƌŝĐĞ͘

Kĸ ĐŝĞů ī ĞĐƚƵĞƌ ĚĞƐ ŽƉĠƌĂƟ ŽŶƐ 25

ī ĞĐƚƵĞƌ ƐĞůŽŶ ƵŶĞ ŵĠƚŚŽĚĞ ĂƉƉƌŽƉƌŝĠĞ ;ĐĂůĐƵů ŵĞŶƚĂů͕ ĐĂůĐƵů ĠĐƌŝƚ͕ ĐĂůĐƵůĂƚƌŝĐĞͿ ĚĞƐ ĂĚĚŝƟ ŽŶƐ͕ ĚĞƐ ƐŽƵƐƚƌĂĐƟ ŽŶƐ͕ ĚĞƐ ŵƵůƟ ƉůŝĐĂƟ ŽŶƐ Ğƚ ĚĞƐ ĚŝǀŝƐŝŽŶƐ ĚĞ ŶŽŵďƌĞƐ ŶĂƚƵƌĞůƐ Ğƚ ĚĞ ŶŽŵďƌĞƐ ĚĠĐŝŵĂƵǆ ƉŽƐŝƟ ĨƐ͘

ƐƟ ŵĞƌ ů͛ŽƌĚƌĞ ĚĞ ŐƌĂŶĚĞƵƌ Ğƚ ǀĠƌŝĮ Ğƌ ă ůĂ ĐĂůĐƵůĂƚƌŝĐĞ ůĂ ƉůĂƵƐŝďŝůŝƚĠ Ě͛ƵŶ ƌĠƐƵůƚĂƚ͘

ĂůĐƵůĞƌ ƵŶĞ ĞǆƉƌĞƐƐŝŽŶ ĐŽŵƉƌĞŶĂŶƚ ĂƵ ƉůƵƐ ƚƌŽŝƐ ŽƉĠƌĂƟ ŽŶƐ Ěŝī ĠƌĞŶƚĞƐ͘

ĐƌŝƌĞ ƵŶĞ ĞǆƉƌĞƐƐŝŽŶ ƋƵŝ ĐŽƌƌĞƐƉŽŶĚ ă ƵŶĞ ƐƵĐĐĞƐƐŝŽŶ ĚŽŶŶĠĞ Ě͛ŽƉĠƌĂƟ ŽŶƐ͘

hƟ ůŝƐĞƌ ůĂ ĐŽŵŵƵƚĂƟ ǀŝƚĠ Ğƚ ů͛ĂƐƐŽĐŝĂƟ ǀŝƚĠ ĚĞ ů͛ĂĚĚŝƟ ŽŶ Ğƚ ĚĞ ůĂ ŵƵůƟ ƉůŝĐĂƟ ŽŶ͘

hƟ ůŝƐĞƌ ůĂ ĚŝƐƚƌŝďƵƟ ǀŝƚĠ ;ƐŝŵƉůĞͿ ĚĞ ůĂ ŵƵůƟ ƉůŝĐĂƟ ŽŶ ƉĂƌ ƌĂƉƉŽƌƚ ă ů͛ĂĚĚŝƟ ŽŶ Ğƚ ă ůĂ ƐŽƵƐƚƌĂĐƟ ŽŶ͘ 9

ACTIVITÉS

Chapitre 1 Calcul mental

ĐƚŝǀŝƚĠ ϭ Vocabulaire des opérations 1

^ŽƉŚŝĞ͕ ŝŶƐƚŝƚƵƚƌŝĐĞ ĞŶ ϲe ĂŶŶĠĞ ƉƌŝŵĂŝƌĞ ĚŝƐƉŽƐĞ Ě͛ƵŶ ďƵĚŐĞƚ ĚĞ ϰϬϬϬ Φ ƉŽƵƌ ĠƋƵŝƉĞƌ ƐĂ ĐůĂƐƐĞ ĚĞ ŵĂƚĠƌŝĞů ŝŶĨŽƌŵĂƚŝƋƵĞ͘ ůůĞ ĐŽŵŵĂŶĚĞ ĐŝŶƋ ŽƌĚŝŶĂƚĞƵƌƐ ǀĂůĂŶƚ ĐŚĂĐƵŶ ϱϲϬ Φ͕ ĚŝĨĨĠƌĞŶƚƐ ůŽŐŝĐŝĞůƐ ƉŽƵƌ ƵŶ ƚŽƚĂů ĚĞ ϰϵϬ Φ͕ ƵŶĞ ŝŵƉƌŝŵĂŶƚĞ ŵƵůƚŝĨŽŶĐƚŝŽŶ ă ϭϭϬ Φ Ğƚ ƵŶĞ ĂƌŵŽŝƌĞ ĚĞ ƌĂŶŐĞŵĞŶƚ͘ >Ğ ŵŽŶƚĂŶƚ ƚŽƚĂů ĚĞ ƐĂ ĨĂĐƚƵƌĞ ĞƐƚ ĚĞ ϯϱϱϬ Φ͘ ĂͿ ĐƌŝƐ ůĞ ĐĂůĐƵů ƋƵŝ ƚĞ ƉĞƌŵĞƚ ĚĞ ƚƌŽƵǀĞƌ͙ ;ϭͿ ůĞ Ɖƌŝǆ ă ƉĂǇĞƌ ƉŽƵƌ ů͛ĂĐŚĂƚ ĚĞƐ ĐŝŶƋ ŽƌĚŝŶĂƚĞƵƌƐ Ğƚ ĞĨĨĞĐƚƵĞͲůĞ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;ϮͿ ůĞ ĐŽƸƚ ƚŽƚĂů ĚƵ ŵĂƚĠƌŝĞů ŝŶĨŽƌŵĂƚŝƋƵĞ Ğƚ ĞĨĨĞĐƚƵĞͲůĞ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;ϯͿ ůĞ Ɖƌŝǆ ĚĞ ů͛ĂƌŵŽŝƌĞ ĚĞ ƌĂŶŐĞŵĞŶƚ Ğƚ ĞĨĨĞĐƚƵĞͲůĞ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;ϰͿ ůĂ ƐŽŵŵĞ Ě͛ĂƌŐĞŶƚ ƌĞƐƚĂŶƚĞ ĂƉƌğƐ ůĞ ƉĂŝĞŵĞŶƚ ĚĞ ůĂ ĨĂĐƚƵƌĞ Ğƚ ĞĨĨĞĐƚƵĞͲůĞ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;ϱͿ ůĞ ŶŽŵďƌĞ ĚĞ ĐĂůĐƵůĂƚƌŝĐĞƐ ƐĐŝĞŶƚŝĨŝƋƵĞƐ ă Ϯϱ Φ ƉŝğĐĞ ƋƵĞ ^ŽƉŚŝĞ ƉŽƵƌƌĂ ĂĐŚĞƚĞƌ ĂǀĞĐ ů͛ĂƌŐĞŶƚ ƌĞƐƚĂŶƚ Ğƚ ĞĨĨĞĐƚƵĞͲůĞ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ďͿ ŽŵƉůğƚĞ ůĞƐ ƉŚƌĂƐĞƐ ĞŶ ƵƚŝůŝƐĂŶƚ ůĞƐ ŵŽƚƐ ͨ ƐŽŵŵĞ͕ ĚŝĨĨĠƌĞŶĐĞƐ͕ ƉƌŽĚƵŝƚ͕ ƋƵŽƚŝĞŶƚ͕ ƚĞƌŵĞƐ͕ ĨĂĐƚĞƵƌƐ͕ ƉƌĞŵŝĞƌƐ ƚĞƌŵĞƐ͕ ƐĞĐŽŶĚƐ ƚĞƌŵĞƐ͕ ĚŝǀŝĚĞŶĚĞ͕ ĚŝǀŝƐĞƵƌ ͩ ŽƵ ĚĞƐ ŶŽŵďƌĞƐ ĚĠƚĞƌŵŝŶĠƐ ă ůĂ ƋƵĞƐƚŝŽŶ ĂͿ͘ ƚƚĞŶƚŝŽŶ͕ ƵŶ ŵġŵĞ ŵŽƚ ƉĞƵƚ ġƚƌĞ ƵƚŝůŝƐĠ ƉůƵƐŝĞƵƌƐ ĨŽŝƐ͘ >Ğ ĐĂůĐƵů ;ϭͿ ĞƐƚ ƵŶ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ĚĞ ĚĞƵǆ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘͘ >Ğ ĐĂůĐƵů ;ϮͿ ĞƐƚ ƵŶĞ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ĚĞ ƚƌŽŝƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘͘ >ĞƐ ĐĂůĐƵůƐ ;ϯͿ Ğƚ ;ϰͿ ƐŽŶƚ ĚĞƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ĚĞ ĚĞƵǆ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

et ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ en sont les ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

>Ğ ĐĂůĐƵů ;ϱͿ ĞƐƚ ƵŶ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

est le ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ et ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ est le ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

p.31 A

ACTIVITÉS

Chapitre 1 Calcul mental

2 DŽĚŝĨŝĞ ͙

ůĂ ƐŽŵŵĞ ϭϮ н ϯϭ ĞŶ ĂũŽƵƚĂŶƚ ϯ ĂƵǆ ĚĞƵǆ ƚĞƌŵĞƐ͘

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ůĂ ĚŝĨĨĠƌĞŶĐĞ ϰϲ ʹ ϭϱ ĞŶ ĂũŽƵƚĂŶƚ ϱ ĂƵ ƐĞĐŽŶĚ ƚĞƌŵĞ͘

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ůĞ ƉƌŽĚƵŝƚ ϭϱ . ϲ ĞŶ ŵƵůƚŝƉůŝĂŶƚ ůĞƐ ĚĞƵǆ ĨĂĐƚĞƵƌƐ ƉĂƌ ϯ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ůĞ ƋƵŽƚŝĞŶƚ ϱϲϬ ͗ ϴ ĞŶ ĚŝǀŝƐĂŶƚ ůĞ ĚŝǀŝĚĞŶĚĞ ƉĂƌ ϳ͘

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ůĞ ƉƌŽĚƵŝƚ ϯ . ϭϱ ĞŶ ƌĞƚƌĂŶĐŚĂŶƚ Ϯ ĚƵ ƐĞĐŽŶĚ ĨĂĐƚĞƵƌ͘

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ůĂ ƐŽŵŵĞ ϴϰ н ϭϵ ĞŶ ĚŝǀŝƐĂŶƚ ůĞ ƉƌĞŵŝĞƌ ƚĞƌŵĞ ƉĂƌ Ϯ͘

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ůĞ ƋƵŽƚŝĞŶƚ ϰϴ ͗ ϲ ĞŶ ĚŽƵďůĂŶƚ ůĞ ĚŝǀŝƐĞƵƌ͘

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

3 Ŷ Ŷ͛ƵƚŝůŝƐĂŶƚ ƋƵĞ ĚĞƐ ŶŽŵďƌĞƐ ŶĂƚƵƌĞůƐ͕ ĠĐƌŝƐ͕ Ɛŝ ƉŽƐƐŝďůĞ͕ ůĞ ŶŽŵďƌĞ ϰϬ ƐŽƵƐ ůĂ ĨŽƌŵĞ͙ Ě͛ƵŶĞ ƐŽŵŵĞ ĚĞ ĚĞƵǆ ƚĞƌŵĞƐ ĠŐĂƵǆ ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ Ě͛ƵŶ ƋƵŽƚŝĞŶƚ ĚŽŶƚ ůĞ ĚŝǀŝĚĞŶĚĞ ĞƐƚ ϭϮϬ ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ Ě͛ƵŶĞ ĚŝĨĨĠƌĞŶĐĞ ĚŽŶƚ ůĞ ƐĞĐŽŶĚ ƚĞƌŵĞ ĞƐƚ ϭϱ ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ Ě͛ƵŶ ƉƌŽĚƵŝƚ ĚĞ ƚƌŽŝƐ ĨĂĐƚĞƵƌƐ ĚŝĨĨĠƌĞŶƚƐ ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ Ě͛ƵŶĞ ƐŽŵŵĞ ĚĞ ĚĞƵǆ ƚĞƌŵĞƐ ĚŝĨĨĠƌĞŶƚƐ ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ Ě͛ƵŶĞ ĚŝĨĨĠƌĞŶĐĞ ĚĞ ĚĞƵǆ ƚĞƌŵĞƐ ĚŝĨĨĠƌĞŶƚƐ ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ Ě͛ƵŶ ƉƌŽĚƵŝƚ ĚĞ ĚĞƵǆ ĨĂĐƚĞƵƌƐ ĠŐĂƵǆ ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ 4 ů͛ĂŝĚĞ ĚĞƐ ƌĞŶƐĞŝŐŶĞŵĞŶƚƐ ĐŝͲĚĞƐƐŽƵƐ͕ ĐŽŵƉůğƚĞ ůĂ ŐƌŝůůĞ ĚĞ ŶŽŵďƌĞƐ ĐƌŽŝƐĠƐ͘ KŶ ŶĞ ĚŽŶŶĞ ůĞƐ ĚĠĨŝŶŝƚŝŽŶƐ ƋƵĞ ĚĞƐ ŶŽŵďƌĞƐ ĐŽŵƉŽƐĠƐ ĚĞ ƉůƵƐ Ě͛ƵŶ ĐŚŝĨĨƌĞ͘ dƵ ŶĞ ƉĞƵǆ ŝŶƐĐƌŝƌĞ ƋƵ͛ƵŶ ƐĞƵů ĐŚŝĨĨƌĞ ƉĂƌ ĐĂƐĞ Ğƚ ůĞƐ ĐĂƐĞƐ ĐŽůŽƌĠĞƐ ƌĞƐƚĞŶƚ ǀŝĚĞƐ͘ ,ŽƌŝǌŽŶƚĂůĞŵĞŶƚ ϭ͘ WƌŽĚƵŝƚ ĚĞ ƚƌŽŝƐ ĨĂĐƚĞƵƌƐ ĠŐĂƵǆ ă ϱ Ϯ͘ ^ŽŵŵĞ ĚĞ ϮϮϴϲ Ğƚ ĚĞ ϳϰϮ ϯ͘ EŽŵďƌĞ ĚŽŶƚ ůĂ ƐŽŵŵĞ ĚĞƐ ĐŚŝĨĨƌĞƐ ƋƵŝ ůĞ ĐŽŵƉŽƐĞŶƚ ǀĂƵƚ ϭϭ ϰ͘ WƌŽĚƵŝƚ ĚĞ ϯ ƉĂƌ ϱ ʹ YƵĂƌƚ ĚĞ ϴϰ ϱ͘ EŽŵďƌĞ ĚŽŶƚ ůĞ ƉƌŽĚƵŝƚ ĚĞƐ ĐŚŝĨĨƌĞƐ ƋƵŝ ůĞ ĐŽŵƉŽƐĞŶƚ ǀĂƵƚ ϰϮ

1 2 3

sĞƌƚŝĐĂůĞŵĞŶƚ ͘ ŝĨĨĠƌĞŶĐĞ ĞŶƚƌĞ ϵϱϭ Ğƚ ϯϯϮ ͘ EŽŵďƌĞ ĨŽƌŵĠ ĚĞ ƋƵĂƚƌĞ ĐŚŝĨĨƌĞƐ ĐŽŶƐĠĐƵƚŝĨƐ ͘ YƵŽƚŝĞŶƚ ĚĞ ϭϬϬϬ ƉĂƌ Ϯ ͘ EŽŵďƌĞ ŶĂƚƵƌĞů ĐŽŶƐĠĐƵƚŝĨ ă ϮϭϮϮ ͘ ŽƵďůĞ ĚĞ ϵ ʹ ŝĨĨĠƌĞŶĐĞ ĞŶƚƌĞ ϲϬ Ğƚ ϰϯ

4 5

ACTIVITÉS

Chapitre 1 Calcul mental

ĐƚŝǀŝƚĠ Ϯ Propriétés de l’addition 1

1 ŽŵƉůğƚĞ ĐĞ ĐĂƌƌĠ ͨ ŵĂŐŝƋƵĞ ͩ ĂĨŝŶ ƋƵĞ ůĂ ƐŽŵŵĞ ĚĞƐ ŶŽŵďƌĞƐ ĚĞ ĐŚĂƋƵĞ ůŝŐŶĞ͕ ĚĞ ĐŚĂƋƵĞ ĐŽůŽŶŶĞ Ğƚ ĚĞ ĐŚĂƋƵĞ ĚŝĂŐŽŶĂůĞ ƐŽŝƚ ƚŽƵũŽƵƌƐ ĠŐĂůĞ ă ϭϮ͘

ĐƌŝƐ ůĞ ĐĂůĐƵů ƋƵŝ ƚĞ ƉĞƌŵĞƚ ĚĞ ǀĠƌŝĨŝĞƌ ůĂ ƐŽŵŵĞ ĚĞƐ ŶŽŵďƌĞƐ ĚĞ ůĂ ŵĠĚŝĂŶĞ ŚŽƌŝǌŽŶƚĂůĞ͘

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ŽŵƉůğƚĞ ůĞƐ ƉŚƌĂƐĞƐ͘ ĂŶƐ ĐĞƚƚĞ ƐŽŵŵĞ͕ ůĞ ŶŽŵďƌĞ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ŶĞ ŵŽĚŝĨŝĞ ƉĂƐ ůĞ ƌĠƐƵůƚĂƚ͘ ũŽƵƚĞƌ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ă ƵŶ ŶŽŵďƌĞ ĚŽŶŶĞ ƵŶĞ ƐŽŵŵĞ ĠŐĂůĞ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ >ΖĂĚĚŝƚŝŽŶ ĞƐƚ ƵŶĞ ŽƉĠƌĂƟ ŽŶ ƋƵŝ ĂĚŵĞƚ ͘ ͘ ͘ ͘ ͘ ͘ ĐŽŵŵĞ ĠůĠŵĞŶƚ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ 2 ŽŵƉůğƚĞ ĐĞ ĐĂƌƌĠ ͨ ŵĂŐŝƋƵĞ ͩ ĂĨŝŶ ƋƵĞ ůĂ ƐŽŵŵĞ ĚĞƐ ŶŽŵďƌĞƐ ĚĞ ĐŚĂƋƵĞ ůŝŐŶĞ͕ ĚĞ ĐŚĂƋƵĞ ĐŽůŽŶŶĞ Ğƚ ĚĞ ĐŚĂƋƵĞ ĚŝĂŐŽŶĂůĞ ƐŽŝƚ ƚŽƵũŽƵƌƐ ĠŐĂůĞ ă ϮϬ͘ ĐƌŝƐ ůĞ ĐĂůĐƵů ƋƵŝ ƚĞ ƉĞƌŵĞƚ ĚĞ ǀĠƌŝĨŝĞƌ ůĞƐ ƐŽŵŵĞƐ ĚĞƐ ŶŽŵďƌĞƐ ϭϬ ϰ ĚĞ ĐŚĂƋƵĞ ĚŝĂŐŽŶĂůĞ͘ ϭ ϰ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ŽŵƉůğƚĞ ůĞƐ ƉŚƌĂƐĞƐ͘

>ĞƐ ƐŽŵŵĞƐ ƐŽŶƚ ĐŽŵƉŽƐĠĞƐ ĚĞƐ ŶŽŵďƌĞƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϭϬ ϭ

ĂŶƐ ƵŶĞ ƐŽŵŵĞ͕ ůΖ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ĚĞƐ ƚĞƌŵĞƐ Ŷ͛ŝŶŇ ƵĞŶĐĞ ƉĂƐ ůĞ ƌĠƐƵůƚĂƚ͘ >ΖĂĚĚŝƚŝŽŶ ĞƐƚ ƵŶĞ ŽƉĠƌĂƟ ŽŶ

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

3 ĂůĐƵůĞ͕ ĚĞ ĚĞƵǆ ŵĂŶŝğƌĞƐ ĚŝĨĨĠƌĞŶƚĞƐ͕ ůĂ ƐŽŵŵĞ ĚĞƐ ŶŽŵďƌĞƐ ĚĞ ůĂ ƚƌŽŝƐŝğŵĞ ůŝŐŶĞ ĚĞ ĐĞ ĐĂƌƌĠ ͨരŵĂŐŝƋƵĞരͩ͘

ϭϲ

ϮϬ

ϰϰ

ϱϲ

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϲϬ

ϰϬ

ϯϮ

Ϯϰ

ϭϮ

ϱϮ

ϰϴ

ϯϲ

ϲϰ

Ϯϲ

ŽŵƉůğƚĞ ůĞƐ ƉŚƌĂƐĞƐ͘ ĂŶƐ ƵŶĞ ƐŽŵŵĞ ĚĞ ƉůƵƐ ĚĞ ĚĞƵǆ ƚĞƌŵĞƐ͕ ůĂ ŵĂŶŝğƌĞ ĚĞ ůĞƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ Ŷ͛ŝŶĨůƵĞŶĐĞ ƉĂƐ ůĞ ƌĠƐƵůƚĂƚ͘ >͛ĂĚĚŝƚŝŽŶ ĞƐƚ ƵŶĞ ŽƉĠƌĂƚŝŽŶ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ 4 ZĞůŝĞ ĐŚĂƋƵĞ ĐĂůĐƵů ă ůĂ ƉƌŽƉƌŝĠƚĠ ƋƵ͛ŝů ŝůůƵƐƚƌĞ͘

ϳ н Ϭ с ϳ

•

>͛ĂĚĚŝƚŝŽŶ ĞƐƚ ƵŶĞ ŽƉĠƌĂƚŝŽŶ ĂƐƐŽĐŝĂƚŝǀĞ͘

ϲ н ϳ н ϯ с ϲ н ;ϳ н ϯͿ

•

ϯ н ϰ с ϰ н ϯ

•

>͛ĂĚĚŝƚŝŽŶ ĞƐƚ ƵŶĞ ŽƉĠƌĂƚŝŽŶ ĐŽŵŵƵƚĂƚŝǀĞ͘ >͛ĂĚĚŝƚŝŽŶ ĂĚŵĞƚ ůĞ ŶŽŵďƌĞ Ϭ ĐŽŵŵĞ ĠůĠŵĞŶƚ ŶĞƵƚƌĞ͘

•

p.32 B1

ACTIVITÉS

Chapitre 1 Calcul mental

5 WŽƵƌ ĐŚĂƋƵĞ ĠƚĂƉĞ ĚƵ ĐĂůĐƵů ĐŝͲĚĞƐƐŽƵƐ͕ Ɛŝ ƵŶĞ ƉƌŽƉƌŝĠƚĠ ĚĞ ů͛ĂĚĚŝƚŝŽŶ ĞƐƚ ƵƚŝůŝƐĠĞ͕ ĠĐƌŝƐͲůĂ͘ ϱϰ н ϭϮϱ н Ϭ н Ϯϰϲ н ϳϱ с ϱϰ н ϭϮϱ н Ϯϰϲ н ϳϱ

с ϱϰ н Ϯϰϲ н ϭϮϱ н ϳϱ

с ;ϱϰ н ϮϰϲͿ н ;ϭϮϱ н ϳϱͿ

с ϯϬϬ н ϮϬϬ

с ϱϬϬ

6 ĂůĐƵůĞ ĞŶ ƵƚŝůŝƐĂŶƚ ůĞƐ ƉƌŽƉƌŝĠƚĠƐ ĚĞ ů͛ĂĚĚŝƚŝŽŶ͘ ϱϭ н ϭϯϰ н ϭϲ н ϵ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϰϮϭ н ϭϲϯ н Ϯϳϵ н Ϯϯϳ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϭϯϱϲ н ϳϭϬϰ н Ϯϯϰϰ н Ϯϰϵϲ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϲϮ н ϯ͕ϰϱ н ϰ͕ϱϱ н Ϯϴ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϱ͕ϯ н ϵ͕Ϭϱ н ϰ͕ϵϱ н ϲ͕ϳ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ Ϯϳ͕Ϭϲ н ϴϵ͕ϱϴ н ϰϮ͕ϵϰ н Ϯϭ͕ϰϮ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ĐƚŝǀŝƚĠ ϯ Propriétés de la multiplication 1 ĂͿ ĂůĐƵůĞ͘ ϭϯ . Ϯ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϯ . Ϭ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϭϴ . ϭ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϭϵ . Ϭ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Ϯϭ . ϰ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϳ . ϭ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Ϯϰ . ϱ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϭϮ . ϭϭ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϭ . ϭ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϴ . ϵ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ďͿ ŽŵƉůğƚĞ ůĞƐ ƉŚƌĂƐĞƐ͘ DƵůƚŝƉůŝĞƌ ƵŶ ŶŽŵďƌĞ ƉĂƌ Ϭ ĚŽŶŶĞ ƵŶ ƌĠƐƵůƚĂƚ ĠŐĂů ă ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ >Ă ŵƵůƚŝƉůŝĐĂƚŝŽŶ ĞƐƚ ƵŶĞ ŽƉĠƌĂƚŝŽŶ ƋƵŝ ĂĚŵĞƚ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ĐŽŵŵĞ ĠůĠŵĞŶƚ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘͘ DƵůƚŝƉůŝĞƌ ƵŶ ŶŽŵďƌĞ ƉĂƌ ϭ ĚŽŶŶĞ ƵŶ ƌĠƐƵůƚĂƚ ĠŐĂů ă ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘͘ >Ă ŵƵůƚŝƉůŝĐĂƚŝŽŶ ĞƐƚ ƵŶĞ ŽƉĠƌĂƚŝŽŶ ƋƵŝ ĂĚŵĞƚ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ĐŽŵŵĞ ĠůĠŵĞŶƚ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘͘ 2 ZĞůŝĞ ĐŚĂƋƵĞ ĐĂůĐƵů ă ůĂ ƉƌŽƉƌŝĠƚĠ ƋƵ͛ŝů ŝůůƵƐƚƌĞ͘ ϲ . ϭ с ϲ •

• >Ă ŵƵůƚŝƉůŝĐĂƚŝŽŶ ĞƐƚ ƵŶĞ ŽƉĠƌĂƚŝŽŶ ĂƐƐŽĐŝĂƚŝǀĞ͘

Ϭ . ϰ с Ϭ •

• >Ă ŵƵůƚŝƉůŝĐĂƚŝŽŶ ĂĚŵĞƚ ϭ ĐŽŵŵĞ ĠůĠŵĞŶƚ ŶĞƵƚƌĞ͘

Ϯ . ϯ с ϯ . Ϯ •

• >Ă ŵƵůƚŝƉůŝĐĂƚŝŽŶ ĂĚŵĞƚ Ϭ ĐŽŵŵĞ ĠůĠŵĞŶƚ ĂďƐŽƌďĂŶƚ͘

p.32 B2

ϯ . ϱ . Ϯ с ϯ . ;ϱ . ϮͿ •

• >Ă ŵƵůƚŝƉůŝĐĂƚŝŽŶ ĞƐƚ ƵŶĞ ŽƉĠƌĂƚŝŽŶ ĐŽŵŵƵƚĂƚŝǀĞ͘ 13

ACTIVITÉS

Chapitre 1 Calcul mental

3 WŽƵƌ ĐŚĂƋƵĞ ĠƚĂƉĞ ĚƵ ĐĂůĐƵů ĐŝͲĚĞƐƐŽƵƐ͕ Ɛŝ ƵŶĞ ƉƌŽƉƌŝĠƚĠ ĚĞ ůĂ ŵƵůƚŝƉůŝĐĂƚŝŽŶ ĞƐƚ ƵƚŝůŝƐĠĞ͕ ĠĐƌŝƐͲůĂ͘

ϭϮϱ . ϭϳ . Ϭ͕ϱ . ϴ ͘ Ϯ с ϭϮϱ . ϴ . Ϭ͕ϱ . Ϯ . ϭϳ

с ;ϭϮϱ . ϴͿ . ;Ϭ͕ϱ . ϮͿ . ϭϳ

с ϭϬϬϬ . ϭ . ϭϳ

с ϭϬϬϬ . ϭϳ

с ϭϳ ϬϬϬ

4 ĂůĐƵůĞ ĞŶ ĞŶ ƵƚŝůŝƐĂŶƚ ůĞƐ ƉƌŽƉƌŝĠƚĠƐ ĚĞ ůĂ ŵƵůƚŝƉůŝĐĂƚŝŽŶ͘ ϳ ͘ ϰ . ϯ . Ϯϱ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϭϳ . Ϯ . ϱ . Ϭ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ Ϯ . Ϯϭ . ϱϬ . ϯ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ Ϯϱ . ϲϳ . ϭ . ϰϬ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϰϯ . ϭϮϱ . ϰ . Ϯ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ Ϭ͕Ϯϱ ͘ Ϯϰ . ϰ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ Ϭ͕ϱ . ϳ͕ϱ . ϮϬ . Ϯ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϴϬ . Ϭ͕ϰ . Ϯϱ . Ϭ͕ϭϮϱ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ĐƚŝǀŝƚĠ ϰ Distributivité simple 1 ĞƐ ĠůğǀĞƐ ƉƌŽũĞƚƚĞŶƚ Ě͛ĂŵĠŶĂŐĞƌ ƵŶ ĞƐƉĂĐĞ ǀĞƌƚ ĂƵ ƐĞŝŶ ĚĞ ůĞƵƌ ĠĐŽůĞ͘ ^ŽƵƐ ůĞƐ ƉƌĠĐŝĞƵǆ ĐŽŶƐĞŝůƐ Ě͛ƵŶ ũĂƌĚŝŶŝĞƌ͕ ŝůƐ ǀŽŶƚ ƌĠĂůŝƐĞƌ ůĂ ĚĠĐŽƌĂƚŝŽŶ ĚĞ ƐĞƉƚ ƉĂƌƚĞƌƌĞƐ͘ ĂŶƐ ĐŚĂĐƵŶ Ě͛ĞŶƚƌĞ ĞƵǆ͕ ŝůƐ ĚĞǀƌŽŶƚ ƉůĂŶƚĞƌ Ϯϰ ũĂĐŝŶƚŚĞƐ͕ ϯϲ ŶĂƌĐŝƐƐĞƐ Ğƚ ϰϴ ĐƌŽĐƵƐ͘ ĠƚĞƌŵŝŶĞ ůĞ ŶŽŵďƌĞ ĚĞ ďƵůďĞƐ ĚĞ ĐŚĂƋƵĞ ƐŽƌƚĞ ƋƵ͛ŝůƐ ĚŽŝǀĞŶƚ ĂĐŚĞƚĞƌ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

2 ĠĐŽŵƉŽƐĞ ƵŶ ĚĞƐ ĚĞƵǆ ĨĂĐƚĞƵƌƐ ĞŶ ƵŶĞ ƐŽŵŵĞ ŽƵ ĞŶ ƵŶĞ ĚŝĨĨĠƌĞŶĐĞ͕ ƉƵŝƐ ĐĂůĐƵůĞ ĞŶ ĚĠƚĂŝůůĂŶƚ ƚŽŶ ƌĂŝƐŽŶŶĞŵĞŶƚ͘ sĠƌŝĨŝĞ ƚŽŶ ƌĠƐƵůƚĂƚ ă ůĂ ĐĂůĐƵůĂƚƌŝĐĞ͘ ϳ . ϭϲ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ Ϯϯ . ϲ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϵϰ . ϯ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϳϮ . ϭϭ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ Ϯϲ . ϵϴ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ 14

p.33

ACTIVITÉS

Chapitre 1 Calcul mental

ϭϬϭ . Ϯϳ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϯϳ . ϭϵ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϳ . Ϯϰϯ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϳ͕ϱ . ϴ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϭϯ͕ϱ . ϲ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ĐƚŝǀŝƚĠ ϱ Mise en évidence 1 ĂͿ ƐƐĞŵďůĞ ůĞƐ ƚƌŽŝƐ ƌĞĐƚĂŶŐůĞƐ ǀĞƌƚƐ ƉƌŽƉŽƐĠƐ ĂĨŝŶ ĚĞ ĨŽƌŵĞƌ ƵŶ ƐĞƵů ŐƌĂŶĚ ƌĞĐƚĂŶŐůĞ͘

1,5 cm 1,7 cm 1,5 cm

2,3 cm

1,5 cm

6 cm

ďͿ ĂůĐƵůĞ͕ ůĞ ƉůƵƐ ƌĂƉŝĚĞŵĞŶƚ ƉŽƐƐŝďůĞ͕ ů͛ĂŝƌĞ ĚĞ ĐĞ ŶŽƵǀĞĂƵ ƌĞĐƚĂŶŐůĞ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

2 ĂͿ &ƌĂŶĕŽŝƐ ĂĐŚğƚĞ ƉŽƵƌ ĐŚĂĐƵŶ ĚĞƐ ϭϳ ĠůğǀĞƐ ĚĞ ƐĂ ĐůĂƐƐĞ ƵŶĞ ŐŽŵŵĞ Ğƚ ƵŶĞ ƉĂŝƌĞ ĚĞ ĐŝƐĞĂƵǆ͘ ĂůĐƵůĞ͕ ƐĂŶƐ ƵƚŝůŝƐĞƌ ůĂ ĐĂůĐƵůĂƚƌŝĐĞ͕ ůĞ ŵŽŶƚĂŶƚ ƚŽƚĂů ĚĞ ƐĞƐ ĂĐŚĂƚƐ͘

p.33 D

ąƚŽŶ ĚĞ ĐŽůůĞ ;Ϯϭ ŐͿ WĂŝƌĞ ĚĞ ĐŝƐĞĂƵǆ 'ŽŵŵĞ dĂŝůůĞͲĐƌĂǇŽŶ ϭer Ɖƌŝǆ ƌĂǇŽŶ ƉĂƉŝĞƌ , ϭer Ɖƌŝǆ ĂŚŝĞƌ ϱ ;ϭϴϬ ƉͿ ůŽĐ ĚĞ ĐŽƵƌƐ ϰ ;ϭϬϬ ĨͿ ŽŵƉĂƐ ƋƵĞƌƌĞ

Ϭ͕ϳϬ Φ ϭ͕ϱϲ Φ Ϭ͕ϰϰ Φ Ϭ͕ϱϬ Φ Ϭ͕ϭϬ Φ ϭ͕ϳϱ Φ ϯ͕Ϯϱ Φ ϯ͕ϬϬ Φ ϭ͕ϬϬ Φ

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ďͿ Ŷ ƵƚŝůŝƐĂŶƚ ůĞƐ ŵġŵĞƐ ƚĂƌŝĨƐ͕ ĐĂůĐƵůĞ͕ ůĞ ƉůƵƐ ƌĂƉŝĚĞŵĞŶƚ ƉŽƐƐŝďůĞ͕ ůĞ ŵŽŶƚĂŶƚ ă ƉĂǇĞƌ ƉŽƵƌ ŵƵŶŝƌ ůĞƐ ϭϳ ĠůğǀĞƐ ĚĞ ƐĂ ĐůĂƐƐĞ͙ ;ϭͿ Ě͛ƵŶ ĐŽŵƉĂƐ Ğƚ Ě͛ƵŶ ĐƌĂǇŽŶ ƉĂƉŝĞƌ , ϭer Ɖƌŝǆ ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ACTIVITÉS

Chapitre 1 Calcul mental

;ϮͿ ĚĞ ƚƌŽŝƐ ĐĂŚŝĞƌƐ ϱ ;ϭϴϬ ƉͿ Ğƚ ĚĞ ƚƌŽŝƐ ďůŽĐƐ ĚĞ ĐŽƵƌƐ ϰ ;ϭϬϬ ĨͿ ͗

;ϯͿ Ě͛ƵŶ ĐƌĂǇŽŶ ƉĂƉŝĞƌ , ϭer Ɖƌŝǆ Ğƚ Ě͛ƵŶ ƚĂŝůůĞͲĐƌĂǇŽŶ ϭer Ɖƌŝǆ ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

3 ĂůĐƵůĞ ĞŶ ƵƚŝůŝƐĂŶƚ ůĂ ŵŝƐĞ ĞŶ ĠǀŝĚĞŶĐĞ͘ sĠƌŝĨŝĞ ƚŽŶ ƌĠƐƵůƚĂƚ ă ůĂ ĐĂůĐƵůĂƚƌŝĐĞ͘ ϴ . ϲ н Ϯ . ϲ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϳ . Ϯϭ н ϯ . Ϯϭ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϴϱ . ϭϳ н ϭϱ . ϭϳ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϭϭϬ . ϴ н ϭϱ . ϴ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϱϰ . ϭϲ н Ϯϳ . ϭϲ н ϭϵ . ϭϲ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϯϵ . ϳ͕ϱ н ϯϵ . Ϯ͕ϱ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ Ϭ͕ϯ . ϳ н ϳ . Ϭ͕ϳ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϰ͕Ϯϱ . ϱ͕ϰ н ϰ͕ϲ . ϰ͕Ϯϱ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϲ͕ϳ . ϭϮ͕ϰ н ϳ͕ϲ . ϲ͕ϳ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ 4 >Ă ƐŽŵŵĞ ϲϰϬϬ н ϲϰϬ н ϲϰ ĞƐƚ ůĞ ƉƌŽĚƵŝƚ ĚĞ ϲϰ ƉĂƌ ƵŶ ŶŽŵďƌĞ͘ >ĞƋƵĞů ͍ ĠƚĞƌŵŝŶĞ ĐĞůƵŝͲĐŝ ĞŶ ĠĐƌŝǀĂŶƚ ƚŽƵƚ ƚŽŶ ƌĂŝƐŽŶŶĞŵĞŶƚ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

5 ĂůĐƵůĞ ĞŶ ƚƌŽƵǀĂŶƚ ƵŶ ƉƌŽĐĠĚĠ ĞĨĨŝĐĂĐĞ͘ ϭϰ . ϯ н ϳ ͘ ϱ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϯϲ . ϳ н ϭϮ . ϰ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϲϯ . ϯϬ н Ϯϭ . ϭϬ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϳϱ . ϭϮ н ϱϬ . ϯϮ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϭϰ . Ϯϯ н Ϯϭ . ϭϴ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ Ϯϭ . ϭ͕ϱ н ϯϱ . ϭ͕ϭ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ACTIVITÉS

Chapitre 1 Calcul mental

ĐƚŝǀŝƚĠ ϲ Priorités des opérations 1

1 sŽŝĐŝ ƵŶ ƚŝƌĂŐĞ ĚĞ ů͛ĠŵŝƐƐŝŽŶ ĚĞ ƚĠůĠǀŝƐŝŽŶ ͨ ĞƐ ĐŚŝĨĨƌĞƐ Ğƚ ĚĞƐ ůĞƚƚƌĞƐ ͩ͘ dƵ ĚŝƐƉŽƐĞƐ ĚĞƐ ƋƵĂƚƌĞ ŽƉĠƌĂƚŝŽŶƐ Ğƚ ĚĞƐ Ɛŝǆ ŶŽŵďƌĞƐ ĚŽŶŶĠƐ ƋƵĞ ƚƵ ŶĞ ƉĞƵǆ ƵƚŝůŝƐĞƌ ƋƵ͛ƵŶĞ ƐĞƵůĞ ĨŽŝƐ ƉŽƵƌ ĂƚƚĞŝŶĚƌĞ ůĞ ƌĠƐƵůƚĂƚ͘ ĂͿ EŽƚĞ͕ ůĞƐ ƵŶĞƐ ĞŶͲĚĞƐƐŽƵƐ ĚĞƐ ĂƵƚƌĞƐ͕ ůĞƐ ŽƉĠƌĂƚŝŽŶƐ ƌĠĂůŝƐĠĞƐ ƉŽƵƌ ŽďƚĞŶŝƌ ůĞ ŶŽŵďƌĞ ĚĞŵĂŶĚĠ͘ ϳ

ϭͿ

ϯͿ

Ϯϱϰ

ϱϬ

ϮͿ

Ϯϱ

ϮϲϬ

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϭϬϴ

ϰͿ

ϯϵϬ

ďͿ EŽƚĞ ůĞƐ ĐĂůĐƵůƐ ĚĞ ĐŚĂƋƵĞ ƐŽůƵƚŝŽŶ ĞŶ ƵŶĞ ƐĞƵůĞ ĞǆƉƌĞƐƐŝŽŶ ĞŶ ƉƌĞŶĂŶƚ ƐŽŝŶ ĚΖĠĐƌŝƌĞ ĐŚĂƋƵĞ ĐĂůĐƵů ĞŶƚƌĞ ƉĂƌĞŶƚŚğƐĞƐ͕ ă ůΖĞǆĐĞƉƚŝŽŶ ĚƵ ĚĞƌŶŝĞƌ͘ ϭͿ

ϮͿ

ϯͿ

ϰͿ

ACTIVITÉS

Chapitre 1 Calcul mental

ĐͿ ĂŶƐ ůĂ ƉƌĞŵŝğƌĞ ĐŽůŽŶŶĞ ĚƵ ƚĂďůĞĂƵ ĐŝͲĚĞƐƐŽƵƐ͕ ƌĞĐŽƉŝĞ ůĞƐ ĞǆƉƌĞƐƐŝŽŶƐ ƚƌŽƵǀĠĞƐ ĞŶ ďͿ͘

ĨĨĞĐƚƵĞ ĞŶƐƵŝƚĞ ĐĞƐ ĐĂůĐƵůƐ ă ůĂ ĐĂůĐƵůĂƚƌŝĐĞ ƐĐŝĞŶƚŝĨŝƋƵĞ ĞŶ ŝŶƚƌŽĚƵŝƐĂŶƚ ůĞƐ ƉĂƌĞŶƚŚğƐĞƐ ƉƵŝƐ͕ ƐĂŶƐ ůĞƐ ŝŶƚƌŽĚƵŝƌĞ͘ ZĞĐŽƉŝĞ ĞŶĨŝŶ ĚĂŶƐ ůĂ ĚĞƌŶŝğƌĞ ĐŽůŽŶŶĞ ĚƵ ƚĂďůĞĂƵ ůĞƐ ĐĂůĐƵůƐ ĞŶ ƐƵƉƉƌŝŵĂŶƚ ůĞƐ ƉĂƌĞŶƚŚğƐĞƐ ŝŶƵƚŝůĞƐ͘ ZĠƐƵůƚĂƚ ŽďƚĞŶƵ ĂůĐƵů

ĂǀĞĐ ůĞƐ ƐĂŶƐ ůĞƐ ƉĂƌĞŶƚŚğƐĞƐ ƉĂƌĞŶƚŚğƐĞƐ

^ƵƉƉƌĞƐƐŝŽŶ ĚĞƐ ƉĂƌĞŶƚŚğƐĞƐ ŝŶƵƚŝůĞƐ

ϭͿ ϮͿ ϯͿ ϰͿ 2 ĂŶƐ ĐŚĂƋƵĞ ĐĂƐ͕ ĐŚŽŝƐŝƐ ƚƌŽŝƐ ŶŽŵďƌĞƐ ƉĂƌŵŝ ϰ͕ ϳ͕ ϭϬ Ğƚ Ϯϴ ƉŽƵƌ ĐŽŵƉůĠƚĞƌ ůĞƐ ĐĂůĐƵůƐ ĐŝͲĚĞƐƐŽƵƐ͕ ƐĂŶƐ ĂũŽƵƚĞƌ ĚĞ ƉĂƌĞŶƚŚğƐĞƐ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

. ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ н ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ с ϳϰ

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

н ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ . ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ с ϲϴ

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

. ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ʹ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ с ϭϴ ʹ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ . ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ с Ϭ

3 ĂůĐƵůĞ ĞŶ ƵƚŝůŝƐĂŶƚ ůĞƐ ƉƌŝŽƌŝƚĠƐ ĚĞƐ ŽƉĠƌĂƚŝŽŶƐ͘ ^ŽƵůŝŐŶĞ ůĞ;ƐͿ ĐĂůĐƵů;ƐͿ ƉƌŝŽƌŝƚĂŝƌĞ;ƐͿ ă ĐŚĂƋƵĞ ĠƚĂƉĞ͘

ϰ н Ϯ . ϱ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϭ͕ϱ н Ϯ͕ϱ . ϰ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϵ . Ϯ н ϴ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϲ . ϳ ʹ Ϯ͕ϱ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϭϳ ʹ Ϯ . ϯ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Ϯ͕ϱ н Ϭ . ϭϲ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϲ . ϳ н ϱ . ϰ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;ϯ͕ϰ н Ϭ͕ϲͿ ͗ Ϯ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϭϴ ʹ ϱ . Ϯ н ϭϭ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϭ . ;Ϯ͕ϯ н ϭ͕ϴͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϱ н Ϯ . Ϯ н ϯ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;ϭϬ͕ϱ ʹ ϯͿ . Ϯ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϵ . ;Ϯ н ϴͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Ϯ н ϯ . ϳ н ϯ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;ϭϳ ʹ ϮͿ ͗ ϯ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;Ϯ н ϯͿ . ;ϳ н ϯͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;ϱ н ϮͿ . ;Ϯ н ϯͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;Ϯ н ϯͿ . ϳ н ϯ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;ϭϮ ʹ ϱͿ . ;ϭϭ ʹ ϰͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϭϳ ʹ Ϯ . ;ϴ ʹ ϱͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;ϱ н ϯͿ . ϴ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Ϯ н ϯ ͗ ;ϳ н ϯͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϱ н ϯ . ϴ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϰ . ;ϲ н ϱͿ ʹ Ϯ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

p.33

ACTIVITÉS

Chapitre 1 Calcul mental

4 YƵĂŶĚ Đ͛ĞƐƚ ŶĠĐĞƐƐĂŝƌĞ͕ ƉůĂĐĞ ĚĞƐ ƉĂƌĞŶƚŚğƐĞƐ ƉŽƵƌ ƋƵĞ ůĞ ƌĠƐƵůƚĂƚ ƐŽŝƚ ĐŽƌƌĞĐƚ͘

ϴ н Ϯ . ϱ с ϱϬ

ϰ н ϱ . Ϯ н ϯ с ϭϳ

ϰ . ϱ н Ϯ . ϯ с ϴϰ

ϰ . ϴ н ϱ с ϯϳ

ϰ н ϱ . Ϯ н ϯ с ϰϱ

ϰ н ϱ . Ϯ н ϯ с Ϯϵ

ϰ . ϰ н ϯ н ϱ с ϯϯ

ϰ . ϱ н Ϯ . ϯ с Ϯϲ

ϰ . ϱ н Ϯ . ϯ с ϲϲ

>ĞƐ ĠůğǀĞƐ ĚĞƐ ĐůĂƐƐĞƐ ĚĞ ϱe Ğƚ ĚĞ ϲe ƉƌŝŵĂŝƌĞƐ͕ ĂĐĐŽŵƉĂŐŶĠƐ ĚĞ ůĞƵƌƐ ĚĞƵǆ ŝŶƐƚŝƚƵƚĞƵƌƐ͕ ĚĠĐŝĚĞŶƚ ĚĞ ƉĂƐƐĞƌ ƵŶĞ ũŽƵƌŶĠĞ ĚĂŶƐ ƵŶ ƉĂƌĐ Ě͛ĂƚƚƌĂĐƚŝŽŶƐ͘ ĂͿ sŽŝĐŝ ůĂ ƐƵŝƚĞ ĚĞ ĐĂůĐƵůƐ ƋƵŝ ƉĞƌŵĞƚ ĚĞ ƚƌŽƵǀĞƌ ůĞ ŵŽŶƚĂŶƚ ĚĞ ůĂ ƉĂƌƚŝĐŝƉĂƚŝŽŶ ĚĞŵĂŶĚĠĞ ă ĐŚĂƋƵĞ ĠůğǀĞ ͗ ;ϲ . ϳϬ н ϰϬ . Ϯϲ ʹ ϮϲϬͿ ͗ ϰϬ Ŷ ŽďƐĞƌǀĂŶƚ ĂƚƚĞŶƚŝǀĞŵĞŶƚ ĐĞƚƚĞ ƐƵŝƚĞ Ě͛ŽƉĠƌĂƚŝŽŶƐ͕ ĠĐƌŝƐ ůĞƐ ĚŽŶŶĠĞƐ ƋƵŝ ŽŶƚ ĠƚĠ ĞĨĨĂĐĠĞƐ ĚĂŶƐ ůĞ ƚĞǆƚĞ ĐŝͲĚĞƐƐŽƵƐ͘ ͨ hŶĞ ĠĐŽůĞ ŽƌŐĂŶŝƐĞ͕ ƉŽƵƌ ƐĞƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ĠůğǀĞƐ ĚĞ ϱe Ğƚ ĚĞ ϲe ƉƌŝŵĂŝƌĞƐ ƵŶĞ ũŽƵƌŶĠĞ ƌĠĐƌĠĂƚŝǀĞ ĚĂŶƐ ƵŶ ƉĂƌĐ Ě͛ĂƚƚƌĂĐƚŝŽŶƐ͘ >͛ĞŶƚƌĠĞ ĂƵ ƉĂƌĐ ĞƐƚ ĚĞ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ Φ͘ >͛ĞŶƚƌĠĞ ƉŽƵƌ ůĞƐ ĚĞƵǆ ŝŶƐƚŝƚƵƚĞƵƌƐ ĞƐƚ ŐƌĂƚƵŝƚĞ͘ >Ğ ǀŽǇĂŐĞ ĚĞ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ Ŭŵ Ɛ͛ĞĨĨĞĐƚƵĞ ĞŶ ĐĂƌ͘ >Ğ Ɖƌŝǆ ĚƵ ĐĂƌ ĞƐƚ ĚĞ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ Φ ƉĂƌ ŬŝůŽŵğƚƌĞ ƉĂƌĐŽƵƌƵ͘ >͛ĠĐŽůĞ ŝŶƚĞƌǀŝĞŶƚ ƉŽƵƌ ƵŶ ŵŽŶƚĂŶƚ ĚĞ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ Φ͘ ͩ ďͿ ĂůĐƵůĞ ůĂ ƉĂƌƚŝĐŝƉĂƚŝŽŶ ĚĞŵĂŶĚĠĞ ă ĐŚĂƋƵĞ ĠůğǀĞ͘ sĠƌŝĨŝĞ ƚŽŶ ƌĠƐƵůƚĂƚ ă ůĂ ĐĂůĐƵůĂƚƌŝĐĞ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

6 ĂůĐƵůĞ ĞŶ ƵƚŝůŝƐĂŶƚ ůĞƐ ƉƌŝŽƌŝƚĠƐ ĚĞƐ ŽƉĠƌĂƚŝŽŶƐ͘ ^ŽƵůŝŐŶĞ ůĞ;ƐͿ ĐĂůĐƵů;ƐͿ ƉƌŝŽƌŝƚĂŝƌĞ;ƐͿ ă ĐŚĂƋƵĞ ĠƚĂƉĞ͘ ϯ . ;ϳ н Ϯ . ϯͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ;ϯ н ϳ . ϮͿ н ϯ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϭϬ н ;Ϯ . ϯ ʹ ϰͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ;ϭϬ н Ϯ . ϯͿ ʹ ϰ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ;ϮϬ ʹ ϯ . ϮͿ н ϵ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϮϬ ʹ ;ϯ . Ϯ н ϵͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϱ . ;Ϯ . ϯ н ϰͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ;Ϯ н ϯ . ϱͿ . ϯ н ϭϭ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϯ . ;ϵ н Ϯ . ϳͿ ʹ ϭ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϰ н ϯ . ;ϵ ʹ ϰ ͗ ϮͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ACTIVITÉS

Chapitre 1 Calcul mental

7 >ƵĐ ƉŽƐƐğĚĞ ƵŶ ƉŽƚĂŐĞƌ ĚĞ ϭϮ ŵ ĚĞ ůŽŶŐ ƐƵƌ ϯ ŵ ĚĞ ůĂƌŐĞ ĚĠůŝŵŝƚĠ ƉĂƌ ĚĞƐ ďŽƌĚƵƌĞƐ ĞŶ ďĠƚŽŶ ĚĞ ϭ ŵ ĚĞ ůŽŶŐ͘ /ů ĚĠĐŝĚĞ ĚĞ ŵŽĚŝĨŝĞƌ ůĞƐ ĚŝŵĞŶƐŝŽŶƐ ĚĞ ĐĞ ƉŽƚĂŐĞƌ ĞŶ ĚŝŵŝŶƵĂŶƚ ƐĂ ůŽŶŐƵĞƵƌ ĚĞ Ϯ ŵ Ğƚ ĞŶ ĂƵŐŵĞŶƚĂŶƚ ƐĂ ůĂƌŐĞƵƌ ĚĞ ϭ ŵ͘

dƌĂĐĞ ĚĂŶƐ ůĞ ƋƵĂĚƌŝůůĂŐĞ ĐŝͲĚĞƐƐŽƵƐ͕ ă ů͛ĠĐŚĞůůĞ ϭ ͗ ϭϬϬ͕ ůĞ ƉůĂŶ ĚƵ ƉŽƚĂŐĞƌ ĂǀĂŶƚ Ğƚ ĂƉƌğƐ ƚƌĂŶƐĨŽƌŵĂƚŝŽŶƐ͘

>ƵĐ ĚŽŝƚͲŝů ƌĠƵƚŝůŝƐĞƌ ů͛ĞŶƐĞŵďůĞ ĚĞ ƐĞƐ ďŽƌĚƵƌĞƐ ĞŶ ďĠƚŽŶ ƉŽƵƌ ďŽƌŶĞƌ ůĞ ŶŽƵǀĞĂƵ ƉŽƚĂŐĞƌ ͍ :ƵƐƚŝĨŝĞ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

>ƵĐ ĚŝƐƉŽƐĞͲƚͲŝů ĚĞ ůĂ ŵġŵĞ ƐƵƉĞƌĨŝĐŝĞ ĐƵůƚŝǀĂďůĞ ͍ :ƵƐƚŝĨŝĞ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

8 hŶ ĐůƵď ĚĞ ĨŽŽƚďĂůů ĚŽŝƚ ƌĞŶŽƵǀĞůĞƌ ůĞƐ ĠƋƵŝƉĞŵĞŶƚƐ ĚĞ ƐĞƐ ϮϮ ũŽƵĞƵƌƐ͘ /ů ĚŽŝƚ ĂĐŚĞƚĞƌ͕ ƉŽƵƌ ĐŚĂƋƵĞ ũŽƵĞƵƌ͕ ƵŶ ŵĂŝůůŽƚ ă ϭϰ͕ϱϬ Φ͕ ƵŶ ƐŚŽƌƚ ă ϭϭ͕ϲϬ Φ͕ ƵŶĞ ƉĂŝƌĞ ĚĞ ĐŚĂƵƐƐƵƌĞƐ ă ϰϵ Φ Ğƚ ƵŶĞ ƉĂŝƌĞ ĚĞ ĐŚĂƵƐƐĞƚƚĞƐ ă ϰ͕ϵϬ Φ͘ ^ĂĐŚĂŶƚ ƋƵĞ ůĞ ŵĂŐĂƐŝŶ ĚĞ ƐƉŽƌƚ ĂĐĐŽƌĚĞ ƵŶĞ ƌĞŵŝƐĞ ĚĞ ϭϬ й ƐƵƌ ůĞ ŵŽŶƚĂŶƚ ƚŽƚĂů ĚĞ ůĂ ĨĂĐƚƵƌĞ͕ ĐĂůĐƵůĞ ůĞ Ɖƌŝǆ ă ƉĂǇĞƌ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ACTIVITÉS

Chapitre 1 Calcul mental

9 ůĠŵĞŶƚ ĂĐŚğƚĞ ƋƵĂƚƌĞ ĐůĂƐƐĞƵƌƐ Ğƚ ĚĞƵǆ ďůŽĐƐ ĚĞ ĨĞƵŝůůĞƐ ƋƵĂĚƌŝůůĠĞƐ ƉŽƵƌ ůĂ ƐŽŵŵĞ ĚĞ ϭϳ͕ϰϬ Φ͘ ^ŝ ƚƵ ƐĂŝƐ ƋƵ͛ƵŶ ĐůĂƐƐĞƵƌ ĐŽƸƚĞ ϯ͕ϳϬ Φ͕ ĚĠƚĞƌŵŝŶĞ ůĞ Ɖƌŝǆ Ě͛ƵŶ ďůŽĐ ĚĞ ĨĞƵŝůůĞƐ ƋƵĂĚƌŝůůĠĞƐ͘ ĐƌŝƐ ůĂ ƐƵŝƚĞ ĚĞ ĐĂůĐƵůƐ ƋƵŝ ƚĞ ƉĞƌŵĞƚ ĚĞ ƚƌŽƵǀĞƌ ůĂ ƐŽůƵƚŝŽŶ ĞŶ ƵŶĞ ƐĞƵůĞ ĞǆƉƌĞƐƐŝŽŶ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ĐƚŝǀŝƚĠ ϳ Dénombrement 1 KďƐĞƌǀĞ ĐĞƚƚĞ ƐƵŝƚĞ ĚĞ ŵŽƚŝĨƐ ĐŽŵƉŽƐĠƐ ĚĞ ĐĂƌƌĠƐ ƚŽƵƐ ŝĚĞŶƚŝƋƵĞƐ͘ DŽƚŝĨ ϭ

DŽƚŝĨ Ϯ

DŽƚŝĨ ϯ

ĂͿ ŽŵƉůğƚĞ ůĞ ƚĂďůĞĂƵ ĐŝͲĚĞƐƐŽƵƐ͘ EƵŵĠƌŽ ĚƵ ŵŽƚŝĨ

EŽŵďƌĞ ĚĞ ĐĂƌƌĠƐ

ďͿ ĂůĐƵůĞ ůĞ ŶŽŵďƌĞ ĚĞ ĐĂƌƌĠƐ ŶĠĐĞƐƐĂŝƌĞƐ ƉŽƵƌ ĐŽŶƐƚŝƚƵĞƌ ůĞ ϯϮe ŵŽƚŝĨ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ĐͿ ĂůĐƵůĞ ůĞ ŶƵŵĠƌŽ ĚƵ ŵŽƚŝĨ ĐŽŶƐƚŝƚƵĠ ĚĞ ϰϴ ĐĂƌƌĠƐ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

2 ŽŵƉůğƚĞ͕ ĚĞ ŵĂŶŝğƌĞ ůŽŐŝƋƵĞ͕ ůĞƐ ƐƵŝƚĞƐ ĚĞ ŶŽŵďƌĞƐ ĐŝͲĚĞƐƐŽƵƐ͘ 7e ŶŽŵďƌĞ ĚĞ ůĂ ƐƵŝƚĞ

^ƵŝƚĞ ůŽŐŝƋƵĞ ϳ

ϭϮ

ϭϳ

ϮϮ

Ϯϳ

ϯϮ

ϯϬ

Ϯϲ

ϮϮ

ϭϴ

ϭϰ

ϭϬ

ϭϲ

ϯϮ

ϭϬ

ϭϮ

ϭϳ

ϭϬ

ϭϳ

Ϯϲ

ϭϬ

ϭϭ

ϮϮ

ϭϵϮ

ϵϲ

ϰϴ

Ϯϰ

ϭϮ

EXERCICES COMPLÉMENTAIRES

Chapitre 1 Calcul mental

Connaître 1

DŽĚŝĮ Ğ ͙ ĂͿ ůĂ ƐŽŵŵĞ ϭϰ н Ϯϯ ĞŶ ƌĞƚƌĂŶĐŚĂŶƚ Ϯ ĚƵ ƐĞĐŽŶĚ ƚĞƌŵĞ͘ ďͿ ůĞ ƋƵŽƟ ĞŶƚ ϭϱ ͗ ϯ ĞŶ ŵƵůƟ ƉůŝĂŶƚ ůĞ ĚŝǀŝƐĞƵƌ ƉĂƌ ϱ͘ ĐͿ ůĂ Ěŝī ĠƌĞŶĐĞ Ϯϳ ʹ ϭϴ ĞŶ ĂũŽƵƚĂŶƚ ϯ ĂƵǆ ĚĞƵǆ ƚĞƌŵĞƐ͘ ĚͿ ůĞ ƉƌŽĚƵŝƚ ϲ . Ϯϲ ĞŶ ĚŝǀŝƐĂŶƚ ůĞƐ ĚĞƵǆ ĨĂĐƚĞƵƌƐ ƉĂƌ Ϯ͘

2 Ŷ Ŷ͛ƵƟ ůŝƐĂŶƚ ƋƵĞ ĚĞƐ ŶŽŵďƌĞƐ ŶĂƚƵƌĞůƐ͕ ĠĐƌŝƐ ůĞ ŶŽŵďƌĞ ϲϰ ƐŽƵƐ ůĂ ĨŽƌŵĞ ͙

ĂͿ Ě͛ƵŶĞ ƐŽŵŵĞ ĚĞ ĚĞƵǆ ƚĞƌŵĞƐ ŝĚĞŶƟ ƋƵĞƐ͘ ďͿ Ě͛ƵŶ ƋƵŽƟ ĞŶƚ ĚŽŶƚ ůĞ ĚŝǀŝƐĞƵƌ ǀĂƵƚ ϯ͘ ĐͿ Ě͛ƵŶ ƉƌŽĚƵŝƚ ĚĞ ĚĞƵǆ ĨĂĐƚĞƵƌƐ ŝĚĞŶƟ ƋƵĞƐ͘ ĚͿ Ě͛ƵŶ ƉƌŽĚƵŝƚ ĚĞ ƚƌŽŝƐ ĨĂĐƚĞƵƌƐ ŝĚĞŶƟ ƋƵĞƐ͘ ĞͿ Ě͛ƵŶ ƉƌŽĚƵŝƚ ĚĞ ĚĞƵǆ ĨĂĐƚĞƵƌƐ Ěŝī ĠƌĞŶƚƐ͘

ĨͿ Ě͛ƵŶ ƉƌŽĚƵŝƚ ĚŽŶƚ ůĞ ƉƌĞŵŝĞƌ ĨĂĐƚĞƵƌ ǀĂƵƚ ϰ͘ ŐͿ Ě͛ƵŶĞ ƐŽŵŵĞ ĚŽŶƚ ůĞ ƉƌĞŵŝĞƌ ƚĞƌŵĞ ǀĂƵƚ ϰϭ͘ ŚͿ Ě͛ƵŶĞ Ěŝī ĠƌĞŶĐĞ ĚŽŶƚ ůĞ ƉƌĞŵŝĞƌ ƚĞƌŵĞ ǀĂƵƚ ϴϮ͘ ŝͿ Ě͛ƵŶĞ Ěŝī ĠƌĞŶĐĞ ĚĞ ĚĞƵǆ ƚĞƌŵĞƐ Ěŝī ĠƌĞŶƚƐ͘ ũͿ Ě͛ƵŶ ƋƵŽƟ ĞŶƚ ĚŽŶƚ ůĞ ĚŝǀŝĚĞŶĚĞ ĞƐƚ ϭϵϮ͘

3 WŽƵƌ ĐŚĂƋƵĞ ĠƚĂƉĞ ĚĞƐ ĐĂůĐƵůƐ ĐŝͲĚĞƐƐŽƵƐ͕ Ɛŝ ƵŶĞ ƉƌŽƉƌŝĠƚĠ ĚĞ ů͛ĂĚĚŝƟ ŽŶ ŽƵ ĚĞ ůĂ ŵƵůƟ ƉůŝĐĂƟ ŽŶ ĞƐƚ

ƵƟ ůŝƐĠĞ͕ ĠĐƌŝƐͲůĂ͘ ĂͿ ϴϭ н ϲϯ н ϰϵ н Ϭ н ϭϳ с ϴϭ н ϲϯ н ϰϵ н ϭϳ ďͿ Ϯ . ϰϳ . ϭ . ϰ . ϱϬ . Ϯϱ с Ϯ . ϰϳ . ϰ . ϱϬ . Ϯϱ с ϴϭ н ϰϵ н ϲϯ н ϭϳ с Ϯ . ϱϬ . ϰ . Ϯϱ . ϰϳ с ;ϴϭ н ϰϵͿ н ;ϲϯ н ϭϳͿ с ;Ϯ . ϱϬͿ . ;ϰ . ϮϱͿ . ϰϳ с ϭϯϬ н ϴϬ с ϭϬϬ . ϭϬϬ . ϰϳ с ϮϭϬ с ;ϭϬϬ . ϭϬϬͿ . ϰϳ с ϭϬ ϬϬϬ . ϰϳ с ϰϳ ϬϬϬ 4 ZĞůŝĞ ůĞƐ ĞǆƉƌĞƐƐŝŽŶƐ ĠƋƵŝǀĂůĞŶƚĞƐ͘ ϰϴ . ;ϵ н ϱͿ • • ϰϴ . ϵ ʹ ϰϴ . ϱ ;ϰϴ н ϵͿ . ϱ • • ϰϴ . ϱ ʹ ϵ . ϱ ϰϴ . ;ϵ ʹ ϱͿ • • ϰϴ . ϵ н ϰϴ . ϱ ;ϰϴ ʹ ϵͿ . ϱ • • ϰϴ . ϱ н ϵ . ϱ 5 ŽŵŵĞ ůĞ ŵŽŶƚƌĞ ů͛ĞǆĞŵƉůĞ͕ ƐŽƵůŝŐŶĞ͕ ĚĂŶƐ ů͛ŽƌĚƌĞ͕ ůĞƐ ŽƉĠƌĂƟ ŽŶƐ Ğī ĞĐƚƵĠĞƐ͘ ϱ . ;Ϯ н ϯͿ н ϲ с ϯϭ

ϰ н ϱ . ϯ с ϭϵ

Ϯ . ϯ н ϱ . ϰ с Ϯϲ

ϰ . ;Ϯ н ϱͿ . ϱ с ϭϰϬ

Ϯ н ϱ . ϳ ʹ ϰ с ϯϯ

ϰ н Ϯ . ;ϰ н ϲͿ с Ϯϰ

;Ϯ н ϯͿ . Ϯ н ϵ с ϭϵ

ϱ . ;ϲ . ϴ ʹ ϭͿ с Ϯϯϱ

Ϯ н ϯ . ;ϰ н ϴ . ϳͿ с ϭϴϮ

Appliquer 1

ǆƉƌŝŵĞ ĐŚĂƋƵĞ ƉŚƌĂƐĞ ƉĂƌ ƵŶ ĐĂůĐƵů Ğƚ Ğī ĞĐƚƵĞͲůĞ͘ ĂͿ >Ă ƐŽŵŵĞ ĚĞ Ϯϯ Ğƚ ĚĞ ϭϰ ďͿ >Ğ ƉƌŽĚƵŝƚ ĚĞ ϰ ƉĂƌ ϱ ĚͿ >Ğ ƋƵŽƚŝĞŶƚ ĚĞ ϯϮ ƉĂƌ ϴ ĞͿ >Ğ ĚŽƵďůĞ ĚĞ ϱϭ

ĐͿ >Ă ĚŝĨĨĠƌĞŶĐĞ ĞŶƚƌĞ ϰϲ Ğƚ ϭϳ ĨͿ >Ğ ƚŝĞƌƐ ĚĞ ϲϯ

ĂͿ >Ă Ěŝī ĠƌĞŶĐĞ ĞŶƚƌĞ ĚĞƵǆ ŶŽŵďƌĞƐ ŶĂƚƵƌĞůƐ ǀĂƵƚ ϭϮϳ͘ ^ĂĐŚĂŶƚ ƋƵĞ ůĂ ǀĂůĞƵƌ ĚƵ ƉƌĞŵŝĞƌ ƚĞƌŵĞ ĞƐƚ ϳϲϰ͕ ĚĠƚĞƌŵŝŶĞ ĐĞůůĞ ĚƵ ƐĞĐŽŶĚ͘ ďͿ >Ă ƐŽŵŵĞ ĚĞ ĚĞƵǆ ŶŽŵďƌĞƐ ŶĂƚƵƌĞůƐ ǀĂƵƚ ϱϳϯ͘ ^ĂĐŚĂŶƚ ƋƵĞ ůĂ ǀĂůĞƵƌ ĚƵ ƉƌĞŵŝĞƌ ƚĞƌŵĞ ĞƐƚ ϯϰϮ͕ ĚĠƚĞƌŵŝŶĞ ĐĞůůĞ ĚƵ ƐĞĐŽŶĚ͘

ĂůĐƵůĞ ĞŶ ƵƟ ůŝƐĂŶƚ ůĞƐ ƉƌŽƉƌŝĠƚĠƐ ĚĞ ů͛ĂĚĚŝƟ ŽŶ Ğƚ ĚĞ ůĂ ŵƵůƟ ƉůŝĐĂƟ ŽŶ͘ ĂͿ ϭϰϯ н ϴϰ н ϱϳ н ϲ с ďͿ ϭϯ͕Ϯ н ϭϱ͕ϭ н ϰ͕ϴ н ϯ͕ϵ с ĐͿ ϵϭϰ н Ϭ н ϯϴϭ н ϭϴϲ с ϮϬ͕ϳ н ϰϱ͕ϲ н ϭϭ͕ϰ н ϭ͕ϯ с ϰϮ н Ϯϳϲ н ϲϴ н Ϯϰ с ϭϱϰ н ϰ͕ϳ н Ϯϯ н ϭϱ͕ϯ с Ϯϳϱ н ϭϮϭϬ н ϳϮϱ н ϴϵϬ с ϰ͕ϯ н ϯ͕ϴ н Ϭ͕ϳ н ϭ͕Ϯ н ϯ͕ϲ с Ϯϰϲ н ϱϳϴ н ϯϭϭ н ϭϰϯ с ϭϮϱ н ϴ͕Ϯϱ н Ϭ͕ϳϱ н ϯ н ϳϱ с

ϴ͕Ϯϱ н ϲ͕ϳϱ н Ϯ͕ϱ н ϭϯ͕ϱ с ϲ͕Ϯϵ н ϰ͕ϭϱ н ϳ͕ϴϱ н ϯ͕ϭϭ с ϴ͕ϬϮ н Ϭ͕ϭϱ н ϭ͕ϴϴ н ϯ͕ϴϱ с ϳ͕ϭ н Ϯ͕ϱ н Ϭ͕ϴ н ϯ͕ϭ с ϰ͕ϯ н ϲ͕ϳϱ н ϯ͕Ϯϱ н ϭ͕ϳ с

Chapitre 1 Calcul mental

EXERCICES COMPLÉMENTAIRES

ĚͿ ϳ . ϱϬ . ϲ . Ϯ с ĞͿ ϭ͕Ϯϱ . ϳ . ϰ с ĨͿ Ϭ͕ϱ . ϳϬ . ϰϬϬ . ϮϬ с Ϯϱ . Ϯϲ . Ϭ . ϰ с ϲ . Ϭ͕Ϯϱ . ϳ . ϰ с ϭ͕Ϯϱ . ϭ͕ϱ . ϰϬ . Ϯ с ϭϮϱ . ϭϳ . ϴ с ϭϯ . ϭ͕ϱ . ϰ с ϮϬϬ . Ϯ͕ϱ . ϰ . Ϭ͕ϱ с ϱ . ϴϰ . ϭ . Ϯ с Ϭ͕ϱ . ϭϮ . ϰ . ϴ . ϭϮ͕ϱ с Ϭ͕ϰ . ϱϬ . Ϯ͕ϱ . Ϯ с Ϯϲ . ϭϮϱ . ϯ . ϰ . Ϯ с ϰ . Ϯ . ϳ͕ϱ . ϱ . ϵ с Ϭ͕ϱ . ϴ . ϮϬ . Ϭ͕Ϯϱ с 4 ī ĞĐƚƵĞ ůĞƐ ĐĂůĐƵůƐ ĐŝͲĚĞƐƐŽƵƐ ĞŶ ĚĠĐŽŵƉŽƐĂŶƚ ƵŶ ĚĞƐ ĚĞƵǆ ĨĂĐƚĞƵƌƐ ĞŶ ƵŶĞ ƐŽŵŵĞ ŽƵ ĞŶ ƵŶĞ Ěŝī ĠƌĞŶĐĞ͘ ĂͿ ϭϰ . ϵ с ďͿ ϵ . ϭϮ с ĐͿ ϵ . ϭϯϬ с ĚͿ ϵϵϵ . Ϯ͕ϴ с ĞͿ Ϯϰϭ . Ϭ͕ϵ с Ϯϰ . ϭϭ с Ϯϳ . ϭϱ с ϰϱ . ϭϬϭ с ϭϬϭ . ϯ͕ϱ с ϱϰϮ . ϭ͕ϭ с ϭϬϭ . Ϯϴ с ϭϬϭ . ϭϵ с ϱϲ . ϯϭ с ϱ͕ϴ . ϵϵ с ϭ͕Ϭϭ . ϴϳ с ϲϱ . ϭϮ с ϵϵ . ϭϮ с ϱϮ . Ϯϳ с ϵ . ϭ͕ϰ с ϰ͕Ϯ . ϭϭϬ с ϭϳ . Ϯϭ с ϱϲ . ϵϵ с ϱϲ . ϭϵ с ϭϭ . ϱ͕ϭ с ϵϬ . ϯϱ͕ϳ с 5 ĂůĐƵůĞ ĞŶ ƵƟ ůŝƐĂŶƚ ůĂ ŵŝƐĞ ĞŶ ĠǀŝĚĞŶĐĞ Ě͛ƵŶ ĨĂĐƚĞƵƌ ĐŽŵŵƵŶ͘ ĂͿ ϭϮ . Ϯ н ϭϮ . ϴ с ďͿ Ϯ͕ϱ . ϭϳ н ϳ͕ϱ . ϭϳ с ĐͿ Ϯ͕ϱ . ϭϲ͕ϰ н Ϯ͕ϱ . ϯ͕ϲ с ϭϳ . ϳ н ϭϳ . ϯ с ϴϰ . ϴ͕ϭ н ϴϰ . ϭ͕ϵ с ϰ͕ϴ . Ϭ͕ϳ н Ϭ͕ϳ . ϱ͕Ϯ с ϱϮ . ϴϵ н ϱϮ . ϭϭ с Ϭ͕ϲ . ϭϱ н Ϭ͕ϰ . ϭϱ с ϭϮ͕ ϱ . ϱ н ϯ . ϭϮ͕ϱ с ϴ . ϭϰ н ϴ . ϴϲ с ϵ͕ϭ . ϱϰ н Ϭ͕ϵ . ϱϰ с ϰϮ͕ϴ . Ϯ͕Ϯϱ н ϱϳ͕Ϯ . Ϯ͕Ϯϱ с ϳϱ . ϭϵ н ϳϱ с Ϯ͕ϯ . ϯ͕ϱ н Ϯ͕ϯ . ϲ͕ϱ с Ϯ͕ϰϲ . Ϯϯ͕ϲ н Ϯϲ͕ϰ . Ϯ͕ϰϲ с ĂůĐƵůĞ ĞŶ ƵƟ ůŝƐĂŶƚ ůĞƐ ƉƌŝŽƌŝƚĠƐ ĚĞƐ ŽƉĠƌĂƟ ŽŶƐ͘ ^ŽƵůŝŐŶĞ ůĞ ĐĂůĐƵů ƉƌŝŽƌŝƚĂŝƌĞ ă ĐŚĂƋƵĞ ĠƚĂƉĞ͘ 6 ĂͿ ϯ н Ϯ . ϱ с ďͿ ϯ . Ϯ н ϳ н ϰ с ĐͿ Ϯ . ϱ . ϳ н ϵ с ĚͿ Ϯ͕ϱ . ϰ ʹ ϱ . Ϭ͕ϭ с ϱ н ϯ . Ϯ ʹ ϰ с ϲ н ϱ . ϰ ʹ ϭ с ϰ н ϱ ͗ Ϯ н ϯ . ϳ с Ϯ͕ϱ . ϰ н ϱ с ϯ н Ϯ . ϳ н ϰ с Ϯ . ϯ н ϱ . ϲ с ϴ ʹ ϯ . Ϯ н ϳ с ϰ н ϱ ͗ Ϭ͕ϭ с ϯ ͗ Ϯ н ϳ . ϰ с Ϯ н ϱ . ϳ н ϱ с ϴ . ϵ н ϰ . Ϯ . ϯ с Ϯ͕ϱ н ϰ . ϱ н Ϭ͕ϭ с ϯ . Ϯ . ϳ ʹ ϰ с Ϯ . ϱ н ϳ . ϱ с ϱ н ϯ . ϲ н ϰ с Ϯ͕ϱ н ϰ . ϱ . Ϭ͕ϭ с ŐͿ ϱ . ;Ϯ . ϱ ʹ ϯͿ с ŚͿ Ϯ͕ϱ н Ϭ͕ϱ . ϴ с ĞͿ ;ϯ н ϮͿ . ϳ с ĨͿ ϱ н Ϯ . ;ϰ н ϯͿ с ;Ϯ н ϱͿ ͗ ;ϳ ʹ ϱͿ с ;ϱ ʹ ϮͿ . ϰ н ϯ с ;Ϯ . ϯ н ϱͿ . ϲ с ;ϰ͕ϱ ʹ ϭ͕ϱͿ . ϰ с ϰ н ϯ ͗ ;Ϯ н ϴͿ с ϰ н ϱ . ;Ϯ н ϯ . ϳͿ с Ϭ͕ϭϮ ͗ ϲ н Ϯ͕Ϯϴ с ;Ϯ н ϯͿ . ;ϱ н ϲͿ с Ϯ . ϱ . ;ϳ ʹ ϱͿ с ;ϰ н ϯͿ . Ϯ н ϴ с ϰ . ϱ . ;Ϯ н ϯ . ϳͿ с ;ϭ͕ϴ н ϯ͕ϮͿ . Ϯ͕ϰ с ;ϰ н ϭͿ . Ϯ н ϯ . ϵ с ϯ . ;Ϯ н ϯ . ϱͿ с Ϯ . Ϯ н ϭ͕Ϯϱ . ϰ с ;ϰ н ϱͿ . Ϯ . ;ϯ н ϳͿ с 7 YƵĂŶĚ Đ͛ĞƐƚ ŶĠĐĞƐƐĂŝƌĞ͕ ƉůĂĐĞ ĚĞƐ ƉĂƌĞŶƚŚğƐĞƐ ƉŽƵƌ ƋƵĞ ůĞ ƌĠƐƵůƚĂƚ ƐŽŝƚ ĐŽƌƌĞĐƚ͘ ĂͿ ϱ н ϰ . ϱ н ϰ с ϴϭ ďͿ Ϯ . ϯ н ϯ . Ϯ с Ϯϰ ĐͿ ϰ . ϰ н ϰ . ϰ с ϴϬ ϱ н ϰ . ϱ н ϰ с ϰϵ Ϯ . ϯ н ϯ . Ϯ с ϭϴ ϰ . ϰ н ϰ . ϰ с ϭϮϴ ϱ н ϰ . ϱ н ϰ с Ϯϵ Ϯ н ϯ . Ϯ ʹ Ϯ с Ϭ ϰ н ϰ . ϰ н ϰ с Ϯϰ ϱ н ϰ . ϱ н ϰ с ϰϭ Ϯ н ϯ . Ϯ ʹ Ϯ с Ϯ ϰ н ϰ . ϰ н ϰ с ϯϲ

Transférer 1

ZĞůŝĞ ĐŚĂƋƵĞ ƐŝƚƵĂƟ ŽŶ ă ů͛ŽƉĠƌĂƟ ŽŶ ƋƵŝ ĐŽŶǀŝĞŶƚ͘ ĂͿ YƵĂƚƌĞ ƉĞƌƐŽŶŶĞƐ ƐŽŶƚ ĂƵ ƌĞƐƚĂƵƌĂŶƚ͘ ůůĞƐ ĐŽŵŵĂŶĚĞŶƚ ƋƵĂƚƌĞ ƉůĂƚƐ ĚƵ ũŽƵƌ ă ϭϰ Φ ƉŝğĐĞ Ğƚ ĚĞƵǆ ďŽƵƚĞŝůůĞƐ Ě͛ĞĂƵ ă ϭ͕ϱϬ Φ ƉŝğĐĞ͘ • ^ĂĐŚĂŶƚ ƋƵĞ ů͛ĂĚĚŝƚŝŽŶ ĞƐƚ ƉĂƌƚĂŐĠĞ ĠƋƵŝƚĂďůĞŵĞŶƚ͕ ƋƵĞůůĞ ƐŽŵŵĞ ƐĞƌĂ ĚĠďŽƵƌƐĠĞ ƉĂƌ ĐŚĂĐƵŶĞ ĚĞ ĐĞƐ ƉĞƌƐŽŶŶĞƐ ͍ ďͿ YƵĂƚƌĞ ĞŶĨĂŶƚƐ ƐĞ ƉĂƌƚĂŐĞŶƚ ůĞƐ ϭϰ Φ ƋƵ͛ŝů ƌĞƐƚĞ ĚĂŶƐ ůĂ ƚŝƌĞůŝƌĞ ĐŽŵŵƵŶĞ͘ /ůƐ ĚĠĐŝĚĞŶƚ ĞŶƐƵŝƚĞ Ě͛ĂĐŚĞƚĞƌ ĐŚĂĐƵŶ ĚĞƵǆ ŐĂƵĨƌĞƐ ă ϭ͕ϱϬ Φ ƉŝğĐĞ͘ YƵĞůůĞ ƐŽŵŵĞ ƌĞƐƚĞͲƚͲŝů ă ĐŚĂƋƵĞ ĞŶĨĂŶƚ ͍ ĐͿ YƵĂƚƌĞ ĂŵŝƐ ƐĞ ƌĞŶĚĞŶƚ ĂƵ ƚŚĠąƚƌĞ͘ >Ğ Ɖƌŝǆ ĚĞ ů͛ĞŶƚƌĠĞ ĞƐƚ ĨŝǆĠ ă ϭϰ Φ͘ ĞƵǆ Ě͛ĞŶƚƌĞ ĞƵǆ ƉŽƐƐğĚĞŶƚ ƵŶ ďŽŶ ĚĞ ƌĠĚƵĐƚŝŽŶ Ě͛ƵŶĞ ǀĂůĞƵƌ ĚĞ ϭ͕ϱϬ Φ͘ YƵĞůůĞ ƐŽŵŵĞ ĞƐƚ ƉĂǇĠĞ ƉĂƌ ů͛ĞŶƐĞŵďůĞ ĚƵ ŐƌŽƵƉĞ ͍

•

• ϰ . ϭϰ ʹ Ϯ . ϭ͕ϱϬ

• ;ϭϰ ʹ Ϯ . ϭ͕ϱϬͿ ͗ ϰ

• ;ϰ . ϭϰ н Ϯ . ϭ͕ϱϬͿ ͗ ϰ

• ϰ . ;ϭϰ ʹ ϭ͕ϱϬͿ • • ϭϰ ͗ ϰ ʹ Ϯ . ϭ͕ϱϬ

EXERCICES COMPLÉMENTAIRES 2

Chapitre 1 Calcul mental

ĐƌŝƐ͕ ĞŶ ƵŶĞ ƐĞƵůĞ ĞǆƉƌĞƐƐŝŽŶ͕ ůĂ ƐƵŝƚĞ ĚĞ ĐĂůĐƵůƐ ƋƵŝ ƚĞ ƉĞƌŵĞƚ ĚĞ ƐŽůƵƟ ŽŶŶĞƌ ůĞƐ ƉƌŽďůğŵĞƐ ĐŝͲĚĞƐƐŽƵƐ͘ ī ĞĐƚƵĞ ĞŶƐƵŝƚĞ ĐĞƐ ĐĂůĐƵůƐ ĞŶ ƵƟ ůŝƐĂŶƚ ůĞƐ ƉƌŝŽƌŝƚĠƐ ĚĞƐ ŽƉĠƌĂƟ ŽŶƐ͘ ĂͿ ǇůĂŶ ĂĐŚğƚĞ ƋƵĂƚƌĞ ĐĂŚŝĞƌƐ Ğƚ ƵŶ ƉŽƌƚĞͲŵŝŶĞ ƉŽƵƌ ůĂ ƐŽŵŵĞ ĚĞ ϲ Φ͘ ^ŝ ƚƵ ƐĂŝƐ ƋƵĞ ůĞ ƉŽƌƚĞͲ ŵŝŶĞ ĐŽƸƚĞ ϭ Φ͕ ĚĠƚĞƌŵŝŶĞ ůĞ Ɖƌŝǆ Ě͛ƵŶ ĐĂŚŝĞƌ͘ ďͿ hŶ ĐĂŵŝŽŶŶĞƵƌ ƉŽƐƐğĚĞ ƵŶ ƐĞŵŝͲƌĞŵŽƌƋƵĞ ĚŽŶƚ ůĂ ŵĂƐƐĞ ă ǀŝĚĞ ĞƐƚ ĚĞ ϱ͕Ϯ ƚŽŶŶĞƐ͘ KŶ ĐŚĂƌŐĞ ĐĞ ƐĞŵŝͲƌĞŵŽƌƋƵĞ ĚĞ ŚƵŝƚ ƉĂůĞƩ ĞƐ ĚĞ ĐĂƌƌĞůĂŐĞƐ ĚĞ ϭϯϱϬ ŬŐ ĐŚĂĐƵŶĞ͘ WŽƵƌ ůŝǀƌĞƌ ƐĂ ŵĂƌĐŚĂŶĚŝƐĞ͕ ůĞ ƐĞŵŝͲƌĞŵŽƌƋƵĞ ĚŽŝƚ ƉĂƐƐĞƌ ƐƵƌ ƵŶ ƉŽŶƚ ĚŽŶƚ ůĂ ĐŚĂƌŐĞ ŵĂǆŝŵĂůĞ ĂƵƚŽƌŝƐĠĞ ĞƐƚ ĚĞ ϭϱ ƚŽŶŶĞƐ͘ WĞƵƚͲŝů ƉĂƐƐĞƌ ƐƵƌ ĐĞ ƉŽŶƚ ĂŝŶƐŝ ĐŚĂƌŐĠ ͍ ĐͿ >ƵĐĂƐ ĂĐŚğƚĞ ƐƵƌ ůĞ ŵĂƌĐŚĠ ϱ ŬŐ ĚĞ ƉŽŵŵĞƐ ĚĞ ƚĞƌƌĞ ă ϭ͕ϯϬ Φ ůĞ ŬŐ͕ Ϯ ŬŐ ĚĞ ƚŽŵĂƚĞƐ ă ϭ͕ϵϬ Φ ůĞ ŬŐ͕ ϭ ƌĂǀŝĞƌ ĚĞ ϱϬϬ Ő ĚĞ ĨƌĂŝƐĞƐ ă ϲ͕ϳϬ Φ ůĞ ŬŐ Ğƚ Ϯ ƐĂůĂĚĞƐ ă Ϭ͕ϳϱ Φ ůĂ ƉŝğĐĞ͘ /ů ƉĂŝĞ ƐĞƐ ĂĐŚĂƚƐ ĂǀĞĐ ƵŶ ďŝůůĞƚ ĚĞ ϮϬ Φ͘ YƵĞůůĞ ƐŽŵŵĞ ůĂ ǀĞŶĚĞƵƐĞ ĚŽŝƚͲĞůůĞ ůƵŝ ƌĞŶĚƌĞ ͍ ĚͿ hŶĞ ĐůĂƐƐĞ ĚĞ Ϯe ĂŶŶĠĞ ƉƌŝŵĂŝƌĞ͕ ĐŽŵƉŽƐĠĞ ĚĞ Ϯϲ ĠůğǀĞƐ͕ ƐŽƵŚĂŝƚĞ ƐĞ ƌĞŶĚƌĞ ĚĂŶƐ ƵŶ ƉĂƌĐ ĂŶŝŵĂůŝĞƌ͘ >Ğ Ɖƌŝǆ ĚĞƐ ĞŶƚƌĠĞƐ ĞƐƚ Į ǆĠ ă ϭϱ Φ ƉĂƌ ĞŶĨĂŶƚ Ğƚ ϮϮ Φ ƉĂƌ ĂĚƵůƚĞ͘ ^ĂĐŚĂŶƚ ƋƵĞ ůĂ ƐŽŵŵĞ ƚŽƚĂůĞ ĚĠďŽƵƌƐĠĞ ƉŽƵƌ ĐĞƩ Ğ ǀŝƐŝƚĞ ĞƐƚ ĚĞ ϰϳϴ Φ͕ ĚĠƚĞƌŵŝŶĞ ůĞ ŶŽŵďƌĞ ĚĞ ƉĞƌƐŽŶŶĞƐ ĂĚƵůƚĞƐ ĂĐĐŽŵƉĂŐŶĂŶƚ ĐĞƐ ĞŶĨĂŶƚƐ͘ ĞͿ ĂŶƐ ƵŶĞ ƐĂůůĞ ĚĞ ƚŚĠąƚƌĞ͕ ŝů Ǉ Ă ϭϰ ƌĂŶŐĠĞƐ ĚĞ Ϯϳ ĨĂƵƚĞƵŝůƐ ĂƵ ďĂůĐŽŶ Ğƚ Ϯϲ ƌĂŶŐĠĞƐ ĚĞ Ϯϳ ĨĂƵƚĞƵŝůƐ ă ů͛ŽƌĐŚĞƐƚƌĞ͘ ŽŵďŝĞŶ Ǉ ĂͲƚͲŝů ĚĞ ƉůĂĐĞƐ ĂƐƐŝƐĞƐ ĚĂŶƐ ĐĞ ƚŚĠąƚƌĞ ͍

17 m

ĨͿ ĠƚĞƌŵŝŶĞ ů͛ĂŝƌĞ ĚĞ ů͛ĂůůĠĞ ƌĞƉƌĠƐĞŶƚĠĞ ĐŝͲĐŽŶƚƌĞ ƐĂĐŚĂŶƚ ƋƵĞ ƐĂ ůĂƌŐĞƵƌ ǀĂƵƚ ϴ ŵ͘

30 m

33 m

ŽŵƉůğƚĞ͕ ĚĞ ŵĂŶŝğƌĞ ůŽŐŝƋƵĞ͕ ůĞƐ ƐƵŝƚĞƐ ĚĞ ŶŽŵďƌĞƐ ĐŝͲĚĞƐƐŽƵƐ͘ ĂͿ

ϭϬ

ďͿ

ĐͿ

ϮϬ

Ϯϭ

Ϯϰ

Ϯϵ

ĚͿ

ϰϰ

ϯϰ

Ϯϲ

ϯϬ

ĞͿ

ϭϱ

ϯϭ

ϲϯ

ĨͿ

ϭϮ

ϭϭ

ϯϯ

ϯϮ

ŐͿ

ϳϰ

ϯϳ

ϯϰ

ϭϳ

ϮϮ

Ϯϴ

ϯϰ

ϴϭ

Ϯϰϯ

ϯϲ ϭϰ

DŽƚŝĨ ŶΣϮ

DŽƚŝĨ ŶΣϯ

ŽŵďŝĞŶ ĚĞ ĐĂƌƌĠƐ ƚƌŽƵǀĞƌĂͲƚͲŽŶ ĚĂŶƐ ůĞƐ ŵŽƟ ĨƐ ŶΣ ϱ͕ ŶΣ ϭϬ Ğƚ ŶΣ ϰϬ ͍

ϭϮϳ

sŽŝĐŝ ƵŶĞ ƐƵŝƚĞ ĚĞ ŵŽƟ ĨƐ ĐŽŶƐƚƌƵŝƚƐ ƐĞůŽŶ ƵŶ ŵġŵĞ ƉƌŝŶĐŝƉĞ͘

DŽƚŝĨ ŶΣϭ

20 m

DŽƚŝĨ ŶΣϰ

Chapitre 2 Diviseurs et multiples Tableaux de compétences Libre Nombres naturels 1

:ƵƐƟ Į Ğƌ ůĞ ĐŚŽŝǆ Ě͛ƵŶĞ ĚĠĐŽŵƉŽƐŝƟ ŽŶ Ě͛ƵŶ ŶŽŵďƌĞ ƉŽƵƌ ǀĠƌŝĮ Ğƌ ƵŶĞ ĚŝǀŝƐŝďŝůŝƚĠ͘

:ƵƐƟ Į Ğƌ ƵŶ ĐĂƌĂĐƚğƌĞ ĚĞ ĚŝǀŝƐŝďŝůŝƚĠ ĞŶ ĐŝƚĂŶƚ ůĞƐ ƉƌŽƉƌŝĠƚĠƐ ƵƟ ůŝƐĠĞƐ͘

:ƵƐƟ Į Ğƌ ƵŶĞ ƉƌŽƉƌŝĠƚĠ ĚĞ ĚŝǀŝƐŝďŝůŝƚĠ ĞŶ ĠǀŽƋƵĂŶƚ ƵŶĞ ƌĞƉƌĠƐĞŶƚĂƟ ŽŶ ĚƵ ŶŽŵďƌĞ͘

ĠĐŽŵƉŽƐĞƌ ƵŶ ŶŽŵďƌĞ ƉŽƵƌ ǀĠƌŝĮ Ğƌ ƵŶĞ ĚŝǀŝƐŝďŝůŝƚĠ͘

dƌŽƵǀĞƌ ƚŽƵƐ ůĞƐ ĚŝǀŝƐĞƵƌƐ Ě͛ƵŶ ŶŽŵďƌĞ ă ƉĂƌƟ ƌ ĚĞ ƐĂ ĚĠĐŽŵƉŽƐŝƟ ŽŶ ĞŶ ĨĂĐƚĞƵƌƐ ƉƌĞŵŝĞƌƐ͘

ZĞƚƌŽƵǀĞƌ ƵŶ ŶŽŵďƌĞ ĚĠĐŽŵƉŽƐĠ ĞŶ ĨĂĐƚĞƵƌƐ ƉƌĞŵŝĞƌƐ͘

EŽŵďƌĞƐ ƌĂƟ ŽŶŶĞůƐ 16

sĠƌŝĮ Ğƌ ĂǀĞĐ ƵŶĞ ĐĂůĐƵůĂƚƌŝĐĞ ůĂ ƉůĂƵƐŝďŝůŝƚĠ Ě͛ƵŶ ƌĠƐƵůƚĂƚ͘

ZĞƐƉĞĐƚĞƌ ůĞƐ ƉƌŝŽƌŝƚĠƐ ĚĞƐ ŽƉĠƌĂƟ ŽŶƐ ƉŽƵƌ Ğī ĞĐƚƵĞƌ ĚĞƐ ŽƉĠƌĂƟ ŽŶƐ ĚĂŶƐ ĚĞƐ ƐŝƚƵĂƟ ŽŶƐ ǀĂƌŝĠĞƐ͘

ƐƟ ŵĞƌ ů͛ŽƌĚƌĞ ĚĞ ŐƌĂŶĚĞƵƌ Ě͛ƵŶ ƌĠƐƵůƚĂƚ ĂǀĂŶƚ Ě͛ŽƉĠƌĞƌ͘

ī ĞĐƚƵĞƌ ƵŶ ĐĂůĐƵů ĐŽŵƉŽƌƚĂŶƚ ƉůƵƐŝĞƵƌƐ ĠƚĂƉĞƐ ă ů͛ĂŝĚĞ Ě͛ƵŶĞ ĐĂůĐƵůĂƚƌŝĐĞ͘

ĂůĐƵů ůŝƩ ĠƌĂů Ğƚ ĠƋƵĂƟ ŽŶƐ 21

ƐƐŽĐŝĞƌ ƵŶĞ ĞǆƉƌĞƐƐŝŽŶ ůŝƩ ĠƌĂůĞ ă ƵŶĞ ĨĂŵŝůůĞ ĚĞ ŶŽŵďƌĞƐ͘

ĠŶŽŵďƌĞƌ ƉĂƌ ƵŶ ĐĂůĐƵů Ğƚ ůĞ ĐĂƐ ĠĐŚĠĂŶƚ ƉĂƌ ƵŶĞ ĨŽƌŵƵůĞ͘

ůĂďŽƌĞƌ ƵŶĞ ĨŽƌŵƵůĞ ƋƵŝ ƚƌĂĚƵŝƚ ůĂ ƌĠŐƵůĂƌŝƚĠ ĚĂŶƐ ĚĞƐ ƐƵŝƚĞƐ ĚĞ ŵŽƟ ĨƐ ;ŽƵ ĚĞ ŶŽŵďƌĞƐͿ͘ 25

ACTIVITÉS

Chapitre 2 Diviseurs et multiples

ŽŶƐƚƌƵŝƌĞ ĚĞƐ ĞǆƉƌĞƐƐŝŽŶƐ ůŝƩ ĠƌĂůĞƐ Žƶ ůĂ ůĞƩ ƌĞ Ă ůĞ ƐƚĂƚƵƚ Ě͛ŝŶĚĠƚĞƌŵŝŶĠĞ͕ ĚĞ ǀĂƌŝĂďůĞ ŽƵ Ě͛ŝŶĐŽŶŶƵĞ͘

Kĸ ĐŝĞů Dénombrer 1

ZĠƐŽƵĚƌĞ ĚĞƐ ƉƌŽďůğŵĞƐ ĚĞ ĚĠŶŽŵďƌĞŵĞŶƚ ĚĂŶƐ ĚĞƐ ĐŽŶƚĞǆƚĞƐ ŶƵŵĠƌŝƋƵĞƐ Ğƚ ŐĠŽŵĠƚƌŝƋƵĞƐ͘

^ƚƌƵĐƚƵƌĞƌ ůĞƐ ŶŽŵďƌĞƐ ŶĂƚƵƌĞůƐ ă ů͛ĂŝĚĞ ĚĞ ůĂ ƌĞůĂƟ ŽŶ ĚĞ ĚŝǀŝƐŝďŝůŝƚĠ 18

hƟ ůŝƐĞƌ ƵŶĞ ĞǆƉƌĞƐƐŝŽŶ ƚĞůůĞ ƋƵĞ Ă с ď . Đ ƉŽƵƌ ŝŶƚƌŽĚƵŝƌĞ ůĞƐ ŶŽƟ ŽŶƐ ͗ ĚŝǀŝƐĞƵƌ ĚĞ͕ ŵƵůƟ ƉůĞ ĚĞ͕ ĚŝǀŝƐŝďůĞ ƉĂƌ͘

ĠƚĞƌŵŝŶĞƌ ů͛ĞŶƐĞŵďůĞ ĚĞƐ ĚŝǀŝƐĞƵƌƐ Ğƚ ů͛ĞŶƐĞŵďůĞ ĚĞƐ ŵƵůƟ ƉůĞƐ Ě͛ƵŶ ŶŽŵďƌĞ͘

ZĞĐŚĞƌĐŚĞƌ ůĞƐ ĚŝǀŝƐĞƵƌƐ Ğƚ ůĞƐ ŵƵůƟ ƉůĞƐ ĐŽŵŵƵŶƐ Ě͛ƵŶ ŶŽŵďƌĞ͘

hƟ ůŝƐĞƌ ůĞƐ ĐĂƌĂĐƚğƌĞƐ ĚĞ ĚŝǀŝƐŝďŝůŝƚĠ ƉĂƌ Ϯ͕ ϱ͕ ϰ͕ ϴ͕ Ϯϱ͕ ϭϮϱ͕ ϯ Ğƚ ϵ͘

ǆƉůŽŝƚĞƌ ůĞƐ ĚĞƵǆ ƉƌŽƉƌŝĠƚĠƐ ƐƵŝǀĂŶƚĞƐ ͗ ƚŽƵƚ ŶŽŵďƌĞ ƋƵŝ ĚŝǀŝƐĞ ĚĞƵǆ ĂƵƚƌĞƐ ŶŽŵďƌĞƐ ĚŝǀŝƐĞ ůĞƵƌ ƐŽŵŵĞ Ğƚ ůĞƵƌ Ěŝī ĠƌĞŶĐĞ͖ ƚŽƵƚ ŶŽŵďƌĞ ƋƵŝ ĚŝǀŝƐĞ ƵŶ ĂƵƚƌĞ ŶŽŵďƌĞ ĚŝǀŝƐĞ ĂƵƐƐŝ ƐĞƐ ŵƵůƟ ƉůĞƐ͘

ZĞĐŽŶŶĂŠƚƌĞ ůĞƐ ŶŽŵďƌĞƐ ƉƌĞŵŝĞƌƐ ŝŶĨĠƌŝĞƵƌƐ ă ϭϬϬ͘

&ĂĐƚŽƌŝƐĞƌ ƵŶ ŶŽŵďƌĞ ŶĂƚƵƌĞů͘

ī ĞĐƚƵĞƌ ĚĞƐ ŽƉĠƌĂƟ ŽŶƐ 25

ī ĞĐƚƵĞƌ ƐĞůŽŶ ƵŶĞ ŵĠƚŚŽĚĞ ĂƉƉƌŽƉƌŝĠĞ ;ĐĂůĐƵů ŵĞŶƚĂů͕ ĐĂůĐƵů ĠĐƌŝƚ͕ ĐĂůĐƵůĂƚƌŝĐĞͿ ĚĞƐ ĂĚĚŝƟ ŽŶƐ͕ ĚĞƐ ƐŽƵƐƚƌĂĐƟ ŽŶƐ͕ ĚĞƐ ŵƵůƟ ƉůŝĐĂƟ ŽŶƐ Ğƚ ĚĞƐ ĚŝǀŝƐŝŽŶƐ ĚĞ ŶŽŵďƌĞƐ ŶĂƚƵƌĞůƐ͘

ĂůĐƵůĞƌ ĚĞƐ ƉƵŝƐƐĂŶĐĞƐ ă ĞǆƉŽƐĂŶƚƐ ŶĂƚƵƌĞůƐ͘

ƐƟ ŵĞƌ ů͛ŽƌĚƌĞ ĚĞ ŐƌĂŶĚĞƵƌ Ğƚ ǀĠƌŝĮ Ğƌ ă ůĂ ĐĂůĐƵůĂƚƌŝĐĞ ůĂ ƉůĂƵƐŝďŝůŝƚĠ Ě͛ƵŶ ƌĠƐƵůƚĂƚ͘

ĂůĐƵůĞƌ ƵŶĞ ĞǆƉƌĞƐƐŝŽŶ ĐŽŵƉƌĞŶĂŶƚ ĂƵ ƉůƵƐ ƚƌŽŝƐ ŽƉĠƌĂƟ ŽŶƐ Ěŝī ĠƌĞŶƚĞƐ͘

ǆƉƌĞƐƐŝŽŶƐ ůŝƩ ĠƌĂůĞƐ 42

ĂŶƐ ƵŶĞ ĨŽƌŵƵůĞ͕ ƌĞŵƉůĂĐĞƌ ĚĞƐ ǀĂƌŝĂďůĞƐ ƉĂƌ ĚĞƐ ŶŽŵďƌĞƐ ĚŽŶŶĠƐ ĂĮ Ŷ ĚĞ ĚĠƚĞƌŵŝŶĞƌ ůĂ ǀĂůĞƵƌ ĚĞ ů͛ŝŶĐŽŶŶƵĞ͘

Chapitre 2 Diviseurs et multiples

ACTIVITÉS

ĐƚŝǀŝƚĠ ϭ ŝǀŝƐĞƵƌƐ ĚΖƵŶ ŶŽŵďƌĞ 1 ĂͿ ĞƐƐŝŶĞ ƚŽƵƐ ůĞƐ ƌĞĐƚĂŶŐůĞƐ ĚĞ ĚŝŵĞŶƐŝŽŶƐ ĚŝĨĨĠƌĞŶƚĞƐ ƋƵĞ ƚƵ ƉĞƵǆ ĨŽƌŵĞƌ ĂǀĞĐ ƵŶ ŶŽŵďƌĞ ĚŽŶŶĠ ĚĞ ƉĞƚŝƚƐ ĐĂƌƌĠƐ ŝĚĞŶƚŝƋƵĞƐ ă ĐĞƵǆ ĚƵ ƋƵĂĚƌŝůůĂŐĞ͘

;ϭͿ dƵ ĚŽŝƐ ƵƚŝůŝƐĞƌ Ϯϰ ƉĞƚŝƚƐ ĐĂƌƌĠƐ ŝĚĞŶƚŝƋƵĞƐ͘

ŽŵďŝĞŶ ĚĞ ƌĞĐƚĂŶŐůĞƐ ĚĞ ĚŝŵĞŶƐŝŽŶƐ Ěŝī ĠƌĞŶƚĞƐ ĂƐͲƚƵ ĚĞƐƐŝŶĠƐ ͍ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ŽŶŶĞ ůĞƵƌƐ ĚŝŵĞŶƐŝŽŶƐ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ŽŵƉůğƚĞ ůĞƐ ƉŚƌĂƐĞƐ ĐŝͲĚĞƐƐŽƵƐ͘ >ĞƐ ŶŽŵďƌĞƐ ƋƵŝ ĚŽŶŶĞŶƚ ůĞƐ ĚŝŵĞŶƐŝŽŶƐ ĚĞƐ ƌĞĐƚĂŶŐůĞƐ ƐŽŶƚ ůĞƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ĚĞ Ϯϰ͘ Ϯϰ ƉŽƐƐğĚĞ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ĚŝǀŝƐĞƵƌƐ͘ ;ϮͿ dƵ ĚŽŝƐ ƵƟ ůŝƐĞƌ ϭϲ ƉĞƟ ƚƐ ĐĂƌƌĠƐ ŝĚĞŶƟ ƋƵĞƐ͘

ŽŵƉůğƚĞ ůĞƐ ƉŚƌĂƐĞƐ ĐŝͲĚĞƐƐŽƵƐ͘ >ĞƐ ŶŽŵďƌĞƐ ƋƵŝ ĚŽŶŶĞŶƚ ůĞƐ ĚŝŵĞŶƐŝŽŶƐ ĚĞƐ ƌĞĐƚĂŶŐůĞƐ ƐŽŶƚ ůĞƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ĚĞ ϭϲ͘ ϭϲ ƉŽƐƐğĚĞ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ĚŝǀŝƐĞƵƌƐ͘

ACTIVITÉS

Chapitre 2 Diviseurs et multiples

;ϯͿ dƵ ĚŽŝƐ ƵƟ ůŝƐĞƌ ϳ ƉĞƟ ƚƐ ĐĂƌƌĠƐ ŝĚĞŶƟ ƋƵĞƐ͘

ŽŵƉůğƚĞ ůĞƐ ƉŚƌĂƐĞƐ ĐŝͲĚĞƐƐŽƵƐ͘ >ĞƐ ŶŽŵďƌĞƐ ƋƵŝ ĚŽŶŶĞŶƚ ůĞƐ ĚŝŵĞŶƐŝŽŶƐ ĚĞ ĐĞ ƌĞĐƚĂŶŐůĞ ƐŽŶƚ ůĞƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ĚĞ ϳ͘ ϳ ƉŽƐƐğĚĞ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ĚŝǀŝƐĞƵƌƐ͘ ďͿ ŽŵƉůğƚĞ ůĞƐ ƉŚƌĂƐĞƐ ĐŝͲĚĞƐƐŽƵƐ͘ >Ğ ŶŽŵďƌĞ ϭϲ ƉĞƵƚ ġƚƌĞ ƌĞƉƌĠƐĞŶƚĠ ƉĂƌ ƵŶ ƌĞĐƚĂŶŐůĞ ƉĂƌƟ ĐƵůŝĞƌ͘ Ŷ Ğī Ğƚ͕ ϭϲ ƉĞƵƚ ġƚƌĞ ƌĞƉƌĠƐĞŶƚĠ ƉĂƌ ƵŶ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ĚĞ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ƐƵƌ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ Ğ ŶŽŵďƌĞ ĞƐƚ Ěŝƚ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ /ů ƉĞƵƚ Ɛ͛ĠĐƌŝƌĞ ƐŽƵƐ ůĂ ĨŽƌŵĞ Ě͛ƵŶ ƉƌŽĚƵŝƚ ĚĞ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ĨĂĐƚĞƵƌƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ >Ğ ŶŽŵďƌĞ ϳ Ŷ͛ĞƐƚ ƌĞƉƌĠƐĞŶƚĠ ƋƵĞ ƉĂƌ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ Ğ ŶŽŵďƌĞ ĞƐƚ Ěŝƚ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ hŶ ŶŽŵďƌĞ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ŶĞ ƉŽƐƐğĚĞ ƋƵĞ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ĚŝǀŝƐĞƵƌƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

2 ĠƚĞƌŵŝŶĞ ůĞƐ ĚŝŵĞŶƐŝŽŶƐ ĚĞ ƚŽƵƐ ůĞƐ ƌĞĐƚĂŶŐůĞƐ ĚŝĨĨĠƌĞŶƚƐ ƋƵĞ ƚƵ ƉĞƵǆ ĨŽƌŵĞƌ ĂǀĞĐ ϮϬ͕ ϭϯ͕ Ϯϱ͕ ϯϬ͕ ϯϲ͕ ϰϬ Ğƚ ϲϬ ƉĞƚŝƚƐ ĐĂƌƌĠƐ ŝĚĞŶƚŝƋƵĞƐ͘ ĐƌŝƐ ĐĞƐ ĚŝŵĞŶƐŝŽŶƐ ĐŝͲĚĞƐƐŽƵƐ͘ ǀĞĐ ϮϬ ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ǀĞĐ ϭϯ ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ǀĞĐ Ϯϱ ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ǀĞĐ ϯϬ ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ǀĞĐ ϯϲ ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ǀĞĐ ϰϬ ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ǀĞĐ ϲϬ ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ 3 ĂͿ ^ŝ ů͛ĞŶƐĞŵďůĞ ĚĞƐ ĚŝǀŝƐĞƵƌƐ ŶĂƚƵƌĞůƐ Ě͛ƵŶ ŶŽŵďƌĞ ͨ Ŷ ͩ ƐĞ ŶŽƚĞ ͨ Ěŝǀ Ŷ ͕ͩ ĠĐƌŝƐ ƚŽƵƐ ůĞƐ ĠůĠŵĞŶƚƐ ĚĞƐ ĞŶƐĞŵďůĞƐ ƐƵŝǀĂŶƚƐ͘ Ěŝǀ ϭ с ΂ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ Ěŝǀ ϵ с ΂ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ Ěŝǀ ϭϭ с ΂ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ 28

p.34 A3

Chapitre 2 Diviseurs et multiples

ACTIVITÉS

Ěŝǀ ϭϮ с ΂ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ Ěŝǀ Ϯϵ с ΂ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ Ěŝǀ ϰϱ с ΂ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ Ěŝǀ ϱϭ с ΂ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ Ěŝǀ ϱϲ с ΂ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

p.34 ϭͳϮ

Ěŝǀ ϭϬϬ с ΂ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ďͿ ŝƚĞ ůĞƐ ŶŽŵďƌĞƐ ĐĂƌƌĠƐ ƌĞŶĐŽŶƚƌĠƐ ĚĂŶƐ ů͛ĞǆĞƌĐŝĐĞ ϯĂͿ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ŝƚĞ ƚŽƵƐ ůĞƐ ŶŽŵďƌĞƐ ĐĂƌƌĠƐ ŝŶĨĠƌŝĞƵƌƐ ă ϭϬϬ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ĐͿ ŝƚĞ ůĞƐ ŶŽŵďƌĞƐ ƉƌĞŵŝĞƌƐ ƌĞŶĐŽŶƚƌĠƐ ĚĂŶƐ ů͛ĞǆĞƌĐŝĐĞ ϯĂͿ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ŝƚĞ ƚŽƵƐ ůĞƐ ŶŽŵďƌĞƐ ƉƌĞŵŝĞƌƐ ŝŶĨĠƌŝĞƵƌƐ ă ϮϬ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

4 ĂͿ KŶ ǀĞƵƚ ƉĂǀĞƌ ƵŶ ƌĞĐƚĂŶŐůĞ ĚĞ Ϯϴ ŵŵ ƐƵƌ ϰϮ ŵŵ ĂǀĞĐ ĚĞƐ ĐĂƌƌĠƐ ĞŶƟ ĞƌƐ͕ ƚŽƵƐ ŝĚĞŶƟ ƋƵĞƐ͕ ĚŽŶƚ ůĞ ĐƀƚĠ ĞƐƚ ŵĞƐƵƌĠ ƉĂƌ ƵŶ ŶŽŵďƌĞ ĞŶƟ Ğƌ ĚĞ ŵŵ͘ ĠƚĞƌŵŝŶĞ ůĞƐ ĚŝŵĞŶƐŝŽŶƐ ƉŽƐƐŝďůĞƐ ƉŽƵƌ ĐĞƐ ĐĂƌƌĠƐ Ğƚ͕ ĚĂŶƐ ĐŚĂƋƵĞ ĐĂƐ͕ ĐĂůĐƵůĞ ůĞ ŶŽŵďƌĞ ƚŽƚĂů ĚĞ ĐĞƵǆͲĐŝ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ďͿ ZĞƉƌĠƐĞŶƚĞ ůĂ ƐŽůƵƟ ŽŶ ĂǀĞĐ ůĞƐ ĐĂƌƌĠƐ ůĞƐ ƉůƵƐ ŐƌĂŶĚƐ ƉŽƐƐŝďůĞƐ͘

ĐͿ WŽƵƌ ƚƌŽƵǀĞƌ͕ ĚĞ ŵĂŶŝğƌĞ ŵĠƚŚŽĚŝƋƵĞ͕ ƚŽƵƚĞƐ ůĞƐ ĚŝŵĞŶƐŝŽŶƐ ƉŽƐƐŝďůĞƐ ƉŽƵƌ ĐĞƐ ĐĂƌƌĠƐ͕ ĠĐƌŝƐ ƚŽƵƐ ůĞƐ ĚŝǀŝƐĞƵƌƐ ĚĞ Ϯϴ Ğƚ ĚĞ ϰϮ͘ Ěŝǀ Ϯϴ с ΂ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ Ěŝǀ ϰϮ с ΂ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ŽŵƉůğƚĞ ůĞƐ ƉŚƌĂƐĞƐ ĐŝͲĚĞƐƐŽƵƐ͘ >ĞƐ ĚŝŵĞŶƐŝŽŶƐ ƉŽƐƐŝďůĞƐ ƉŽƵƌ ĐĞƐ ĐĂƌƌĠƐ ƐŽŶƚ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ĞƐ ŶŽŵďƌĞƐ ƐŽŶƚ ůĞƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ĚĞ Ϯϴ Ğƚ ĚĞ ϰϮ͘ p.35 A4

>Ğ ƉůƵƐ ŐƌĂŶĚ ĐĂƌƌĠ ƵƟ ůŝƐĂďůĞ Ă ĚŽŶĐ ƵŶ ĐƀƚĠ ĚĞ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ŵŵ ͖ ĐĞ ŶŽŵďƌĞ ĞƐƚ ůĞ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ĚĞ Ϯϴ Ğƚ ĚĞ ϰϮ͘ 29

ACTIVITÉS 5

Chapitre 2 Diviseurs et multiples

ĂͿ YƵĞůƐ ƐŽŶƚ ůĞƐ ĚŝǀŝƐĞƵƌƐ ĐŽŵŵƵŶƐ ĚĞ ϰϴ Ğƚ ĚĞ ϴϬ ͍ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

YƵĞů ĞƐƚ ůĞ ƉůƵƐ ŐƌĂŶĚ ĚŝǀŝƐĞƵƌ ĐŽŵŵƵŶ ĚĞ ϰϴ Ğƚ ĚĞ ϴϬ ͍ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ďͿ ŝǀŝƐĞ ůĞ ŶƵŵĠƌĂƚĞƵƌ Ğƚ ůĞ ĚĠŶŽŵŝŶĂƚĞƵƌ ĚĞ ůĂ 48 ĨƌĂĐƟ ŽŶ ƉĂƌ ůĞƵƌ ƉůƵƐ ŐƌĂŶĚ ĐŽŵŵƵŶ ĚŝǀŝƐĞƵƌ͘ 80 ŽŵƉůğƚĞ ůĂ ƉŚƌĂƐĞ ƐƵŝǀĂŶƚĞ͘

48 с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ 80

>Ă ĨƌĂĐƟ ŽŶ ŽďƚĞŶƵĞ ĞƐƚ ĚŝƚĞ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ĐͿ ZĞŶĚƐ ŝƌƌĠĚƵĐƟ ďůĞƐ ůĞƐ ĨƌĂĐƟ ŽŶƐ ĐŝͲĚĞƐƐŽƵƐ͘ 6 с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ 8

5 с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ 10

12 с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ 6

120 с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ 180

12 с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ 18

2 с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ 3

28 с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ 35

200 с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ 320

9 с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ 6

75 с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ 50

33 с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ 55

144 с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ 108

p.35 A5

ĐƚŝǀŝƚĠ Ϯ DƵůƚŝƉůĞƐ ĚΖƵŶ ŶŽŵďƌĞ 1 ĂͿ ů͛ŽĐĐĂƐŝŽŶ ĚĞ ůĂ ƌĞŶƚƌĠĞ ƐĐŽůĂŝƌĞ͕ ƵŶĞ ƐŽŝƌĠĞ ĚĞ ũĞƵǆ Ğƚ Ě͛ĂŶŝŵĂƟ ŽŶƐ ĞƐƚ ŽƌŐĂŶŝƐĠĞ ĂƵ ƐĞŝŶ ĚĞ ŶŽƚƌĞ ĠĐŽůĞ͘ >͛ĞŶƚƌĠĞ ĞƐƚ ŐƌĂƚƵŝƚĞ͕ ůĞƐ ďŽŝƐƐŽŶƐ ;ĞĂƵǆ͕ ƐŽĚĂƐ͕ ũƵƐ ĚĞ ĨƌƵŝƚƐͿ ƐŽŶƚ Žī ĞƌƚĞƐ͕ Ğƚ ĚĞƐ ƉĂƌƚƐ ĚĞ ƉŝǌǌĂ ƐŽŶƚ ǀĞŶĚƵĞƐ ĂƵ Ɖƌŝǆ ĚĞ ϯ Φ ů͛ƵŶŝƚĠ͘ ŵŝůǇ ƐĞ ƌĞŶĚ ă ĐĞƩ Ğ ĨġƚĞ ĂĐĐŽŵƉĂŐŶĠĞ ĚĞ ĚĞƵǆ ĚĞ ƐĞƐ ĂŵŝĞƐ͘ ^ĂĐŚĂŶƚ ƋƵ͛ĞůůĞƐ ĐŽŶƐŽŵŵĞŶƚ͕ ĞŶƐĞŵďůĞ͕ Ɛŝǆ ƉĂƌƚƐ ĚĞ ƉŝǌǌĂ͕ ĐĂůĐƵůĞ ůĂ ƐŽŵŵĞ ĚĠƉĞŶƐĠĞ ƉĂƌ ůĞ ŐƌŽƵƉĞ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Ce 1er septembre dès 18h00

Jeux et Animations Entrée gratuite Boissons (eaux, sodas, jus de fruits) offertes Part de pizza : 3€/pièce

ďͿ ŽŵƉůğƚĞ ůĞ ƚĂďůĞĂƵ ĐŝͲĚĞƐƐŽƵƐ͘ EŽŵďƌĞ ĚĞ ƉĂƌƚƐ ĚĞ ƉŝǌǌĂ ĂĐŚĞƚĠĞƐ

^ŽŵŵĞ ĚĠƉĞŶƐĠĞ ;ĞŶ ΦͿ ŽŵƉůğƚĞ ůĂ ƉŚƌĂƐĞ ĐŝͲĚĞƐƐŽƵƐ͘ >ĞƐ ŶŽŵďƌĞƐ ƚƌŽƵǀĠƐ ƐŽŶƚ ĚĞƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ĚĞ ϯ͘ 30

ACTIVITÉS

Chapitre 2 Diviseurs et multiples

^ŝ ůΖĞŶƐĞŵďůĞ ĚĞƐ ŵƵůƟ ƉůĞƐ ŶĂƚƵƌĞůƐ ĚΖƵŶ ŶŽŵďƌĞ ͨരĂരͩ ƐĞ ŶŽƚĞ ͨരĂNര͕ͩ ĠĐƌŝƐ ůĞƐ ϭϮ ƉƌĞŵŝĞƌƐ ĠůĠŵĞŶƚƐ ĚĞƐ ĞŶƐĞŵďůĞƐ ĐŝͲĚĞƐƐŽƵƐ͘ ϲN с ΂ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϮϬN с ΂ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

p.35 ϭͳϮ

ϭϭN с ΂ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ 3 ZĞƚƌŽƵǀĞ ƚŽŶ ĐŚĞŵŝŶ ĚĂŶƐ ůĞ ůĂďǇƌŝŶƚŚĞ ĞŶ ƚĞ ĚĠƉůĂĕĂŶƚ ŚŽƌŝǌŽŶƚĂůĞŵĞŶƚ ŽƵ ǀĞƌƟ ĐĂůĞŵĞŶƚ ƵŶŝƋƵĞŵĞŶƚ ƐƵƌ ĚĞƐ ĐĂƐĞƐ͘͘͘ ŵƵůƟ ƉůĞƐ ĚĞ ϳ͘

ϭϰ Ϯϭ ϯϮ ϲϰ Ϯϰ

ŵƵůƟ ƉůĞƐ ĚĞ ϵ͘

ϭϴ ϰϱ

ϲϰ Ϯϰ

ŵƵůƟ ƉůĞƐ ĚĞ ϴ͘

Ϯϰ ϰϱ ϭϴ ϭϬϬ ϱϮ

Ϯϱ ϰϮ ϭϳ ϱϰ ϴϰ

Ϯϱ ϰϬ Ϯϳ ϱϮ ϴϰ

ϯϮ ϰϮ ϱϲ ϲϰ ϳϮ

ϲϯ ϰϵ ϲϳ ϱϳ ϳϮ

ϯϲ ϱϰ ϲϯ ϱϳ ϳϳ

ϰϬ ϱϰ ϭϲ ϱϴ ϴϴ

ϳϬ ϰϱ ϳϳ ϯϱ ϱϲ

Ϭ ϭϴϮ ϳϬ ϯϱ ϱϲ

ϵϬ ϴϭ ϭϬϴ ϳϮ ϭϴϬ

ϲϬ ϮϮ ϭϲϰ ϳϬ ϴϬ

Ϯϴ ϭϰϬ Ϯϳ ϮϭϬ

ϰϴ ϯϲ ϭϮϬ

4 ĂͿ :ĞĂŶŶĞ Ğƚ EŽĂŚ ƐĞ ƐŽŶƚ ƌĞƚƌŽƵǀĠƐ ă ůĂ ƉŝƐĐŝŶĞ ĐĞ ŵĞƌĐƌĞĚŝ ĂĮ Ŷ Ě͛Ǉ ƉƌĠƉĂƌĞƌ ůĞ ĐŚĂŵƉŝŽŶŶĂƚ ŝŶƚĞƌƐĐŽůĂŝƌĞ͘ :ĞĂŶŶĞ ĚĠĐŝĚĞ ĚĞ ƌĞǀĞŶŝƌ ă ůĂ ƉŝƐĐŝŶĞ ƚŽƵƐ ůĞƐ ϰ ũŽƵƌƐ͘ EŽĂŚ͕ ƋƵĂŶƚ ă ůƵŝ͕ ŶĞ ƉŽƵƌƌĂ Ɛ͛Ǉ ƌĞŶĚƌĞ ƋƵĞ ƚŽƵƐ ůĞƐ ϭϬ ũŽƵƌƐ͘ Ƶ ďŽƵƚ ĚĞ ĐŽŵďŝĞŶ ĚĞ ũŽƵƌƐ ůĞƐ ĚĞƵǆ ĞŶĨĂŶƚƐ ĂƵƌŽŶƚͲŝůƐ͕ ă ŶŽƵǀĞĂƵ͕ ůĂ ƉŽƐƐŝďŝůŝƚĠ ĚĞ Ɛ͛ĞŶƚƌĂŠŶĞƌ ĞŶƐĞŵďůĞ ă ůĂ ƉŝƐĐŝŶĞ ͍ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ďͿ WŽƵƌ ƚƌŽƵǀĞƌ͕ ĚĞ ŵĂŶŝğƌĞ ŵĠƚŚŽĚŝƋƵĞ͕ ĂƵ ďŽƵƚ ĚĞ ĐŽŵďŝĞŶ ĚĞ ũŽƵƌƐ ůĞƐ ĚĞƵǆ ĞŶĨĂŶƚƐ ĂƵƌŽŶƚ͕ ă ŶŽƵǀĞĂƵ͕ ůĂ ƉŽƐƐŝďŝůŝƚĠ ĚĞ Ɛ͛ĞŶƚƌĂŠŶĞƌ ĞŶƐĞŵďůĞ ă ůĂ ƉŝƐĐŝŶĞ͕ ĠĐƌŝƐ ƚŽƵƐ ůĞƐ ŵƵůƟ ƉůĞƐ ĚĞ ϰ Ğƚ ĚĞ ϭϬ͘ ϰN с ΂ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϭϬN с ΂ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ŽŵƉůğƚĞ ůĞƐ ƉŚƌĂƐĞƐ ƐƵŝǀĂŶƚĞƐ͘ >ĞƐ ĞŶĨĂŶƚƐ ƉŽƵƌƌŽŶƚ ƐĞ ƌĞŶĐŽŶƚƌĞƌ ă ŶŽƵǀĞĂƵ ă ůĂ ƉŝƐĐŝŶĞ ĂƉƌğƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ũŽƵƌƐ ĞƐ ŶŽŵďƌĞƐ ƐŽŶƚ ůĞƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ p.36 B3

>Ă ƉƌĞŵŝğƌĞ ƌĞŶĐŽŶƚƌĞ ĂƵƌĂ ůŝĞƵ ĂƉƌğƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ũŽƵƌƐ ͖ ĐĞ ŶŽŵďƌĞ ĞƐƚ ůĞ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ĚĞ ϰ Ğƚ ĚĞ ϭϬ͘

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ACTIVITÉS 5

Chapitre 2 Diviseurs et multiples

YƵĞůƐ ƐŽŶƚ ůĞƐ ƚƌŽŝƐ ƉƌĞŵŝĞƌƐ ŵƵůƟ ƉůĞƐ ĐŽŵŵƵŶƐ ŶŽŶ ŶƵůƐ ĚĞ ϲ Ğƚ ĚĞ ϴ ͍ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

YƵĞů ĞƐƚ ůĞ ƉůƵƐ ƉĞƟ ƚ ĐŽŵŵƵŶ ŵƵůƟ ƉůĞ ŶŽŶ ŶƵů ĚĞ ϲ Ğƚ ĚĞ ϴ ͍ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ĐƚŝǀŝƚĠ ϯ ŝǀŝƐĞƵƌ ŽƵ ŵƵůƚŝƉůĞ 1 ZĞƚƌŽƵǀĞ ƚŽŶ ĐŚĞŵŝŶ ĚĂŶƐ ůĞ ůĂďǇƌŝŶƚŚĞ ĞŶ ƵƟ ůŝƐĂŶƚ ůĞƐ ĐŽŶƐŝŐŶĞƐ ĐŝͲĚĞƐƐŽƵƐ͘ dƵ ŶĞ ƉĞƵǆ ƚĞ ĚĠƉůĂĐĞƌ ƋƵ͛ŚŽƌŝǌŽŶƚĂůĞŵĞŶƚ ŽƵ ǀĞƌƟ ĐĂůĞŵĞŶƚ͘ dƵ ĚŽŝƐ ƉĂƐƐĞƌ Ě͛ƵŶĞ ĐĂƐĞ ă ů͛ĂƵƚƌĞ ĞŶ ĐŚŽŝƐŝƐƐĂŶƚ ƐƵĐĐĞƐƐŝǀĞŵĞŶƚ ͗ ƵŶ ĚŝǀŝƐĞƵƌ ĚƵ ŶŽŵďƌĞ ƐƵƌ ůĞƋƵĞů ƚƵ ƚĞ ƚƌŽƵǀĞƐ͕ ƉƵŝƐ ƵŶ ŵƵůƟ ƉůĞ ĚƵ ŶŽŵďƌĞ ƐƵƌ ůĞƋƵĞů ƚƵ ƚĞ ƚƌŽƵǀĞƐ͕ Ğƚ ĂŝŶƐŝ ĚĞ ƐƵŝƚĞ͘

ϭϱ

ϭϮ Ϯϰ ϰϮ ϭϯ

Ϯϭ ϭϰ ϯϰ ϭϬ

ϭϲ

ϯϱ Ϯϱ Ϯϰ ϭϱ ϮϮ

ϯϳ

ϴϴ ϭϭ

ϮϬ ϭϳ ϭϵ

ϱϰ Ϯϲ ϭϴ

ϯϲ

ϯϭ

2 ŽŵƉůğƚĞ ĐŚĂĐƵŶĞ ĚĞƐ ũƵƐƟ Į ĐĂƟ ŽŶƐ ĐŝͲĚĞƐƐŽƵƐ͘ ϲ ĞƐƚ ƵŶ ĚŝǀŝƐĞƵƌ ĚĞ Ϯϰ ĐĂƌ Ϯϰ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϴϬϬ ĞƐƚ ĚŝǀŝƐŝďůĞ ƉĂƌ ϴ ĐĂƌ ϴϬϬ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϯϱ ĞƐƚ ƵŶ ŵƵůƟ ƉůĞ ĚĞ ϱ ĐĂƌ ϯϱ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϵ ĚŝǀŝƐĞ ϰϱ ĐĂƌ ϰϱ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϭϮ ĞƐƚ ƵŶ ŵƵůƟ ƉůĞ ĚĞ ϰ ĐĂƌ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϱϬ ĞƐƚ ƵŶ ŵƵůƟ ƉůĞ ĚĞ ϭϬ ĐĂƌ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϳϮ ĞƐƚ ĚŝǀŝƐŝďůĞ ƉĂƌ ϭϮ ĐĂƌ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϭϬϬϬ ĞƐƚ ĚŝǀŝƐŝďůĞ ƉĂƌ ϴ ĐĂƌ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϰϮ ĞƐƚ ƵŶ ŵƵůƟ ƉůĞ ĚĞ ͘ ͘ ͘ ͘ ͘ ͘ ĐĂƌ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϱ ĚŝǀŝƐĞ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ĐĂƌ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

3 ŽŵƉůğƚĞ ůĞƐ ƉŚƌĂƐĞƐ ƉĂƌ ƵŶĞ ĚĞƐ ĞǆƉƌĞƐƐŝŽŶƐ ƐƵŝǀĂŶƚĞƐ ͗ ͨ ĞƐƚ ĚŝǀŝƐĞƵƌ ĚĞ ͕ͩ ͨ ĚŝǀŝƐĞ ͕ͩ ͨ ĞƐƚ ŵƵůƟ ƉůĞ ĚĞ ͩ ŽƵ ͨ ĞƐƚ ĚŝǀŝƐŝďůĞ ƉĂƌ ͩ͘ ϱ

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Ϯϱ

ϭϱ

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϭϱ

ϭϮ

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϲϰ

ϭϬϬ

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϭϬ

ϱϬ

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϭϱϬ

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Ϯϰ

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

dƵ ǀŝĞŶƐ Ě͛ƵƟ ůŝƐĞƌ ůĞƐ ĞǆƉƌĞƐƐŝŽŶƐ ͗ ͨ ĞƐƚ ĚŝǀŝƐĞƵƌ ĚĞ ͕ͩ ͨ ĞƐƚ ŵƵůƟ ƉůĞ ĚĞ ͕ͩ ͨ ĞƐƚ ĚŝǀŝƐŝďůĞ ƉĂƌ ͕ͩ ͨ ĚŝǀŝƐĞ ͩ͘ YƵĞůůĞƐ ƐŽŶƚ ĐĞůůĞƐ ƋƵŝ ƐŽŶƚ ĠƋƵŝǀĂůĞŶƚĞƐ ͍ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

p.36 ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Chapitre 2 Diviseurs et multiples

ACTIVITÉS

ŝƚĞ͕ Ɛŝ ƉŽƐƐŝďůĞ͕ ůĞƐ ŶŽŵďƌĞƐ ŶĂƚƵƌĞůƐ ƋƵŝ ƐŽŶƚ ͙ ĚŝǀŝƐĞƵƌƐ ĚĞ Ϯϰ ŝŶĨĠƌŝĞƵƌƐ ă ϭϮ ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ŵƵůƟ ƉůĞƐ ĚĞ ϰ ŝŶĨĠƌŝĞƵƌƐ ă ϮϬ ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ĚŝǀŝƐĞƵƌƐ ĚĞ ϭϮ ŝŵƉĂŝƌƐ ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ŵƵůƟ ƉůĞƐ ĚĞ ϱ͕ ŝŶĨĠƌŝĞƵƌƐ ă ϯϬ Ğƚ ƉĂŝƌƐ ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ĚŝǀŝƐĞƵƌƐ ĚĞ ϭϱ ƉĂŝƌƐ ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ĚŝǀŝƐĞƵƌƐ ĚĞ ϰϮ ƐƵƉĠƌŝĞƵƌƐ ă ϳ ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ŵƵůƟ ƉůĞƐ ĚĞ ϵ ĐŽŵƉƌŝƐ ĞŶƚƌĞ ϯϬ Ğƚ ϴϬ ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ĚŝǀŝƐĞƵƌƐ ĚĞ ϵϴ ŵƵůƟ ƉůĞƐ ĚĞ ϳ ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ĐƚŝǀŝƚĠ ϰ ĂƌĂĐƚğƌĞƐ ĚĞ ĚŝǀŝƐŝďŝůŝƚĠ 1 ĂͿ ƌŝďůĞ Ě͛ ƌĂƚŽƐƚŚğŶĞ ĂƌƌĞ ůĞƐ ŶŽŵďƌĞƐ ƋƵŝ ŶĞ ƐŽŶƚ ƉĂƐ ƉƌĞŵŝĞƌƐ͘ dƌŽƵǀĞ ƵŶĞ ŵĠƚŚŽĚĞ ƌĂƉŝĚĞ Ğƚ ƉƌĂƟ ƋƵĞ ƉŽƵƌ Ǉ ĂƌƌŝǀĞƌ͘ ϭ

ϭϬ

ϭϭ ϭϮ ϭϯ ϭϰ ϭϱ ϭϲ ϭϳ ϭϴ ϭϵ ϮϬ Ϯϭ ϮϮ Ϯϯ Ϯϰ Ϯϱ Ϯϲ Ϯϳ Ϯϴ Ϯϵ ϯϬ ϯϭ ϯϮ ϯϯ ϯϰ ϯϱ ϯϲ ϯϳ ϯϴ ϯϵ ϰϬ ϰϭ ϰϮ ϰϯ ϰϰ ϰϱ ϰϲ ϰϳ ϰϴ ϰϵ ϱϬ ϱϭ ϱϮ ϱϯ ϱϰ ϱϱ ϱϲ ϱϳ ϱϴ ϱϵ ϲϬ ϲϭ ϲϮ ϲϯ ϲϰ ϲϱ ϲϲ ϲϳ ϲϴ ϲϵ ϳϬ ϳϭ ϳϮ ϳϯ ϳϰ ϳϱ ϳϲ ϳϳ ϳϴ ϳϵ ϴϬ ϴϭ ϴϮ ϴϯ ϴϰ ϴϱ ϴϲ ϴϳ ϴϴ ϴϵ ϵϬ ϵϭ ϵϮ ϵϯ ϵϰ ϵϱ ϵϲ ϵϳ ϵϴ ϵϵ ϭϬϬ

Ératosthène est un astronome, géographe, philosophe et mathématicien grec du IIIe siècle avant notre ère. Il est né à Cyrène en -276 et est mort à Alexandrie en -194. Ératosthène est célèbre pour son crible permettant de déterminer des nombres premiers, mais aussi pour la première estimation de la longueur d’un méridien.

ďͿ EŽƚĞ ƚŽƵƐ ůĞƐ ŶŽŵďƌĞƐ ƉƌĞŵŝĞƌƐ ŝŶĨĠƌŝĞƵƌƐ ă ϭϬϬ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

2 ĂͿ ĐƌŝƐ ƚŽƵƐ ůĞƐ ŶŽŵďƌĞƐ ĚĞ ĚĞƵǆ ĐŚŝī ƌĞƐ Ěŝī ĠƌĞŶƚƐ ƋƵĞ ƚƵ ƉĞƵǆ ĨŽƌŵĞƌ ă ů͛ĂŝĚĞ ĚĞƐ ĐŚŝī ƌĞƐ Ϯ͕ ϯ͕ ϳ Ğƚ ϵ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ACTIVITÉS

Chapitre 2 Diviseurs et multiples

ďͿ WĂƌŵŝ ĐĞƵǆͲĐŝ͕ ƋƵĞůƐ ƐŽŶƚ ůĞƐ ŶŽŵďƌĞƐ ƉƌĞŵŝĞƌƐ ͍ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

3 ĂͿ dƌŽƵǀĞ ůĞƐ ƐƵŝƚĞƐ ƐƵŝǀĂŶƚĞƐ ƐƵƌ ůĞ ĐƌŝďůĞ Ğƚ ŶŽƚĞ ĐĞ ƋƵ͛ĞůůĞƐ ŽŶƚ ĚĞ ƉĂƌƟ ĐƵůŝĞƌ͘ ;ϭͿ ϳ ʹ ϭϲ ʹ Ϯϱ ʹ ϯϰ ʹ ϰϯ ʹ ϱϮ ʹ ϲϭ ;ϮͿ ϴ ʹ ϭϳ ʹ Ϯϲ ʹ ϯϱ ʹ ϰϰ ʹ ϱϯ ʹ ϲϮ ʹ ϳϭ ;ϯͿ ϲ ʹ ϭϱ ʹ Ϯϰ ʹ ϯϯ ʹ ϰϮ ʹ ϱϭ ;ϰͿ ϵ ʹ ϭϴ ʹ Ϯϳ ʹ ϯϲ ʹ ϰϱ ʹ ϱϰ ʹ ϲϯ ʹ ϳϮ ʹ ϴϭ

ďͿ hŶĞ ĚĞƐ ƐƵŝƚĞƐ ƉƌŽƉŽƐĠĞƐ ĞƐƚ ƵŶ ĞŶƐĞŵďůĞ ĚĞ ŵƵůƟ ƉůĞƐ Ě͛ƵŶ ŵġŵĞ ŶŽŵďƌĞ͘ >ĂƋƵĞůůĞ Ğƚ ĚĞ ƋƵĞů ŶŽŵďƌĞ Ɛ͛ĂŐŝƚͲŝů ͍ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ĐͿ hƟ ůŝƐĞ ůĞƐ ŽďƐĞƌǀĂƟ ŽŶƐ ĨĂŝƚĞƐ ĂƵǆ ƉŽŝŶƚƐ ĂͿ Ğƚ ďͿ ƉŽƵƌ ĠŶŽŶĐĞƌ ůĞƐ ĐĂƌĂĐƚğƌĞƐ ĚĞ ĚŝǀŝƐŝďŝůŝƚĠ ƉĂƌ ϵ Ğƚ ƉĂƌ ϯ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ĚͿ sĠƌŝĮ Ğ Ɛŝ ůĞƐ ŶŽŵďƌĞƐ ĐŝͲĚĞƐƐŽƵƐ ƐŽŶƚ ĚŝǀŝƐŝďůĞƐ ƉĂƌ ϯ Ğƚ ƉĂƌ ϵ͘ :ƵƐƟ Į Ğ͘ ϴϮϬϱ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϳϯϯϱ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϲϮϱϬ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ACTIVITÉS

Chapitre 2 Diviseurs et multiples

ĂͿ >Ğ ŶŽŵďƌĞ ϭϬ ϱϳϭ ĞƐƚͲŝů ĚŝǀŝƐŝďůĞ ƉĂƌ ϯ ͍ :ƵƐƟ Į Ğ ƚĂ ƌĠƉŽŶƐĞ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ďͿ DŽĚŝĮ Ğ ůĞ ĐŚŝī ƌĞ ĚĞ ƐĞƐ ƵŶŝƚĠƐ ĂĮ Ŷ Ě͛ĠĐƌŝƌĞ ƵŶ ŶŽŵďƌĞ ĚŝǀŝƐŝďůĞ ƉĂƌ ϯ͘ ĐƌŝƐ ƚŽƵƚĞƐ ůĞƐ ƐŽůƵƟ ŽŶƐ ƉŽƐƐŝďůĞƐ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ĐͿ WĂƌŵŝ ůĞƐ ƐŽůƵƟ ŽŶƐ ĚĞ ůĂ ƋƵĞƐƟ ŽŶ ƉƌĠĐĠĚĞŶƚĞ͕ ĐŝƚĞ ůĞƐ ŶŽŵďƌĞƐ ƋƵŝ ƐŽŶƚ ĂƵƐƐŝ͙ ĚŝǀŝƐŝďůĞƐ ƉĂƌ ϵ ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ĚŝǀŝƐŝďůĞƐ ƉĂƌ Ϯ ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ĚŝǀŝƐŝďůĞƐ ƉĂƌ ϰ ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ĚŝǀŝƐŝďůĞƐ ƉĂƌ ϴ ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ĚŝǀŝƐŝďůĞƐ ƉĂƌ ϱ ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ĚŝǀŝƐŝďůĞƐ ƉĂƌ Ϯϱ ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ p.36 D1

ĚŝǀŝƐŝďůĞƐ ƉĂƌ ϭϮϱ ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ 5 ŽŵƉůğƚĞ ůĞ ƚĂďůĞĂƵ ƐƵŝǀĂŶƚ͕ ĞŶ ŶŽƚĂŶƚ ƵŶĞ ĐƌŽŝǆ ĂƵǆ ĞŶĚƌŽŝƚƐ ƋƵŝ ĐŽŶǀŝĞŶŶĞŶƚ͘ ŝǀŝƐŝďůĞ ƉĂƌ

125

ϱϲϬ ϳϱϬ ϭϭϮϱ ϮϱϬϬ ϯϮϰϰ ϯϬϳϮ ϲϯϭϱ ϭϵ ϴϬϬ ϭϯϳ ϲϮϱ

ACTIVITÉS 6

Chapitre 2 Diviseurs et multiples

WĂƌ ƋƵĞů;ƐͿ ĐŚŝī ƌĞƐ;ƐͿ ƉĞƵǆͲƚƵ ƌĞŵƉůĂĐĞƌ x ƉŽƵƌ ƋƵĞ ůĂ ƉŚƌĂƐĞ ƐŽŝƚ ĐŽƌƌĞĐƚĞ ͍ Ϯ ϲ x ϰ ĞƐƚ ĚŝǀŝƐŝďůĞ ƉĂƌ ϰ ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϴ ϵ x Ϯ ĞƐƚ ĚŝǀŝƐŝďůĞ ƉĂƌ Ϯ ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϳ ϯ x ϲ ĞƐƚ ĚŝǀŝƐŝďůĞ ƉĂƌ ϯ ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϴ ϵ x ϭ ĞƐƚ ĚŝǀŝƐŝďůĞ ƉĂƌ ϵ ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϳ ϰ x Ϯ ĞƐƚ ĚŝǀŝƐŝďůĞ ƉĂƌ ϱ ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϰ ϳ x ϱ ĞƐƚ ĚŝǀŝƐŝďůĞ ƉĂƌ Ϯϱ ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϭ ϱ x ϳ ĞƐƚ ĚŝǀŝƐŝďůĞ ƉĂƌ ϵ ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϯ ϴ x ϲ ĞƐƚ ĚŝǀŝƐŝďůĞ ƉĂƌ ϰ ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

7 ŝƐƉŽƐĞ͕ Ɛŝ ƉŽƐƐŝďůĞ͕ ůĞƐ ĐŝŶƋ ĐĂƌƚĞƐ ŝůůƵƐƚƌĠĞƐ ĐŝͲĚĞƐƐŽƵƐ ĚĞ ŵĂŶŝğƌĞ ă ĨŽƌŵĞƌ ƵŶ ŶŽŵďƌĞ ĚĞ ĐŝŶƋ ĐŚŝī ƌĞƐ ƌĠƉŽŶĚĂŶƚ ĂƵǆ ĐƌŝƚğƌĞƐ ĠŶŽŶĐĠƐ͘ ϭ

>Ğ ƉůƵƐ ƉĞƟ ƚ ŶŽŵďƌĞ ĚŝǀŝƐŝďůĞ ƉĂƌ Ϯ ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ >Ğ ƉůƵƐ ŐƌĂŶĚ ŶŽŵďƌĞ ĚŝǀŝƐŝďůĞ ƉĂƌ ϱ ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ >Ğ ƉůƵƐ ƉĞƟ ƚ ŶŽŵďƌĞ ĚŝǀŝƐŝďůĞ ƉĂƌ ϭϮϱ ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ >Ğ ƉůƵƐ ƉĞƟ ƚ ŶŽŵďƌĞ ĚŝǀŝƐŝďůĞ ƉĂƌ ϯ ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ >Ğ ƉůƵƐ ŐƌĂŶĚ ŶŽŵďƌĞ ĚŝǀŝƐŝďůĞ ƉĂƌ ϵ ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ 8 ŝƚĞ ͙ ůĞ ƉůƵƐ ŐƌĂŶĚ ŶŽŵďƌĞ ŶĂƚƵƌĞů ĚĞ ϰ ĐŚŝī ƌĞƐ͕ ŵƵůƟ ƉůĞ ĚĞ ϵ͕ ƐĞ ƚĞƌŵŝŶĂŶƚ ƉĂƌ ϴ ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ůĞ ƉůƵƐ ƉĞƟ ƚ ŶŽŵďƌĞ ŶĂƚƵƌĞů ĚĞ ϰ ĐŚŝī ƌĞƐ͕ ŵƵůƟ ƉůĞ ĚĞ ϵ͕ ƐĞ ƚĞƌŵŝŶĂŶƚ ƉĂƌ ϴ ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ůĞ ƉůƵƐ ƉĞƟ ƚ ŶŽŵďƌĞ ŶĂƚƵƌĞů ĚĞ ϰ ĐŚŝī ƌĞƐ ŵƵůƟ ƉůĞ ĚĞ Ϯ͕ ϯ Ğƚ ϱ ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ůĞ ƉůƵƐ ŐƌĂŶĚ ŶŽŵďƌĞ ŶĂƚƵƌĞů ŝŶĨĠƌŝĞƵƌ ă ϭϬϬϬ Ğƚ ĚŝǀŝƐŝďůĞ ƉĂƌ Ϯ Ğƚ ƉĂƌ ϯ ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ůĞ ƉůƵƐ ƉĞƟ ƚ ŶŽŵďƌĞ ŶĂƚƵƌĞů ĚĞ ϰ ĐŚŝī ƌĞƐ Ěŝī ĠƌĞŶƚƐ ĚŝǀŝƐŝďůĞ ƉĂƌ ϯ Ğƚ ƉĂƌ Ϯϱ ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ĐƚŝǀŝƚĠ ϱ ŝǀŝƐŝďŝůŝƚĠ Ğƚ ƉƌŽƉƌŝĠƚĠƐ 1 hŶ ŵĂƌĐŚĠ ĚĞ EŽģů ĞƐƚ ŽƌŐĂŶŝƐĠ ĚĂŶƐ ƵŶĞ ĠĐŽůĞ͘ >Ğ ĚŝƌĞĐƚĞƵƌ ĚĞŵĂŶĚĞ ă ƐĞƐ ŚƵŝƚ ŝŶƐƟ ƚƵƚĞƵƌƐ Ğƚ ŝŶƐƟ ƚƵƚƌŝĐĞƐ ĚĞ ƐĞ ƌĞůĂǇĞƌ ƉŽƵƌ ƉƌĠƉĂƌĞƌ Ğƚ ǀĞŶĚƌĞ ϱϲϬ ĐƌġƉĞƐ͘ ĞƵǆͲĐŝ ĚĠĐŝĚĞŶƚ ĂůŽƌƐ ĚĞ ƐĞ ƉĂƌƚĂŐĞƌ ĠƋƵŝƚĂďůĞŵĞŶƚ ĐĞƩ Ğ ƚąĐŚĞ͘ ŽŵďŝĞŶ ĚĞ ĐƌġƉĞƐ ĐŚĂĐƵŶ ǀĂͲƚͲŝů ƉƌĠƉĂƌĞƌ ͍ ZĞĐŚĞƌĐŚĞ ƵŶ ƉƌŽĐĠĚĠ ƋƵŝ ƚĞ ƉĞƌŵĞƚ ĚĞ ƌĠƐŽƵĚƌĞ ĐĞ ƉƌŽďůğŵĞ ƐĂŶƐ ů͛ĂŝĚĞ ĚĞ ůĂ ĐĂůĐƵůĂƚƌŝĐĞ͘ ĐƌŝƐ ĐŽƌƌĞĐƚĞŵĞŶƚ ƚŽƵƐ ƚĞƐ ĐĂůĐƵůƐ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Chapitre 2 Diviseurs et multiples

ACTIVITÉS

ŽŵƉůğƚĞ ůĞƐ ƉŚƌĂƐĞƐ ĐŝͲĚĞƐƐŽƵƐ͘ WƵŝƐƋƵĞ ϴ ĚŝǀŝƐĞ ϱϲ͕ ĂůŽƌƐ ϴ ĚŝǀŝƐĞ ϱϲϬ ĐĂƌ ϱϲϬ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ WƵŝƐƋƵĞ ϴ ĚŝǀŝƐĞ ϱϲ͕ ĂůŽƌƐ ϴ ĚŝǀŝƐĞ ϭϭϮ ĐĂƌ ϭϭϮ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ WƵŝƐƋƵĞ ϴ ĚŝǀŝƐĞ ϱϲ͕ ĂůŽƌƐ ϴ ĚŝǀŝƐĞ ϭϲϴ ĐĂƌ ϭϲϴ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ WƵŝƐƋƵĞ ϴ ĚŝǀŝƐĞ ϱϲ͕ ĂůŽƌƐ ϴ ĚŝǀŝƐĞ ϮϮϰ ĐĂƌ ϮϮϰ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ WƵŝƐƋƵĞ ϴ ĚŝǀŝƐĞ ϱϲ͕ ĂůŽƌƐ ϴ ĚŝǀŝƐĞ ϮϴϬ ĐĂƌ ϮϴϬ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ^ŝ Ă ĚŝǀŝƐĞ ϱϲ͕ ĂůŽƌƐ Ă ĚŝǀŝƐĞ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ^ŝ Ă ĚŝǀŝƐĞ ϱϲ͕ ĂůŽƌƐ Ă ĚŝǀŝƐĞ ƚŽƵƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ^ŝ ƵŶ ŶŽŵďƌĞ ĞŶ ĚŝǀŝƐĞ ƵŶ ĂƵƚƌĞ͕ ĂůŽƌƐ ŝů ĚŝǀŝƐĞ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ĚĞ ĐĞƚ ĂƵƚƌĞ ŶŽŵďƌĞ͘

p.37 Ϯa

^ŝ Ă ĚŝǀŝƐĞ ď͕ ĂůŽƌƐ Ă ĚŝǀŝƐĞ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ 3 :ƵƐƟ Į Ğ͘ ϱϱ ϬϬϬ ĞƐƚ ĚŝǀŝƐŝďůĞ ƉĂƌ ϭϭ ĐĂƌ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϮϭϬ ĞƐƚ ĚŝǀŝƐŝďůĞ ƉĂƌ ϳ ĐĂƌ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϰϮϬϬ ĞƐƚ ĚŝǀŝƐŝďůĞ ƉĂƌ ϲ ĐĂƌ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

4 WŽƵƌ ĨġƚĞƌ ůĂ Į Ŷ ĚĞ ů͛ĂŶŶĠĞ ƐĐŽůĂŝƌĞ͕ ůĞƐ ϯϰϴ ĠůğǀĞƐ Ě͛ƵŶĞ ĠĐŽůĞ ƉĂƌƟ ĐŝƉĞŶƚ ă ƵŶĞ ĚĞƐĐĞŶƚĞ ĞŶ ƌĂŌ ŝŶŐ͘ ŚĂƋƵĞ ƌĂŌ ƉĞƵƚ ĂĐĐƵĞŝůůŝƌ Ɛŝǆ ƉĞƌƐŽŶŶĞƐ ĞŶ ƉůƵƐ ĚĞ ů͛ŝŶƐƚƌƵĐƚĞƵƌ͘ YƵĞů ĞƐƚ ůĞ ŶŽŵďƌĞ Ě͛ĞŵďĂƌĐĂƟ ŽŶƐ ƌĠƐĞƌǀĠĞƐ ƉŽƵƌ ĐĞƩ Ğ ĠĐŽůĞ ͍ ZĞĐŚĞƌĐŚĞ ƵŶ ƉƌŽĐĠĚĠ ƋƵŝ ƚĞ ƉĞƌŵĞƚ ĚĞ ƌĠƐŽƵĚƌĞ ĐĞ ƉƌŽďůğŵĞ ƐĂŶƐ ů͛ĂŝĚĞ ĚĞ ůĂ ĐĂůĐƵůĂƚƌŝĐĞ͘ ĐƌŝƐ ĐŽƌƌĞĐƚĞŵĞŶƚ ƚŽƵƚ ƚŽŶ ƌĂŝƐŽŶŶĞŵĞŶƚ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

5 ů͛ŽĐĐĂƐŝŽŶ Ě͛,ĂůůŽǁĞĞŶ͕ ƵŶĞ ŐƌĂŶĚĞ ĨġƚĞ ĞƐƚ ŽƌŐĂŶŝƐĠĞ ĚĂŶƐ ƵŶĞ ĠĐŽůĞ͘ WŽƵƌ ƌĠĂůŝƐĞƌ ůĂ ĚĠĐŽƌĂƟ ŽŶ ĚƵ ƌĠĨĞĐƚŽŝƌĞ͕ ůĞ ĚŝƌĞĐƚĞƵƌ ĚĞŵĂŶĚĞ ĂƵǆ ĞŶĨĂŶƚƐ ĚĞ ĐŽŶĨĞĐƟ ŽŶŶĞƌ ĚĞƐ ůĂŶƚĞƌŶĞƐ ĂǀĞĐ ĚĞƐ ƉŽƟ ƌŽŶƐ͘ /ů ƌĠƉĂƌƟ ƚ ĂůŽƌƐ ĠƋƵŝƚĂďůĞŵĞŶƚ ϭϯϱ ƉŽƟ ƌŽŶƐ ĞŶƚƌĞ ůĞƐ ϭϱ ĐůĂƐƐĞƐ ĚĞ ůĂ ƐĞĐƟ ŽŶ ƉƌŝŵĂŝƌĞ͘ ŽŵďŝĞŶ ĚĞ ƉŽƟ ƌŽŶƐ ĐŚĂƋƵĞ ĐůĂƐƐĞ ĂͲƚͲĞůůĞ ă ƐĂ ĚŝƐƉŽƐŝƟ ŽŶ ͍ ZĞĐŚĞƌĐŚĞ ƵŶ ƉƌŽĐĠĚĠ ƋƵŝ ƚĞ ƉĞƌŵĞƚ ĚĞ ƌĠƐŽƵĚƌĞ ĐĞ ƉƌŽďůğŵĞ ƐĂŶƐ ů͛ĂŝĚĞ ĚĞ ůĂ ĐĂůĐƵůĂƚƌŝĐĞ͘ ĐƌŝƐ ĐŽƌƌĞĐƚĞŵĞŶƚ ƚŽƵƚ ƚŽŶ ƌĂŝƐŽŶŶĞŵĞŶƚ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ACTIVITÉS 6

Chapitre 2 Diviseurs et multiples

ĂůĐƵůĞ ĞŶ ĚĠĐŽŵƉŽƐĂŶƚ ůĞ ĚŝǀŝĚĞŶĚĞ ĞŶ ƵŶĞ ƐŽŵŵĞ ƉƵŝƐ ĞŶ ƵŶĞ Ěŝī ĠƌĞŶĐĞ ĚĞ ĚĞƵǆ ŶŽŵďƌĞƐ ĚŝǀŝƐŝďůĞƐ ƉĂƌ ůĞ ĚŝǀŝƐĞƵƌ ƉƌŽƉŽƐĠ͘ ϰϱϵ ͗ ϵ с

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϴϵϭ ͗ ϵ с

Ϯϰϴ ͗ ϴ с

ϱϳϲ ͗ ϴ с

Ϯϭϳ ͗ ϳ с

ϮϬϯ ͗ ϳ с

ϲϭϮ ͗ ϲ с

ϱϴϴ ͗ ϲ с

7 ŽŵƉůğƚĞ ůĞƐ ƉŚƌĂƐĞƐ ĐŝͲĚĞƐƐŽƵƐ͘ WƵŝƐƋƵĞ ϲ ĚŝǀŝƐĞ ϲϬϬ Ğƚ ϭϮ͕ ĂůŽƌƐ ϲ ĚŝǀŝƐĞ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ Ğƚ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ WƵŝƐƋƵĞ ϳ ĚŝǀŝƐĞ ϮϭϬ Ğƚ ϳ͕ ĂůŽƌƐ ϳ ĚŝǀŝƐĞ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ Ğƚ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ^ŝ Ă ĚŝǀŝƐĞ ϭϬϬ Ğƚ ϭϮ͕ ĂůŽƌƐ Ă ĚŝǀŝƐĞ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ Ğƚ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ^ŝ ƵŶ ŶŽŵďƌĞ ĞŶ ĚŝǀŝƐĞ ĚĞƵǆ ĂƵƚƌĞƐ͕ ĂůŽƌƐ ŝů ĚŝǀŝƐĞ ůĞƵƌ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Ğƚ ůĞƵƌ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

^ŝ Ă ĚŝǀŝƐĞ ď Ğƚ Đ͕ ĂůŽƌƐ Ă ĚŝǀŝƐĞ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Ğƚ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

p.37 Ϯ b-c

Chapitre 2 Diviseurs et multiples

ACTIVITÉS

:ƵƐƟ Į Ğ͘ ϳϮϭ ĞƐƚ ĚŝǀŝƐŝďůĞ ƉĂƌ ϳ ĐĂƌ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϰϬϮ ĞƐƚ ĚŝǀŝƐŝďůĞ ƉĂƌ ϲ ĐĂƌ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϮϮϴ ĞƐƚ ĚŝǀŝƐŝďůĞ ƉĂƌ ϭϮ ĐĂƌ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

9 ĂͿ ů͛ĠĐŽůĞ ƉƌŝŵĂŝƌĞ͕ ƚƵ ĂƐ ǀƵ ůĞ ĐĂƌĂĐƚğƌĞ ĚĞ ĚŝǀŝƐŝďŝůŝƚĠ ƉĂƌ Ϯ͘ ͨ hŶ ŶŽŵďƌĞ ĞƐƚ ĚŝǀŝƐŝďůĞ ƉĂƌ Ϯ Ɛŝ ƐŽŶ ĚĞƌŶŝĞƌ ĐŚŝī ƌĞ ĞƐƚ ƵŶ ŶŽŵďƌĞ ƉĂŝƌ ͩ͘ Ŷ ƵƟ ůŝƐĂŶƚ ĐĞ ĐĂƌĂĐƚğƌĞ ĚĞ ĚŝǀŝƐŝďŝůŝƚĠ͕ ĞǆƉůŝƋƵĞ ƉŽƵƌƋƵŽŝ Ϯϳϵϲ ĞƐƚ ĚŝǀŝƐŝďůĞ ƉĂƌ Ϯ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

WŽƵƌƋƵŽŝ ŶĞ ĨĂƵƚͲŝů ƉĂƐ ǀĠƌŝĮ Ğƌ ƋƵĞ ϮϳϵϬ ĞƐƚ ĚŝǀŝƐŝďůĞ ƉĂƌ Ϯ ͍ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ďͿ dƵ ĂƐ ǀƵ ĠŐĂůĞŵĞŶƚ ůĞ ĐĂƌĂĐƚğƌĞ ĚĞ ĚŝǀŝƐŝďŝůŝƚĠ ƉĂƌ ϰ͘ ͨ hŶ ŶŽŵďƌĞ ĞƐƚ ĚŝǀŝƐŝďůĞ ƉĂƌ ϰ Ɛŝ ƐĞƐ ĚĞƵǆ ĚĞƌŶŝĞƌƐ ĐŚŝī ƌĞƐ ĨŽƌŵĞŶƚ ƵŶ ŶŽŵďƌĞ divisible par 4 ͩ͘ Ŷ ƵƟ ůŝƐĂŶƚ ĐĞ ĐĂƌĂĐƚğƌĞ ĚĞ ĚŝǀŝƐŝďŝůŝƚĠ͕ ĞǆƉůŝƋƵĞ ƉŽƵƌƋƵŽŝ ϮϳϵϮ ĞƐƚ ĚŝǀŝƐŝďůĞ ƉĂƌ ϰ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

WŽƵƌƋƵŽŝ ŶĞ ĨĂƵƚͲŝů ƉĂƐ ǀĠƌŝĮ Ğƌ ƋƵĞ ϮϳϬϬ ĞƐƚ ĚŝǀŝƐŝďůĞ ƉĂƌ ϰ ͍ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ĐͿ ƚ ĞŶĮ Ŷ͕ ƚƵ ĂƐ ǀƵ ůĞ ĐĂƌĂĐƚğƌĞ ĚĞ ĚŝǀŝƐŝďŝůŝƚĠ ƉĂƌ ϴ͘ ͨ hŶ ŶŽŵďƌĞ ĞƐƚ ĚŝǀŝƐŝďůĞ ƉĂƌ ϴ Ɛŝ ƐĞƐ ƚƌŽŝƐ ĚĞƌŶŝĞƌƐ ĐŚŝī ƌĞƐ ĨŽƌŵĞŶƚ ƵŶ ŶŽŵďƌĞ ĚŝǀŝƐŝďůĞ par 8 ͩ͘ Ŷ ƵƟ ůŝƐĂŶƚ ĐĞ ĐĂƌĂĐƚğƌĞ ĚĞ ĚŝǀŝƐŝďŝůŝƚĠ͕ ĞǆƉůŝƋƵĞ ƉŽƵƌƋƵŽŝ ϮϳϵϮ ĞƐƚ ĚŝǀŝƐŝďůĞ ƉĂƌ ϴ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

WŽƵƌƋƵŽŝ ŶĞ ĨĂƵƚͲŝů ƉĂƐ ǀĠƌŝĮ Ğƌ ƋƵĞ ϮϬϬϬ ĞƐƚ ĚŝǀŝƐŝďůĞ ƉĂƌ ϴ ͍ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ACTIVITÉS

Chapitre 2 Diviseurs et multiples

ĐƚŝǀŝƚĠ ϲ :ƵƐƚŝĨŝĐĂƚŝŽŶ ĚĞ ůĂ ĚŝǀŝƐŝďŝůŝƚĠ 1 WŽƵƌ ũƵƐƚŝĨŝĞƌ ƋƵ͛ƵŶ ŶŽŵďƌĞ ĞƐƚ ĚŝǀŝƐŝďůĞ ƉĂƌ ƵŶ ĂƵƚƌĞ͕ ŶŽƵƐ ĂǀŽŶƐ ǀƵ ĚĂŶƐ ůĞƐ ĂĐƚŝǀŝƚĠƐ ƉƌĠĐĠĚĞŶƚĞƐ ƋƵĞ ƉůƵƐŝĞƵƌƐ ŵĠƚŚŽĚĞƐ ƉŽƵǀĂŝĞŶƚ ġƚƌĞ ĞŶǀŝƐĂŐĠĞƐ͘ ĂŶƐ ĐŚĂƋƵĞ ƐĠƌŝĞ͕ ƵƚŝůŝƐĞ ĚĞƐ ŵĠƚŚŽĚĞƐ ĚŝĨĨĠƌĞŶƚĞƐ ƉŽƵƌ ũƵƐƚŝĨŝĞƌ ĐŚĂĐƵŶĞ ĚĞƐ ƉƌŽƉŽƐŝƚŝŽŶƐ͘

ĂͿ ϰϳϰ ĞƐƚ ĚŝǀŝƐŝďůĞ ƉĂƌ ϯ ĐĂƌ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϱϵϰ ĞƐƚ ĚŝǀŝƐŝďůĞ ƉĂƌ ϯ ĐĂƌ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Ϯϳ ϬϬϬ ĞƐƚ ĚŝǀŝƐŝďůĞ ƉĂƌ ϯ ĐĂƌ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ďͿ ϰϱϵ ĞƐƚ ĚŝǀŝƐŝďůĞ ƉĂƌ ϵ ĐĂƌ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϱϰ ϳϴϯ ĞƐƚ ĚŝǀŝƐŝďůĞ ƉĂƌ ϵ ĐĂƌ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ĐͿ ϯϲ ĞƐƚ ĚŝǀŝƐŝďůĞ ƉĂƌ ϰ ĐĂƌ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϳϮϰ ĞƐƚ ĚŝǀŝƐŝďůĞ ƉĂƌ ϰ ĐĂƌ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϳϵϲ ĞƐƚ ĚŝǀŝƐŝďůĞ ƉĂƌ ϰ ĐĂƌ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ĚͿ ϰϬϴ ĞƐƚ ĚŝǀŝƐŝďůĞ ƉĂƌ ϴ ĐĂƌ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϳϴϯϮ ĞƐƚ ĚŝǀŝƐŝďůĞ ƉĂƌ ϴ ĐĂƌ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϱϲϬ ĞƐƚ ĚŝǀŝƐŝďůĞ ƉĂƌ ϴ ĐĂƌ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

p.37 D3

ACTIVITÉS

Chapitre 2 Diviseurs et multiples

ĐƚŝǀŝƚĠ ϳ ĠĐŽŵƉŽƐŝƚŝŽŶ ĚΖƵŶ ŶŽŵďƌĞ ĞŶ ƵŶ produit de facteurs premiers 1 ĂͿ Ŷ Ŷ͛ƵƟ ůŝƐĂŶƚ ƋƵĞ ĚĞƐ ŶŽŵďƌĞƐ ŶĂƚƵƌĞůƐ͕ ĚĠĐŽŵƉŽƐĞ ůĞ ŶŽŵďƌĞ ϭϮ͙ ĞŶ ƵŶĞ ƐŽŵŵĞ ĚĞ ĚĞƵǆ ƚĞƌŵĞƐ ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ĞŶ ƵŶĞ Ěŝī ĠƌĞŶĐĞ ĚĞ ĚĞƵǆ ƚĞƌŵĞƐ ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ĞŶ ƵŶ ƉƌŽĚƵŝƚ ĚĞ ĚĞƵǆ ĨĂĐƚĞƵƌƐ ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ĞŶ ƵŶ ƉƌŽĚƵŝƚ ĚĞ ƚƌŽŝƐ ĨĂĐƚĞƵƌƐ Ěŝī ĠƌĞŶƚƐ ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ĞŶ ƵŶ ƉƌŽĚƵŝƚ ĚĞ ƚƌŽŝƐ ĨĂĐƚĞƵƌƐ ƉƌĞŵŝĞƌƐ ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ďͿ ĂŶƐ ƋƵĞů ĐĂƐ ůĂ ƌĠƉŽŶƐĞ ĞƐƚͲĞůůĞ ƵŶŝƋƵĞ ͍ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

2 EŽƚĞ ůĂ ĨĂĐƚŽƌŝƐĂƟ ŽŶ ƉƌĞŵŝğƌĞ ĚĞƐ ŶŽŵďƌĞƐ ĐŝͲĚĞƐƐŽƵƐ͘ ϱϬ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϳϱ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϯϮ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϭϰϬ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϯϲϬ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ 3 ĠƚĞƌŵŝŶĞ ůĂ ĨĂĐƚŽƌŝƐĂƟ ŽŶ ƉƌĞŵŝğƌĞ ĚĞƐ ŶŽŵďƌĞƐ ƉƌŽƉŽƐĠƐ ĞŶ ƵƟ ůŝƐĂŶƚ ůĂ ĚŝƐƉŽƐŝƟ ŽŶ ƉƌĂƟ ƋƵĞ ĞŶ ĐŽůŽŶŶĞƐ͘ ϭϬϴ

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϭϯϱ

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϭϰϰ

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϭϱϬ

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

p.38 E1

ϭϬϴ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϭϰϰ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϭϯϱ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϭϱϬ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ 41

ACTIVITÉS 4

Chapitre 2 Diviseurs et multiples

ZĞŶĚƐ ŝƌƌĠĚƵĐƟ ďůĞƐ ůĞƐ ĨƌĂĐƟ ŽŶƐ ƐƵŝǀĂŶƚĞƐ ĞŶ ƉĂƐƐĂŶƚ ƉĂƌ ůĂ ĚĠĐŽŵƉŽƐŝƟ ŽŶ ĞŶ ĨĂĐƚĞƵƌƐ ƉƌĞŵŝĞƌƐ͘ 108 с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ 150

150 с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ 135 144 с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ 108

ĐƚŝǀŝƚĠ ϴ Puissances d’un nombre 1 ĂͿ >ŽůĂ Ğī ĞĐƚƵĞ Ɛŝǆ ƉůŝĂŐĞƐ ƐƵĐĐĞƐƐŝĨƐ Ě͛ƵŶĞ ŵġŵĞ ĨĞƵŝůůĞ ĚĞ ƉĂƉŝĞƌ͕ ĐŽŵŵĞ ůĞ ŵŽŶƚƌĞ ů͛ŝůůƵƐƚƌĂƟ ŽŶ ĐŝͲĚĞƐƐŽƵƐ͘

;ϭͿ ŽŵƉůğƚĞ ůĞ ƚĂďůĞĂƵ ĐŝͲĚĞƐƐŽƵƐ ĞŶ ĚĠƚĞƌŵŝŶĂŶƚ ůĞ ŶŽŵďƌĞ ĚĞ ĐŽƵĐŚĞƐ ĚĞ ƉĂƉŝĞƌ ŽďƚĞŶƵĞƐ ĞŶ ĨŽŶĐƟ ŽŶ ĚƵ ŶŽŵďƌĞ ĚĞ ƉůŝĂŐĞƐ ƌĠĂůŝƐĠƐ͘ EŽŵďƌĞ ĚĞ ƉůŝĂŐĞƐ

EŽŵďƌĞ ĚĞ ĐŽƵĐŚĞƐ ĚĞ ƉĂƉŝĞƌ ;ϮͿ ĐƌŝƐ ƐŽƵƐ ůĂ ĨŽƌŵĞ Ě͛ƵŶ ƉƌŽĚƵŝƚ ĚĞ ĨĂĐƚĞƵƌƐ ĠŐĂƵǆ ůĞ ĐĂůĐƵů ƋƵŝ ƚĞ ƉĞƌŵĞƚ ĚĞ ƚƌŽƵǀĞƌ ůĞ ŶŽŵďƌĞ ĚĞ ĐŽƵĐŚĞƐ ĚĞ ƉĂƉŝĞƌ ŽďƚĞŶƵĞƐ ĂƉƌğƐ ĂǀŽŝƌ ƌĠĂůŝƐĠ Ɛŝǆ ƉůŝĂŐĞƐ ƐƵĐĐĞƐƐŝĨƐ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ďͿ ͨ ƚ Ɛ͛ŝů ĠƚĂŝƚ ƉŽƐƐŝďůĞ ĚĞ ƉůŝĞƌ͕ ƐƵĐĐĞƐƐŝǀĞŵĞŶƚ͕ ƵŶĞ ĨĞƵŝůůĞ ĚĞ ƉĂƉŝĞƌ ĞŶ ĚĞƵǆ͕ ĂƵƚĂŶƚ ĚĞ ĨŽŝƐ ƋƵĞ ů͛ŽŶ ǀĞƵƚ ͙ ͩ͘ ;ϭͿ ĐƌŝƐ ƐŽƵƐ ůĂ ĨŽƌŵĞ Ě͛ƵŶ ƉƌŽĚƵŝƚ ĚĞ ĨĂĐƚĞƵƌƐ ĠŐĂƵǆ ůĞ ĐĂůĐƵů ƋƵŝ ƚĞ ƉĞƌŵĞƩ ƌĂŝƚ ĚĞ ƚƌŽƵǀĞƌ ůĞ ŶŽŵďƌĞ ĚĞ ĐŽƵĐŚĞƐ ĚĞ ƉĂƉŝĞƌ ŽďƚĞŶƵĞƐ ĂƉƌğƐ ĂǀŽŝƌ ƌĠĂůŝƐĠ Ěŝǆ ƉůŝĂŐĞƐ ƐƵĐĐĞƐƐŝĨƐ Ğƚ Ğī ĞĐƚƵĞͲůĞ ă ů͛ĂŝĚĞ ĚĞ ƚĂ ĐĂůĐƵůĂƚƌŝĐĞ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;ϮͿ >ŽƌƐƋƵĞ ůĞƐ ĨĂĐƚĞƵƌƐ Ě͛ƵŶ ƉƌŽĚƵŝƚ ƐŽŶƚ ĠŐĂƵǆ͕ ŽŶ ĐŽŶǀŝĞŶƚ Ě͛ĠĐƌŝƌĞ ĐĞ ƉƌŽĚƵŝƚ ƐŽƵƐ ƵŶĞ ĨŽƌŵĞ ĂďƌĠŐĠĞ ͗ ƵŶĞ ƉƵŝƐƐĂŶĐĞ͘

ĐƌŝƐ ůĞ ƉƌŽĚƵŝƚ ĐŝͲĚĞƐƐƵƐ ƐŽƵƐ ůĂ ĨŽƌŵĞ Ě͛ƵŶĞ ƉƵŝƐƐĂŶĐĞ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

p.38 &ϭͳϮ

ACTIVITÉS

Chapitre 2 Diviseurs et multiples

;ϯͿ YƵĞůůĞ ƚŽƵĐŚĞ ĚĞ ƚĂ ĐĂůĐƵůĂƚƌŝĐĞ ƚĞ ƉĞƌŵĞƚ Ě͛Ğī ĞĐƚƵĞƌ ůĞ ĐĂůĐƵů Ě͛ƵŶĞ ƉƵŝƐƐĂŶĐĞ ͍ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ů͛ĂŝĚĞ ĚĞ ƚĂ ĐĂůĐƵůĂƚƌŝĐĞ͕ ĚĠƚĞƌŵŝŶĞ ůĞ ŶŽŵďƌĞ ĚĞ ĐŽƵĐŚĞƐ ĚĞ ƉĂƉŝĞƌ ƋƵĞ ů͛ŽŶ ŽďƟ ĞŶĚƌĂŝƚ Ɛŝ ů͛ŽŶ ƉŽƵǀĂŝƚ ƌĠĂůŝƐĞƌ ϯϬ ƉůŝĂŐĞƐ ƐƵĐĐĞƐƐŝĨƐ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

2 ĐƌŝƐ ůĞƐ ƉƌŽĚƵŝƚƐ ƐƵŝǀĂŶƚƐ ĞŶ ƵƟ ůŝƐĂŶƚ ĚĞƐ ƉƵŝƐƐĂŶĐĞƐ͘ Ϯ . Ϯ . Ϯ . Ϯ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Ϯ . Ϯ . Ϯ . ϯ . ϯ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Ϯ . Ϯ . Ϯ . Ϯ . Ϯ . Ϯ . ϯ . ϯ . ϯ . ϯ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϯ . ϯ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Ϯ . ϯ . ϯ . ϯ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Ϯ . ϱ . ϱ . ϱ . ϱ . ϳ . ϳ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϱ . ϱ . ϱ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Ϯ . ϱ . ϱ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Ϯ . Ϯ . Ϯ . ϱ . ϱ . ϳ . ϳ . ϳ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

3 ƐƐŽĐŝĞ ĐŚĂƋƵĞ ƉŚƌĂƐĞ ă ƐŽŶ ĞǆƉƌĞƐƐŝŽŶ ŵĂƚŚĠŵĂƟ ƋƵĞ͘ ϯ ĂƵ ĐĂƌƌĠ •

• ϱϯ •

>Ă ĐŝŶƋƵŝğŵĞ ƉƵŝƐƐĂŶĐĞ ĚĞ ϯ •

• >Ğ ĐĂƌƌĠ ĚĞ ϯ • Ϯ ĂƵ ĐƵďĞ

Ϯϯ

ϱ ĞǆƉŽƐĂŶƚ ϯ •

•

• ϯ ĞǆƉŽƐĂŶƚ ϱ

Ϯ ĞǆƉŽƐĂŶƚ ϯ •

• ϯϮ •

• >Ğ ĐƵďĞ ĚĞ Ϯ

>Ğ ĐƵďĞ ĚĞ ϱ • p.39 F3

ϯ ĞǆƉŽƐĂŶƚ Ϯ •

• ϯ ă ůĂ ĐŝŶƋƵŝğŵĞ ƉƵŝƐƐĂŶĐĞ •

ϯϱ

•

• ϱ ĂƵ ĐƵďĞ

4 >ĞƐ ƉƌŽĚƵŝƚƐ ĐŝͲĚĞƐƐŽƵƐ ƐŽŶƚ ůĞƐ ƌĠƐƵůƚĂƚƐ ĚĞ ůĂ ĚĠĐŽŵƉŽƐŝƟ ŽŶ ĚĞ ŶŽŵďƌĞƐ ĞŶ ƉƌŽĚƵŝƚƐ ĚĞ ĨĂĐƚĞƵƌƐ ƉƌĞŵŝĞƌƐ͘ YƵĞůƐ ƐŽŶƚ ĐĞƐ ŶŽŵďƌĞƐ ͍ Ϯϯ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϳϮ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϱϮ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϯϰ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϯϯ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Ϯϱ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϯϮ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

p.39 F4

Ϯϰ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϱϯ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϮϮ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Ϯϲ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϱϰ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϭϭϮ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Ϯϯ . ϱ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϯϮ . ϳ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Ϯϱ . ϱ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϮϮ . ϯϮ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Ϯϰ . ϭϭ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Ϯϱ . ϯϮ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Ϯϯ . ϱϯ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϱϮ . ϳ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ACTIVITÉS 5

Chapitre 2 Diviseurs et multiples

ĂůĐƵůĞ͘ ϱ н ϯ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Ϯϰ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϯ н ϯ н ϯ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϭϬϮ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϱϯ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϰϮ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϯ . ϯ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϭϬ . Ϯ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϱ . ϯ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϰ н Ϯ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϯ . ϯ . ϯ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϭϬ н Ϯ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϯϱ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Ϯ . ϰ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϯ . Ϯ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϭϬ . ϭϬ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϱ ʹ ϯ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϰ . Ϯ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϯϯ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϮϭϬ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ĐƚŝǀŝƚĠ ϵ Puissances de 10 1 hŶĞ ƵƐŝŶĞ ĚĞ ƉŽŵƉĂŐĞ Ğƚ ĚĞ ƚƌĂŝƚĞŵĞŶƚ ĚĞƐ ĞĂƵǆ ƵƐĠĞƐ ƉƌŽĚƵŝƚ ϭϬϬ ϬϬϬ ŵϯ Ě͛ĞĂƵ ƉŽƚĂďůĞ ƉĂƌ ũŽƵƌ͘ ĂͿ ŽŵďŝĞŶ ĚĞ ůŝƚƌĞƐ Ě͛ĞĂƵ ƉŽƚĂďůĞ ů͛ƵƐŝŶĞ ƉƌŽĚƵŝƚͲĞůůĞ ĞŶ ƵŶ ũŽƵƌ ͍ ĞŶ ϭϬ ũŽƵƌƐ ͍ ĞŶ ϭϬϬ ũŽƵƌƐ ͍ ĐƌŝƐ ĐŚĂƋƵĞ ƌĠƐƵůƚĂƚ ƐŽƵƐ ůĂ ĨŽƌŵĞ Ě͛ƵŶĞ ƉƵŝƐƐĂŶĐĞ ĚĞ ϭϬ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ďͿ ŽŵďŝĞŶ ĚĞ ůŝƚƌĞƐ Ě͛ĞĂƵ ƉŽƚĂďůĞ ů͛ƵƐŝŶĞ ƉƌŽĚƵŝƚͲĞůůĞ ĞŶ ƵŶĞ ƐĞŵĂŝŶĞ ͍ ĞŶ ƵŶ ĂŶ ͍ ĐƌŝƐ ĐŚĂƋƵĞ ƌĠƐƵůƚĂƚ ƐŽƵƐ ůĂ ĨŽƌŵĞ Ě͛ƵŶ ƉƌŽĚƵŝƚ Ě͛ƵŶ ŶŽŵďƌĞ ŶĂƚƵƌĞů ůĞ ƉůƵƐ ƉĞƟ ƚ ƉŽƐƐŝďůĞ Ğƚ Ě͛ƵŶĞ ƉƵŝƐƐĂŶĐĞ ĚĞ ϭϬ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

p.39 F5 ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

2 >ĞƐ ƉƵŝƐƐĂŶĐĞƐ ĚĞ ϭϬ ƐŽŶƚ ƐŽƵǀĞŶƚ ƵƟ ůŝƐĠĞƐ ƉŽƵƌ ĠĐƌŝƌĞ ĚĞ ŐƌĂŶĚƐ ŶŽŵďƌĞƐ ƐĂŶƐ ĚĞǀŽŝƌ ĂůŝŐŶĞƌ ůĞƐ ǌĠƌŽƐ͘ ĂͿ ĐƌŝƐ ĐŚĂƋƵĞ ŶŽŵďƌĞ ĐŝͲĚĞƐƐŽƵƐ ƐŽƵƐ ůĂ ĨŽƌŵĞ Ě͛ƵŶ ƉƌŽĚƵŝƚ Ě͛ƵŶ ŶŽŵďƌĞ ŶĂƚƵƌĞů ůĞ ƉůƵƐ ƉĞƟ ƚ ƉŽƐƐŝďůĞ Ğƚ Ě͛ƵŶĞ ƉƵŝƐƐĂŶĐĞ ĚĞ ϭϬ͘ ͻ >Ğ ^ŽůĞŝů ĞƐƚ ă ĞŶǀŝƌŽŶ ϭϱϬ ϬϬϬ ϬϬϬ ĚĞ Ŭŵ ĚĞ ůĂ dĞƌƌĞ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ͻ >Ă >ƵŶĞ ƐĞ ƚƌŽƵǀĞ ă ĞŶǀŝƌŽŶ ϰϬϬ ϬϬϬ Ŭŵ ĚĞ ůĂ dĞƌƌĞ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ͻ EŽƚƌĞ 'ĂůĂǆŝĞ ĐŽŵƉŽƌƚĞ ĞŶǀŝƌŽŶ ϯϬ ϬϬϬ ϬϬϬ ϬϬϬ Ě͛ĠƚŽŝůĞƐ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ͻ >Ă ŵĂƐƐĞ ĚĞ ůĂ dĞƌƌĞ ĞƐƚ ĚĞ ϱ ϵϳϳ ϬϬϬ ϬϬϬ ϬϬϬ ϬϬϬ ϬϬϬ ϬϬϬ ϬϬϬ ŬŐ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ACTIVITÉS

Chapitre 2 Diviseurs et multiples

ďͿ WŽƵƌ ĐŚĂĐƵŶĞ ĚĞƐ ƐŝƚƵĂƟ ŽŶƐ ĚĠĐƌŝƚĞƐ ĐŝͲĚĞƐƐŽƵƐ͕ ĠĐƌŝƐ ůĞ ŶŽŵďƌĞ ŶĂƚƵƌĞů ĐŽƌƌĞƐƉŽŶĚĂŶƚ͘ ͻ Ŷ ϮϬϭϲ͕ ůĞ ŶŽŵďƌĞ ĚĞ ǀŝƐŝƚĞƵƌƐ ƋƵŝ ƐĞ ƐŽŶƚ ƌĞŶĚƵƐ ĚĂŶƐ ůĞ ƉĂƌĐ ĚĞ ŝƐŶĞǇůĂŶĚ WĂƌŝƐ ĞƐƚ ĚĞ ϭϯ͕ϰ . ϭϬϲ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ͻ Ŷ ŵĂƌƐ ϮϬϭϴ͕ ůĞƐ ũŽƵƌŶĂƵǆ ƉƵďůŝĞŶƚ ƋƵĞ :Ğī ĞǌŽƐ͕ W ' Ě͛ ŵĂǌŽŶ͕ ƉŽƐƐğĚĞ ůĂ ƉůƵƐ ŐƌŽƐƐĞ ĨŽƌƚƵŶĞ ŵŽŶĚŝĂůĞ͘ ĞůůĞͲĐŝ ĞƐƚ ĞƐƟ ŵĠĞ ă ϭϭϮ . ϭϬϵ ĚŽůůĂƌƐ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ͻ Ƶ ƐŝğĐůĞ ĚĞƌŶŝĞƌ͕ ůΖĞŶƚŽŵŽůŽŐŝƐƚĞ ͘ ͘ tŝůůŝĂŵƐ ĞƐƟ ŵĂ ă ϭϬϭϲ ůĞ ŶŽŵďƌĞ ĚĞ ĨŽƵƌŵŝƐ ĞŶ ǀŝĞ ĚĂŶƐ ůĞ ŵŽŶĚĞ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ͻ >Ă ƋƵĂŶƟ ƚĠ Ě͛ĞĂƵ ƉƌĠƐĞŶƚĞ ƐƵƌ ƚĞƌƌĞ ĞƐƚ ĞƐƟ ŵĠĞ ă ϭ͕ϯϴϲ . ϭϬϭϴ ŵϯ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

3 ĂůĐƵůĞ ůĞ ǀŽůƵŵĞ Ě͛Ăŝƌ ƌĞƐƉŝƌĠ ƉĂƌ ƵŶ ŵŝůůŝĂƌĚ Ě͛ŝŶĚŝǀŝĚƵƐ͕ ĞŶ ƵŶĞ ŚĞƵƌĞ͕ ƐĂĐŚĂŶƚ ƋƵ͛ƵŶ ġƚƌĞ ŚƵŵĂŝŶ ƌĞƐƉŝƌĞ ĞŶ ŵŽǇĞŶŶĞ Ěŝǆ ůŝƚƌĞƐ Ě͛Ăŝƌ ƉĂƌ ŵŝŶƵƚĞ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

4 ŶƚŽƵƌĞ ůĂ ǀĂůĞƵƌ ůĂ ƉůƵƐ ƉƌŽĐŚĞ ĚƵ ƌĠƐƵůƚĂƚ͘ sĠƌŝĮ Ğ ă ů͛ĂŝĚĞ ĚĞ ƚĂ ĐĂůĐƵůĂƚƌŝĐĞ͘ ϵϵϳϮ . ϭϬϭϮ

ϭϬϳ

ϭϬϱ

ϭϬϵ

ϭϬϳ ϬϮϰ . ϵϳϰϬ

ϭϬϴ

ϭϬϵ

ϭϬϳ

ϱϬϮϭ . ϭϵϬ

ϭϬϰ

ϭϬϲ

ϭϬϱ

ϴϬϮϯ . ϭϮϰ ϵϮϭ

ϭϬϴ

ϭϬϭϭ

ϭϬϵ

Ϯϰϵϵ . ϰϬϰϬ

ϭϬϲ

ϭϬϳ

ϭϬϴ

ĐƚŝǀŝƚĠ ϭϬ Priorités des opérations 1 ī ĞĐƚƵĞ ůĞƐ ĐĂůĐƵůƐ ĂǀĞĐ ƉĂƌĞŶƚŚğƐĞƐ ĞŶ ƵƟ ůŝƐĂŶƚ ůĞƐ ƉƌŝŽƌŝƚĠƐ ĚĞƐ ŽƉĠƌĂƟ ŽŶƐ ǀƵĞ ĚĂŶƐ ůĞ ĐŚĂƉŝƚƌĞ ϭ͘ ī ĞĐƚƵĞ ĞŶƐƵŝƚĞ͕ ă ů͛ĂŝĚĞ ĚĞ ůĂ ĐĂůĐƵůĂƚƌŝĐĞ ƐĐŝĞŶƟ Į ƋƵĞ͕ ůĞƐ ĐĂůĐƵůƐ ƐĂŶƐ ŝŶƚƌŽĚƵŝƌĞ ůĞƐ ƉĂƌĞŶƚŚğƐĞƐ͘ ƚ ĞŶĮ Ŷ͕ ĐŽŵƉĂƌĞ ůĞƐ ƌĠƐƵůƚĂƚƐ ŽďƚĞŶƵƐ͘ ĂůĐƵů ĂǀĞĐ ƉĂƌĞŶƚŚğƐĞƐ ;ƌğŐůĞƐ ĚĞ ƉƌŝŽƌŝƚĠͿ

ŽŵƉůğƚĞ ƉĂƌ с ŽƵ т

ĂůĐƵů ƐĂŶƐ ƉĂƌĞŶƚŚğƐĞ ;ĐĂůĐƵůĂƚƌŝĐĞͿ

ϯ . ;ϱϸͿ

ϯ . ϱϸ

;ϯ . ϱͿϸ

ϯ . ϱϸ

;ϯ н ϱͿϸ

ϯ н ϱϸ

p.40 G

ACTIVITÉS 2

Chapitre 2 Diviseurs et multiples

ĂůĐƵůĞ ĞŶ ƵƟ ůŝƐĂŶƚ ůĞƐ ƉƌŝŽƌŝƚĠƐ ĚĞƐ ŽƉĠƌĂƟ ŽŶƐ͘ ^ŽƵůŝŐŶĞ ůĞ ĐĂůĐƵů ƉƌŝŽƌŝƚĂŝƌĞ ă ĐŚĂƋƵĞ ĠƚĂƉĞ͘ ;Ϯ н ϯͿϮ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Ϯ . ϱϮ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Ϯ н ϯϮ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;Ϯ . ϱͿϮ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϭϬϮ ʹ ϰ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;ϭϬ ʹ ϰͿϮ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϱ н ϯϮ . Ϯ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ;ϱ н ϯͿϮ . Ϯ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϱ н ;ϯ . ϮͿϮ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ;ϱ н ϯϮͿ . Ϯ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϭϬϮ ʹ ϲ . Ϯ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ;ϭϬ ʹ ϲͿϮ . Ϯ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϭϬϮ н ϲ ͗ Ϯ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ;ϭϬ ʹ ϲͿϮ ͗ Ϯ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ;ϯ н ϰͿϮ . Ϯ н ϱ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϯ н ϰϮ . Ϯ н ϱ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϯ н ;ϰ . ϮͿϮ н ϱ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϯ н ϰϮ . ;Ϯ н ϱͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ;ϰ н ϲͿϮ . ϯ ʹ ϭ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϰ н ϲϮ . ϯ ʹ ϭ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϰ н ;ϲ ͗ ϯͿϮ ʹ ϭ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϰ н ϲϮ ͗ ;ϯ ʹ ϭͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ĐƚŝǀŝƚĠ ϭϭ Factorisation première d’un nombre ŶĂƚƵƌĞů Ğƚ ĚŝǀŝƐĞƵƌƐ 1 >Ğ ŶŽŵďƌĞ ϭϰϰ ƉŽƐƐğĚĞ ƵŶ ŐƌĂŶĚ ŶŽŵďƌĞ ĚĞ ĚŝǀŝƐĞƵƌƐ ƋƵ͛ŝů ĞƐƚ Ěŝĸ ĐŝůĞ ĚĞ ƚƌŽƵǀĞƌ ƐĂŶƐ ĞŶ ŽƵďůŝĞƌ͘ sŽŝĐŝ ĚĞƵǆ ƚĞĐŚŶŝƋƵĞƐ ƋƵŝ ƚĞ ƉĞƌŵĞƩ ƌŽŶƚ ĚĞ ůĞƐ ĚĠƚĞƌŵŝŶĞƌ ƌĂƉŝĚĞŵĞŶƚ ă ƉĂƌƟ ƌ ĚĞ ƐĂ ĨĂĐƚŽƌŝƐĂƟ ŽŶ ƉƌĞŵŝğƌĞ͘ 46

ACTIVITÉS

Chapitre 2 Diviseurs et multiples

ĂͿ hƟ ůŝƐĂƟ ŽŶ Ě͛ƵŶ ĚŝĂŐƌĂŵŵĞ ĞŶ ĂƌďƌĞ ĠƚĞƌŵŝŶĞ ůĂ ĨĂĐƚŽƌŝƐĂƟ ŽŶ ƉƌĞŵŝğƌĞ ĚĞ ϭϰϰ Ğƚ ĐŽŵƉůğƚĞ ůĞ ͨ ĚŝĂŐƌĂŵŵĞ ĞŶ ĂƌďƌĞ ͩ ĐŝͲ ĚĞƐƐŽƵƐ͘ >ĞƐ ĚŝǀŝƐĞƵƌƐ ĚĞ Ϯϰ ;ϭϲͿ

>ĞƐ ĚŝǀŝƐĞƵƌƐ ĚĞ ϯϮ ;ϵͿ

>ĞƐ ĚŝǀŝƐĞƵƌƐ ĚĞ ϭϰϰ

ϭ . ϭ с ϭ

ϭ . ϯ с ϯ

ϭ . ϵ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Ϯ . ϭ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Ϯ . ϯ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϭϰϰ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϭϰϰ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϭϰϰ

ϭϲ

ďͿ hƟ ůŝƐĂƟ ŽŶ Ě͛ƵŶ ƚĂďůĞĂƵ ă ĚŽƵďůĞ ĞŶƚƌĠĞ͘ ŽŵƉůğƚĞ ůĞ ƚĂďůĞĂƵ ĐŝͲĚĞƐƐŽƵƐ͘ ഩ>ĞƐ ĚŝǀŝƐĞƵƌƐ ĚĞ Ϯϰ .

1 3 9 >ĞƐ ĚŝǀŝƐĞƵƌƐ ĚĞ ϯϮ

ഩ>ĞƐ ĚŝǀŝƐĞƵƌƐ ĚĞ ϭϰϰ

ĐͿ ŽŵƉůğƚĞ ůΖĞŶƐĞŵďůĞ ĐŝͲĚĞƐƐŽƵƐ͘ Ěŝǀ ϭϰϰ с ΂ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ACTIVITÉS

Chapitre 2 Diviseurs et multiples

ĚͿ ĠƚĞƌŵŝŶĞ ůĞ ŶŽŵďƌĞ ĚĞ ĚŝǀŝƐĞƵƌƐ ŶĂƚƵƌĞůƐ ĚĞƐ ŶŽŵďƌĞƐ ĐŝͲĚĞƐƐŽƵƐ͘ EŽŵďƌĞ ĚĞ ĚŝǀŝƐĞƵƌƐ ĚĞ Ϯϰ ;ϭϲͿ ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ EŽŵďƌĞ ĚĞ ĚŝǀŝƐĞƵƌƐ ĚĞ ϯϮ ;ϵͿ ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

EŽŵďƌĞ ĚĞ ĚŝǀŝƐĞƵƌƐ ĚĞ Ϯϰ . ϯϮ ;ϭϰϰͿ ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ 2 ĂͿ ŽŵƉůğƚĞ ůĞ ͨ ĚŝĂŐƌĂŵŵĞ ĞŶ ĂƌďƌĞ ͩ ĐŝͲĚĞƐƐŽƵƐ ƐĂĐŚĂŶƚ ƋƵĞ ϭϮϬ с Ϯϯ . ϯ . ϱ >ĞƐ ĚŝǀŝƐĞƵƌƐ ĚĞ Ϯϯ ;ϴͿ >ĞƐ ĚŝǀŝƐĞƵƌƐ ĚĞ ϯ

>ĞƐ ĚŝǀŝƐĞƵƌƐ ĚĞ ϱ

>ĞƐ ĚŝǀŝƐĞƵƌƐ ĚĞ ϭϮϬ

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ďͿ ŽŵƉůğƚĞ ůΖĞŶƐĞŵďůĞ ĐŝͲĚĞƐƐŽƵƐ͘ Ěŝǀ ϭϮϬ с ΂ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ĐͿ ĠƚĞƌŵŝŶĞ ůĞ ŶŽŵďƌĞ ĚĞ ĚŝǀŝƐĞƵƌƐ ŶĂƚƵƌĞůƐ ĚĞƐ ŶŽŵďƌĞƐ ĐŝͲĚĞƐƐŽƵƐ͘ EŽŵďƌĞ ĚĞ ĚŝǀŝƐĞƵƌƐ ĚĞ Ϯϯ ;ϴͿ ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ EŽŵďƌĞ ĚĞ ĚŝǀŝƐĞƵƌƐ ĚĞ ϯ ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ EŽŵďƌĞ ĚĞ ĚŝǀŝƐĞƵƌƐ ĚĞ ϱ ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ EŽŵďƌĞ ĚĞ ĚŝǀŝƐĞƵƌƐ ĚĞ Ϯϯ . ϯ . ϱ ;ϭϮϬͿ ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ACTIVITÉS

Chapitre 2 Diviseurs et multiples

ĂͿ ŽŵƉůğƚĞ ůĞƐ ƚĂďůĞĂƵǆ ĐŝͲĚĞƐƐŽƵƐ͘ Nombre

&ĂĐƚŽƌŝƐĂƟ ŽŶ EŽŵďƌĞ ĚĞ ƉƌĞŵŝğƌĞ ĚŝǀŝƐĞƵƌƐ

Nombre

144

120

&ĂĐƚŽƌŝƐĂƟ ŽŶ EŽŵďƌĞ ĚĞ ƉƌĞŵŝğƌĞ ĚŝǀŝƐĞƵƌƐ

ďͿ WĞƵƚͲŽŶ͕ ă ƉĂƌƟ ƌ ĚĞ ůĂ ĨĂĐƚŽƌŝƐĂƟ ŽŶ ƉƌĞŵŝğƌĞ Ě͛ƵŶ ŶŽŵďƌĞ͕ ĚĠƚĞƌŵŝŶĞƌ ƐŽŶ ŶŽŵďƌĞ ĚĞ ĚŝǀŝƐĞƵƌƐ ͍ ǆƉůŝƋƵĞ ƚŽŶ ƉƌŽĐĠĚĠ ă ƉĂƌƟ ƌ ĚĞ ĚĞƵǆ ĞǆĞŵƉůĞƐ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

p.38 Ϯ

4 ĠƚĞƌŵŝŶĞ ůĞ ŶŽŵďƌĞ ĚĞ ĚŝǀŝƐĞƵƌƐ ŶĂƚƵƌĞůƐ ĚĞƐ ŶŽŵďƌĞƐ ĐŝͲĚĞƐƐŽƵƐ ĐŽŶŶĂŝƐƐĂŶƚ ůĞƵƌ ĨĂĐƚŽƌŝƐĂƟ ŽŶ ƉƌĞŵŝğƌĞ͘ EŽŵďƌĞ ĚĞ ĚŝǀŝƐĞƵƌƐ ĚĞ ϱϯ ;ϭϮϱͿ ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ EŽŵďƌĞ ĚĞ ĚŝǀŝƐĞƵƌƐ ĚĞ ϮϭϬ ;ϭϬϮϰͿ ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ EŽŵďƌĞ ĚĞ ĚŝǀŝƐĞƵƌƐ ĚĞ ϮϮ . ϯ . ϳ ;ϴϰͿ ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ EŽŵďƌĞ ĚĞ ĚŝǀŝƐĞƵƌƐ ĚĞ ϮϮ . ϱϮ ;ϭϬϬͿ ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ EŽŵďƌĞ ĚĞ ĚŝǀŝƐĞƵƌƐ ĚĞ Ϯϱ . ϱ ;ϭϲϬͿ ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ EŽŵďƌĞ ĚĞ ĚŝǀŝƐĞƵƌƐ ĚĞ ϮϮ . ϱϮ . ϳ ;ϳϬϬͿ ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ 5 ZĞĐŚĞƌĐŚĞ ĚĞ ůĂ ŵĂŶŝğƌĞ ůĂ ƉůƵƐ ĂĚĠƋƵĂƚĞ ůĞ ŶŽŵďƌĞ ĚĞ ĚŝǀŝƐĞƵƌƐ ĚĞ ϱϬϰ͕ ϮϬϬϬ Ğƚ ϮϭϬϬ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ACTIVITÉS

Chapitre 2 Diviseurs et multiples

ĐƚŝǀŝƚĠ ϭϮ Dénombrement 1 >ĞƐ ƐŽůŝĚĞƐ ĐŝͲĚĞƐƐŽƵƐ ŽŶƚ ĠƚĠ ƌĠĂůŝƐĠƐ ă ů͛ĂŝĚĞ ĚĞ ĐƵďĞƐ ĚĞ ŵġŵĞ ĚŝŵĞŶƐŝŽŶ͘ ĂͿ ĠƚĞƌŵŝŶĞ ůĞ ŶŽŵďƌĞ ĚĞ ĐƵďĞƐ ŶĠĐĞƐƐĂŝƌĞƐ ă ůĂ ĐŽŶƐƚƌƵĐƟ ŽŶ ĚĞ ĐŚĂĐƵŶ ĚĞ ĐĞƐ ƐŽůŝĚĞƐ͘ ^ŽůŝĚĞ ϭ ^ŽůŝĚĞ Ϯ ^ŽůŝĚĞ ϯ

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ďͿ ŽŵƉůğƚĞ ůĞ ƚĂďůĞĂƵ ĐŝͲĚĞƐƐŽƵƐ͘ EΣ ĚƵ ƐŽůŝĚĞ

250

EŽŵďƌĞ ĚĞ 2 >ĞƐ ŵŽŶƚĂŐĞƐ ĐŝͲĚĞƐƐŽƵƐ ŽŶƚ ĠƚĠ ƌĠĂůŝƐĠƐ ă ů͛ĂŝĚĞ ĚĞ ĐƵďĞƐ ĚĞ ŵġŵĞ ĚŝŵĞŶƐŝŽŶ͘ DŽŶƚĂŐĞ ϭ

DŽŶƚĂŐĞ Ϯ

DŽŶƚĂŐĞ ϯ

ĂͿ ŽŵƉůğƚĞ ůĞ ƚĂďůĞĂƵ ĐŝͲĚĞƐƐŽƵƐ͘ EΣ ĚƵ ŵŽŶƚĂŐĞ

EŽŵďƌĞ ĚĞ ďͿ ŽŵďŝĞŶ ĚĞ ĐƵďĞƐ ƐĞƌĂŝĞŶƚ ŶĠĐĞƐƐĂŝƌĞƐ ƉŽƵƌ ĐŽŶƐƚƌƵŝƌĞ ůĞ ͙ ϭϬĞ ŵŽŶƚĂŐĞ ͍ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϮϱĞ ŵŽŶƚĂŐĞ ͍ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϮϭϰĞ ŵŽŶƚĂŐĞ ͍ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ĐͿ YƵĞů ƐĞƌĂŝƚ ůĞ ƌĂŶŐ ĚƵ ŵŽŶƚĂŐĞ ĐŽŶƐƚƌƵŝƚ ĂǀĞĐ ͙ ϵϳϮ ĐƵďĞƐ ͍ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϯϰϱϵ ĐƵďĞƐ ͍ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϴϵϰ ĐƵďĞƐ ͍ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ĚͿ ƐƚͲŝů ƉŽƐƐŝďůĞ Ě͛ŽďƚĞŶŝƌ ƵŶ ŵŽŶƚĂŐĞ ĨŽƌŵĠ ĚĞ ͙ ϭϰϲϭ ĐƵďĞƐ ͍ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϳϯϮϮ ĐƵďĞƐ ͍ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϱϲϲϮ ĐƵďĞƐ ͍ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

3 >ĞƐ ƐŽůŝĚĞƐ ĐŝͲĚĞƐƐŽƵƐ ŽŶƚ ĠƚĠ ƌĠĂůŝƐĠƐ ă ů͛ĂŝĚĞ ĚĞ ĐƵďĞƐ ĚĞ ŵġŵĞ ĚŝŵĞŶƐŝŽŶ͘ ^ŽůŝĚĞ ϭ

^ŽůŝĚĞ Ϯ

^ŽůŝĚĞ ϯ

ĂͿ ŽŵƉůğƚĞ ůĞ ƚĂďůĞĂƵ ĐŝͲĚĞƐƐŽƵƐ͘ EΣ ĚƵ ƐŽůŝĚĞ

EŽŵďƌĞ ĚĞ ďͿ ĠƚĞƌŵŝŶĞ ůĞ ƌĂŶŐ ĚĞƐ ƐŽůŝĚĞƐ ĨŽƌŵĠƐ ĚĞ ϲϰ͕ ϲϮϱ Ğƚ ϭϬ ϬϬϬ ĐƵďĞƐ͘

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Chapitre 2 Diviseurs et multiples

EXERCICES COMPLÉMENTAIRES

Connaître 1

ŽŵƉůğƚĞ ůĞƐ ƉŚƌĂƐĞƐ ƐƵŝǀĂŶƚĞƐ ƉĂƌ ů͛ƵŶĞ͕ ĂƵ ŵŽŝŶƐ͕ ĚĞƐ ĞǆƉƌĞƐƐŝŽŶƐ ƋƵĞ ǀŽŝĐŝ ͗ ĞƐƚ ĚŝǀŝƐĞƵƌ ĚĞ͕ ĞƐƚ ŵƵůƚŝƉůĞ ĚĞ͕ ĞƐƚ ĚŝǀŝƐŝďůĞ ƉĂƌ͕ ĚŝǀŝƐĞ͘ ĂͿ ϲഩ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ഩϮϰ ďͿ ϴഩ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ഩϮϰ ϯϱഩ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϱ ϯഩ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϵ ϭϮഩ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ഩϰϴ ϮϬഩ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ഩϮϬ ϳϱഩ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ഩϮϱ Ϭഩ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ഩϭϱ ϭഩ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ഩϯϲ ϰϮഩ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϳ

YƵĞůƐ ƐŽŶƚ ůĞƐ ŶŽŵďƌĞƐ ĐŽŵƉƌŝƐ ĞŶƚƌĞ ϮϬ Ğƚ ϯϬ ƋƵŝ ŶĞ ƉŽƐƐğĚĞŶƚ ƋƵĞ Ϯ ĚŝǀŝƐĞƵƌƐ ͍

ŝƚĞ͙ ĂͿ ƵŶ ŶŽŵďƌĞ ƉƌĞŵŝĞƌ ƉĂŝƌ͘ ďͿ ĚĞƵǆ ŶŽŵďƌĞƐ ƉƌĞŵŝĞƌƐ ĐŽŶƐĠĐƵƚŝĨƐ͘ ĐͿ ĚĞƵǆ ŶŽŵďƌĞƐ ƉƌĞŵŝĞƌƐ ĚŽŶƚ ůĞ ƉƌŽĚƵŝƚ ĞƐƚ ϯϰ͘ ĚͿ ĚĞƵǆ ŶŽŵďƌĞƐ ƉƌĞŵŝĞƌƐ ĚŽŶƚ ůĂ ƐŽŵŵĞ ĞƐƚ ƵŶ ŶŽŵďƌĞ ƉƌĞŵŝĞƌ͘ ĞͿ ĚĞƵǆ ŶŽŵďƌĞƐ ƉƌĞŵŝĞƌƐ ĚŽŶƚ ůĂ ƐŽŵŵĞ Ŷ͛ĞƐƚ ƉĂƐ ƵŶ ŶŽŵďƌĞ ƉƌĞŵŝĞƌ͘ ĨͿ ĚĞƵǆ ŶŽŵďƌĞƐ ƉƌĞŵŝĞƌƐ ĚŽŶƚ ůĂ ƐŽŵŵĞ ĞƐƚ ƵŶ ŶŽŵďƌĞ ĐĂƌƌĠ͘

sƌĂŝ ŽƵ ĨĂƵǆ ͍ :ƵƐƚŝĨŝĞ͘ ĂͿ dŽƵƐ ůĞƐ ĚŝǀŝƐĞƵƌƐ ĚĞ ϰ ƐŽŶƚ ĚŝǀŝƐĞƵƌƐ ĚĞ ϮϬ͘ dŽƵƐ ůĞƐ ŵƵůƚŝƉůĞƐ ĚĞ ϱ ƐŽŶƚ ŵƵůƚŝƉůĞƐ ĚĞ ϭϬ͘ dŽƵƐ ůĞƐ ĚŝǀŝƐĞƵƌƐ ĚĞ ϵ ƐŽŶƚ ĚŝǀŝƐĞƵƌƐ ĚĞ Ϯϭ͘ dŽƵƐ ůĞƐ ŵƵůƚŝƉůĞƐ ĚĞ ϴ ƐŽŶƚ ŵƵůƚŝƉůĞƐ ĚĞ ϰ͘ dŽƵƐ ůĞƐ ĚŝǀŝƐĞƵƌƐ Ě͛ƵŶ ŶŽŵďƌĞ ƉĂŝƌ ƐŽŶƚ ƉĂŝƌƐ͘ ďͿ dŽƵƐ ůĞƐ ŵƵůƚŝƉůĞƐ ĚĞ ϲ ƐŽŶƚ ŵƵůƚŝƉůĞƐ ĚĞ ϯ͘ dŽƵƐ ůĞƐ ĚŝǀŝƐĞƵƌƐ ĚĞ ϭϱ ƐŽŶƚ ĚŝǀŝƐĞƵƌƐ ĚĞ ϰϱ͘ dŽƵƐ ůĞƐ ĚŝǀŝƐĞƵƌƐ ĚĞ ϭϮ ƐŽŶƚ ĚŝǀŝƐĞƵƌƐ ĚĞ ϰϮ͘ dŽƵƐ ůĞƐ ĚŝǀŝƐĞƵƌƐ ĚĞ ϯ ƐŽŶƚ ĚŝǀŝƐĞƵƌƐ ĚĞ ϭϱ͘ >Ă ƐŽŵŵĞ ĚĞ ĚĞƵǆ ŵƵůƚŝƉůĞƐ ĚĞ Ϯ ĞƐƚ ƚŽƵũŽƵƌƐ ƵŶ ŵƵůƚŝƉůĞ ĚĞ ϰ͘ ĐͿ ^ŝ ƵŶ ŶŽŵďƌĞ ĞƐƚ ĚŝǀŝƐŝďůĞ ƉĂƌ ϯ͕ ĂůŽƌƐ ŝů ĞƐƚ ĚŝǀŝƐŝďůĞ ƉĂƌ ϵ͘ ^ŝ ƵŶ ŶŽŵďƌĞ ĚŝǀŝƐĞ ϯϬ͕ ĂůŽƌƐ ŝů ĚŝǀŝƐĞ ϭϬ͘ ^ŝ ƵŶ ŶŽŵďƌĞ ĞƐƚ ĚŝǀŝƐŝďůĞ ƉĂƌ ϭϱ͕ ĂůŽƌƐ ŝů ĞƐƚ ĚŝǀŝƐŝďůĞ ƉĂƌ ϱ͘ ^ŝ ƵŶ ŶŽŵďƌĞ ĚŝǀŝƐĞ ϭϮ͕ ĂůŽƌƐ ŝů ĚŝǀŝƐĞ ƚŽƵƐ ůĞƐ ŵƵůƚŝƉůĞƐ ĚĞ ϭϮ͘ ^ŝ ƵŶ ŶŽŵďƌĞ ĞƐƚ ŵƵůƚŝƉůĞ ĚĞ ϮϬ͕ ĂůŽƌƐ ŝů ĞƐƚ ĚŝǀŝƐŝďůĞ ƉĂƌ Ϯ͘

:ƵƐƚŝĨŝĞ ůĞƐ ƉƌŽƉŽƐŝƚŝŽŶƐ ĐŝͲĚĞƐƐŽƵƐ ĞŶ ƵƚŝůŝƐĂŶƚ ƵŶĞ ĚĞƐ ƉƌŽƉƌŝĠƚĠƐ ĚĞ ůĂ ĚŝǀŝƐŝďŝůŝƚĠ͘ ŝǀŝƐŝďŝůŝƚĠ ĚĞ͙ ĂͿ ϯϱ ƉĂƌ ϳ ďͿ ϳϮϭ ƉĂƌ ϳ ĐͿ ϲϮϬ ƉĂƌ ϯϭ ĚͿ ϲϴϲ ƉĂƌ ϭϰ ϰϴ ƉĂƌ ϴ ϯϰϴ ƉĂƌ ϲ ϯϬϰ ƉĂƌ ϴ ϭϰϰϮ ƉĂƌ ϭϰ ϵϵ ƉĂƌ ϭϭ ϯϲϬϬ ƉĂƌ ϲ ϱϲϭ ƉĂƌ ϭϳ ϯϱϬ ƉĂƌ ϳ

:ƵƐƚŝĨŝĞ ĐŚĂƋƵĞ ƉƌŽƉŽƐŝƚŝŽŶ ĐŝͲĚĞƐƐŽƵƐ ĞŶ ƵƚŝůŝƐĂŶƚ Ě͛ĂďŽƌĚ ƵŶ ĐĂƌĂĐƚğƌĞ ĚĞ ĚŝǀŝƐŝďŝůŝƚĠ Ğƚ ĞŶƐƵŝƚĞ ƵŶĞ ĚĞƐ ƉƌŽƉƌŝĠƚĠƐ ĚĞ ůĂ ĚŝǀŝƐŝďŝůŝƚĠ͘ ĂͿ ϭϮϲ ĞƐƚ ĚŝǀŝƐŝďůĞ ƉĂƌ ϯ͘ ďͿ ϭϮϵ ĞƐƚ ĚŝǀŝƐŝďůĞ ƉĂƌ ϯ͘ ĐͿ ϵϮϳ ĞƐƚ ĚŝǀŝƐŝďůĞ ƉĂƌ ϵ͘ ϭϯϱ ĞƐƚ ĚŝǀŝƐŝďůĞ ƉĂƌ ϱ͘ ϰϳϱ ĞƐƚ ĚŝǀŝƐŝďůĞ ƉĂƌ Ϯϱ͘ ϭϴϳϱ ĞƐƚ ĚŝǀŝƐŝďůĞ ƉĂƌ ϭϮϱ͘ ϳϵϲ ĞƐƚ ĚŝǀŝƐŝďůĞ ƉĂƌ ϰ͘ ϰϵϮ ĞƐƚ ĚŝǀŝƐŝďůĞ ƉĂƌ ϰ͘ ϮϰϯϮ ĞƐƚ ĚŝǀŝƐŝďůĞ ƉĂƌ ϴ͘

EXERCICES COMPLÉMENTAIRES

Chapitre 2 Diviseurs et multiples

ƉƉůŝƋƵĞƌ 1

ĠƚĞƌŵŝŶĞ ƚŽƵƐ ůĞƐ ĚŝǀŝƐĞƵƌƐ ĚĞ ͗ഩĂͿ ϰϴ͕ ϲϬ͕ Ϯϳ͕ ϴϬ͕ ϭϮϱ

ZĞŶĚƐ ŝƌƌĠĚƵĐƚŝďůĞƐ ůĞƐ ĨƌĂĐƚŝŽŶƐ ƐƵŝǀĂŶƚĞƐ͘ 8 24 4 3 35 , , , , ĂͿ 12 36 16 27 5

ďͿ

ďͿ ϳϮ͕ ϮϬϬ͕ ϭϰϰ͕ ϲϬϬ͕ ϴϬϬ

15 56 150 160 120 , , , , 75 48 175 200 180

ĠƚĞƌŵŝŶĞ ůĞƐ ϭϮ ƉƌĞŵŝĞƌƐ ŵƵůƚŝƉůĞƐ ĚĞ ϲ͕ ϵ͕ ϭϭ͕ ϭϮ͕ ϭϱ Ğƚ ϮϬ͘

ĠƚĞƌŵŝŶĞ ůĞ W' ĚĞ ϱϲ Ğƚ ϵϲ͘

ŝƚĞ ůĞƐ ŶŽŵďƌĞƐ ŶĂƚƵƌĞůƐ ƋƵŝ ƐŽŶƚ ͘͘͘ ĂͿ ĚŝǀŝƐĞƵƌƐ ĚĞ ϰϮ͘ ďͿ ĚŝǀŝƐĞƵƌƐ ĚĞ ϯϬ͘ ŵƵůƚŝƉůĞƐ ĚĞ ϲ ŝŶĨĠƌŝĞƵƌƐ ă ϯϬ͘ ŵƵůƚŝƉůĞƐ ĚĞ ϰ ĐŽŵƉƌŝƐ ĞŶƚƌĞ ϯϬ Ğƚ ϰϬ͘ ĚŝǀŝƐĞƵƌƐ ŝŵƉĂŝƌƐ ĚĞ ϮϬ͘ ĚŝǀŝƐĞƵƌƐ ƉĂŝƌƐ ĚĞ ϱϬ͘ ŵƵůƚŝƉůĞƐ ƉĂŝƌƐ ĚĞ ϯ ŝŶĨĠƌŝĞƵƌƐ ă Ϯϱ͘ ŵƵůƚŝƉůĞƐ ŝŵƉĂŝƌƐ ĚĞ ϳ ŝŶĨĠƌŝĞƵƌƐ ă ϱϬ͘ ĚŝǀŝƐĞƵƌƐ ĚĞ ϲϰ ƐƵƉĠƌŝĞƵƌƐ ă ϭϬ͘ ĚŝǀŝƐĞƵƌƐ ĚĞ ϭϬϬ Ğƚ ŵƵůƚŝƉůĞƐ ĚĞ ϱ͘ ŽŵƉůğƚĞ ůĞ ƚĂďůĞĂƵ ƐƵŝǀĂŶƚ͕ ĞŶ ŶŽƚĂŶƚ ƵŶĞ ĐƌŽŝǆ ĂƵǆ ĞŶĚƌŽŝƚƐ ƋƵŝ ĐŽŶǀŝĞŶŶĞŶƚ͘

ŝǀŝƐŝďůĞ ƉĂƌ 324 715 225 360 796 750 900 525 5517 ϯϲ ϯϳϱ 7

125

WĂƌ ƋƵĞů;ƐͿ ĐŚŝĨĨƌĞ;ƐͿ ƉĞƵǆͲƚƵ ƌĞŵƉůĂĐĞƌ x ƉŽƵƌ ƋƵĞ ůĂ ƉŚƌĂƐĞ ƐŽŝƚ ĐŽƌƌĞĐƚĞ ͍ ĂͿ ϴϰxϲ ĞƐƚ ĚŝǀŝƐŝďůĞ ƉĂƌ Ϯ͘ ďͿ ϲϮϳx ĞƐƚ ĚŝǀŝƐŝďůĞ ƉĂƌ Ϯϱ͘ ϯϲϵx ĞƐƚ ĚŝǀŝƐŝďůĞ ƉĂƌ ϱ͘ ϴϳxϲ ĞƐƚ ĚŝǀŝƐŝďůĞ ƉĂƌ ϰ͘ ϰϳxϬ ĞƐƚ ĚŝǀŝƐŝďůĞ ƉĂƌ ϯ͘ ϵϯϮx ĞƐƚ ĚŝǀŝƐŝďůĞ ƉĂƌ ϰ͘ ϵϱxϳ ĞƐƚ ĚŝǀŝƐŝďůĞ ƉĂƌ ϯ͘ ϰϯϮ xϮϰ ĞƐƚ ĚŝǀŝƐŝďůĞ ƉĂƌ ϴ͘ ϳϯx ϲϮϯ ĞƐƚ ĚŝǀŝƐŝďůĞ ƉĂƌ ϵ͘ ϵϰϲ ϯxϱ ĞƐƚ ĚŝǀŝƐŝďůĞ ƉĂƌ ϭϮϱ͘ ĐͿ ϳϮxϱ ĞƐƚ ĚŝǀŝƐŝďůĞ ă ůĂ ĨŽŝƐ ƉĂƌ Ϯϱ Ğƚ ϯ͘ ϴxϰϬ ĞƐƚ ĚŝǀŝƐŝďůĞ ă ůĂ ĨŽŝƐ ƉĂƌ ϴ Ğƚ ϵ͘ ϰϲ xϳϱ ĞƐƚ ĚŝǀŝƐŝďůĞ ă ůĂ ĨŽŝƐ ƉĂƌ ϭϮϱ Ğƚ ϯ͘ ϰϵ ϳxϴ ĞƐƚ ĚŝǀŝƐŝďůĞ ă ůĂ ĨŽŝƐ ƉĂƌ ϰ Ğƚ ϯ͘ ϳϯϴ ϵϮx ĞƐƚ ĚŝǀŝƐŝďůĞ ă ůĂ ĨŽŝƐ ƉĂƌ Ϯ͕ ϱ Ğƚ ϵ͘ hƚŝůŝƐĞ ƵŶĞ ƐĞƵůĞ ĨŽŝƐ ůĞƐ ĐŚŝĨĨƌĞƐ ϱ͕ ϲ͕ ϳ Ğƚ ϵ ĚĞ ŵĂŶŝğƌĞ ă ĨŽƌŵĞƌ ƵŶ ŶŽŵďƌĞ ĚĞ ϰ ĐŚŝĨĨƌĞƐ ƌĠƉŽŶĚĂŶƚ ĂƵǆ ĐƌŝƚğƌĞƐ ĠŶŽŶĐĠƐ͘ ĂͿ >Ğ ƉůƵƐ ŐƌĂŶĚ ŶŽŵďƌĞ ĚŝǀŝƐŝďůĞ ƉĂƌ Ϯ ďͿ >Ğ ƉůƵƐ ƉĞƚŝƚ ŶŽŵďƌĞ ĚŝǀŝƐŝďůĞ ƉĂƌ ϰ >Ğ ƉůƵƐ ƉĞƚŝƚ ŶŽŵďƌĞ ĚŝǀŝƐŝďůĞ ƉĂƌ Ϯϱ >Ğ ƉůƵƐ ƉĞƚŝƚ ŶŽŵďƌĞ ĚŝǀŝƐŝďůĞ ƉĂƌ ϯ >Ğ ƉůƵƐ ŐƌĂŶĚ ŶŽŵďƌĞ ĚŝǀŝƐŝďůĞ ƉĂƌ ϵ >Ğ ƉůƵƐ ŐƌĂŶĚ ŶŽŵďƌĞ ĚŝǀŝƐŝďůĞ ƉĂƌ ϱ ŝƚĞ ͘͘͘ ĂͿ ůĞ ƉůƵƐ ŐƌĂŶĚ ŶŽŵďƌĞ ŶĂƚƵƌĞů ĚĞ ϱ ĐŚŝĨĨƌĞƐ͕ ŵƵůƚŝƉůĞ ĚĞ ϯ͕ ƐĞ ƚĞƌŵŝŶĂŶƚ ƉĂƌ ϱ͘ ďͿ ůĞ ƉůƵƐ ƉĞƚŝƚ ŶŽŵďƌĞ ŶĂƚƵƌĞů ĚĞ ϰ ĐŚŝĨĨƌĞƐ͕ ŵƵůƚŝƉůĞ ĚĞ ϴ͕ ƐĞ ƚĞƌŵŝŶĂŶƚ ƉĂƌ ϲ͘ ĐͿ ůĞ ƉůƵƐ ŐƌĂŶĚ ŶŽŵďƌĞ ŶĂƚƵƌĞů ĚĞ ϰ ĐŚŝĨĨƌĞƐ͕ ŵƵůƚŝƉůĞ ĚĞ ϰ Ğƚ ĚĞ ϵ͕ ƐĞ ƚĞƌŵŝŶĂŶƚ ƉĂƌ Ϯ͘ ĚͿ ůĞ ƉůƵƐ ƉĞƚŝƚ ŶŽŵďƌĞ ŶĂƚƵƌĞů ĚĞ ϯ ĐŚŝĨĨƌĞƐ͕ ŵƵůƚŝƉůĞ ĚĞ ϯ Ğƚ ĚĞ Ϯϱ͘ ĞͿ ůĞ ƉůƵƐ ŐƌĂŶĚ ŶŽŵďƌĞ ŶĂƚƵƌĞů ĚĞ ϰ ĐŚŝĨĨƌĞƐ͕ ŵƵůƚŝƉůĞ ĚĞ ϵ Ğƚ ĚĞ ϭϮϱ͘ ĨͿ ůĞ ƉůƵƐ ŐƌĂŶĚ ŶŽŵďƌĞ ŶĂƚƵƌĞů ĚĞ ϰ ĐŚŝĨĨƌĞƐ ĚŝĨĨĠƌĞŶƚƐ͕ ŵƵůƚŝƉůĞ ĚĞ ϵ Ğƚ ĚĞ ϭϮϱ͘ ŐͿ ůĞ ƉůƵƐ ƉĞƚŝƚ ŶŽŵďƌĞ ŶĂƚƵƌĞů ĚĞ ϯ ĐŚŝĨĨƌĞƐ͕ ŵƵůƚŝƉůĞ ĚĞ Ϯ͕ ĚĞ ϱ Ğƚ ĚĞ ϵ͘ ŚͿ ůĞ ƉůƵƐ ƉĞƚŝƚ ŶŽŵďƌĞ ŶĂƚƵƌĞů ƐƵƉĠƌŝĞƵƌ ă ϭϬϬ͕ ŵƵůƚŝƉůĞ ĚĞ Ϯ Ğƚ ĚĞ ϯ͘

Chapitre 2 Diviseurs et multiples

EXERCICES COMPLÉMENTAIRES

10 ĂůĐƵůĞ ĞŶ ŶŽƚĂŶƚ ƚŽŶ ƌĂŝƐŽŶŶĞŵĞŶƚ͘

ĂͿ ϳϯϱ ͗ ϳ ϴϰϬ ͗ ϰ ϭϲϰ ͗ ϰ ϯϮϱ ͗ ϱ ϲϲϵ ͗ ϯ

ďͿ ϰϯϱ ͗ ϯ Ϯϳϱ ͗ ϱ ϲϯϮ ͗ ϰ ϴϵϭ ͗ ϵ ϮϬϰ ͗ ϯ

ĐͿ ϭϮϴ ͗ ϰ ϭϵϮ ͗ ϰ ϱϵϭ ͗ ϯ ϳϳϲ ͗ ϴ ϲϴϲ ͗ ϳ

ĚͿ ϰϯϮ ͗ ϴ ϯϰϮ ͗ ϲ ϱϳϲ ͗ ϲ ϰϱϵ ͗ ϵ ϰϰϭ ͗ ϵ

ĞͿ ϲϱϭ ͗ ϯ ϱϴϴ ͗ ϲ ϯϵϵ ͗ ϳ ϳϯϲ ͗ ϴ ϯϳϮ ͗ ϰ

ĨͿ ϭϵϮ ͗ Ϯϰ ϯϯϲ ͗ Ϯϴ ϯϵϬ ͗ ϭϱ ϯϵϲ ͗ ϮϮ ϱϬϰϵ ͗ ϱϭ

11 Ŷ ǀĂƌŝĂŶƚ ůĞƐ ŵĠƚŚŽĚĞƐ ĐŚŽŝƐŝĞƐ͕ ũƵƐƚŝĨŝĞ ĐŚĂĐƵŶĞ ĚĞƐ ƉƌŽƉŽƐŝƚŝŽŶƐ ĐŝͲĚĞƐƐŽƵƐ͘

ĂͿ ϳϮ ĞƐƚ ĚŝǀŝƐŝďůĞ ƉĂƌ ϵ͘ ϰϱϳϱ ĞƐƚ ĚŝǀŝƐŝďůĞ ƉĂƌ Ϯϱ͘ ϲϳϮ ĞƐƚ ĚŝǀŝƐŝďůĞ ƉĂƌ ϴ͘ ϭϯ ϱϯϲ ĞƐƚ ĚŝǀŝƐŝďůĞ ƉĂƌ ϰ͘ ϯϱϰ ĞƐƚ ĚŝǀŝƐŝďůĞ ƉĂƌ ϯ͘

ďͿ ϭϮϬϬ ĞƐƚ ĚŝǀŝƐŝďůĞ ƉĂƌ ϯ͘ Ϯϭϱ ĞƐƚ ĚŝǀŝƐŝďůĞ ƉĂƌ ϱ͘ ϵϵϵϵ ĞƐƚ ĚŝǀŝƐŝďůĞ ƉĂƌ ϵ͘ ϳϵϮ ĞƐƚ ĚŝǀŝƐŝďůĞ ƉĂƌ ϰ͘ ϵϰ ϯϳϱ ĞƐƚ ĚŝǀŝƐŝďůĞ ƉĂƌ ϭϮϱ͘

1D 12 JUSTIFIE ƋƵĞ ϯ Ŷ͛ĞƐƚ ƉĂƐ ƵŶ ĚŝǀŝƐĞƵƌ ĚĞ ϭϰϬϯ͘ 13

13 ĠĐŽŵƉŽƐĞ ůĞƐ ŶŽŵďƌĞƐ ƐƵŝǀĂŶƚƐ ĞŶ ƵŶ ƉƌŽĚƵŝƚ ĚĞ ĨĂĐƚĞƵƌƐ ƉƌĞŵŝĞƌƐ͘

ĂͿ ϯϲ͕ ϱϰ͕ ϴϬ͕ ϭϴϬ͕ ϯϱϬ

ďͿ ϳϮ͕ ϭϵϲ͕ ϭϱϬ͕ ϰϯϮ͕ ϯϮϯ

1D 14 DÉCOMPOSE ϭϵϲϬ ĞŶ ĨĂĐƚĞƵƌƐ ƉƌĞŵŝĞƌƐ͘ 15 ÉCRIS ƚĂ ƌĠƉŽŶƐĞ ƐŽƵƐ ĨŽƌŵĞ Ě͛ƵŶ ƉƌŽĚƵŝƚ ĚĞ ƉƵŝƐƐĂŶĐĞƐ ĚĞ ŶŽŵďƌĞƐ ƉƌĞŵŝĞƌƐ͘

15 ZĞŶĚƐ ŝƌƌĠĚƵĐƚŝďůĞƐ ůĞƐ ĨƌĂĐƚŝŽŶƐ ƐƵŝǀĂŶƚĞƐ ĞŶ ƉĂƐƐĂŶƚ ƉĂƌ ůĂ ĚĠĐŽŵƉŽƐŝƚŝŽŶ ĞŶ ĨĂĐƚĞƵƌƐ ƉƌĞŵŝĞƌƐ͘

ĂͿ

75 48 48 120 180 , , , , 45 60 75 180 126

ďͿ

135 132 260 204 84 , , , , 90 140 390 85 294

16 >ĞƐ ƉƌŽĚƵŝƚƐ ĐŝͲĚĞƐƐŽƵƐ ƐŽŶƚ ůĞƐ ƌĠƐƵůƚĂƚƐ ĚĞ ůĂ ĚĠĐŽŵƉŽƐŝƟ ŽŶ ĚĞ ŶŽŵďƌĞƐ ĞŶ ƉƌŽĚƵŝƚƐ ĚĞ ĨĂĐƚĞƵƌƐ

ƉƌĞŵŝĞƌƐ͘ YƵĞůƐ ƐŽŶƚ ĐĞƐ ŶŽŵďƌĞƐ ͍ ĂͿ Ϯϯ . ϱϮ с ϮϮ . ϳϮ с ϯϯ . ϱϮ с ϱϯ . ϳ с ϮϮ . ϭϭ с

ďͿ ϯ . ϭϭϮ с ϱϯ . Ϯϰ с ϱ . ϳϮ с Ϯϱ . ϱϯ с ϯϮ . ϱϯ с

ĐͿ Ϯϯ . ϱϮ . ϳ с ϮϮ . ϱ . ϭϭ с ϮϮ . ϱ . ϭϯ с ϮϮ . ϯϮ . ϱϮ с Ϯ . ϱ . ϳϮ с

1D 17 COMPLÈTE ůĞ ƉƌŽĚƵŝƚ ƐƵŝǀĂŶƚ ƉŽƵƌ ŽďƚĞŶŝƌ ƵŶĞ ĚĠĐŽŵƉŽƐŝƟ ŽŶ ĞŶ ĨĂĐƚĞƵƌƐ ƉƌĞŵŝĞƌƐ͘ 15 ϮϮ ǆ ϯϮ ǆ ͙͙͙͙͘ с ϵϬϬ

18 ĂůĐƵůĞ͘

ĂͿ ϰϯ с ϰ н ϯ с ϰ ʹ ϯ с ϰ . ϯ с ϯϰ с

ďͿ ϱϮ с Ϯϱ с ϱ н Ϯ с Ϯ . ϱ с ϱ . Ϯ с

ĐͿ ϰϰ с ϰ н ϰ н ϰ н ϰ с ϰ . ϰ с ϰ . ϰ . ϰ . ϰ с ϰ . Ϯ с

ĚͿ ϭϬϱ с ϭϬ н ϱ с ϭϬ . ϭϬ . ϭϬ . ϭϬ . ϭϬ с ϱ . ϭϬ с ϭϬ н ϭϬ н ϭϬ н ϭϬ н ϭϬ с

EXERCICES COMPLÉMENTAIRES

Chapitre 2 Diviseurs et multiples

19 ĂůĐƵůĞ͘

ĂͿ ϮϮ н ϱϮ с ϲϮ н ϯϮ с ϴϮ н ϮϮ с ϵϮ н ϱϮ с ϯϯ ʹ ϯϮ с

ďͿ ϰϮ н ϮϮ с ϲϯ ʹ ϯϰ с ϱϯ ʹ Ϯϲ с ϮϮ н ϱϯ с ϲϮ н ϯϯ с

ĐͿ ϭϬϮ с ĚͿ Ϯϳ ϬϬϬ ͗ ϭϬϮ с ĞͿ Ϯϯ . ϭϬϮ с ϱ ϭϬ с ϮϱϭϬ ͗ ϭϬϯ с ϰϱϬϬ ͗ ϭϬϮ с ϱ . ϭϬϯ с ϱϰϯ ͗ ϭϬϮ с Ϭ͕ϲ . ϭϬϰ с ϰ ϯ ϯ͕ϭϰ . ϭϬ с Ϯϰ͕ϱ ͗ ϭϬ с Ϭ͕Ϯϭ ͗ ϭϬϯ с ϯ ϯ Ϭ͕ϬϬϭϮ . ϭϬ с Ϭ͕Ϯ ͗ ϭϬ с ϱ͕ϲϱ ͗ ϭϬϮ с

20 ŽŵƉůğƚĞ ƉĂƌ с ŽƵ т͘

ĂͿ

ĞͿ

ϯϮ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ Ϯϯ ϰϮ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ Ϯϰ ϯϭ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϯ ϭϯ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϯ ϭϰ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϭ

ďͿ ϭϬϮ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϮϬ ϭϬϯ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϭϬ ϬϬϬ ϭϬϱ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϭϬϬ ϬϬϬ ϭϬϭ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϭϬ ϭϬϮ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϭϬϬ

ϭϯ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϯ ϯϮ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϲ ϭϯϮ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϭϲϵ ϭϬϬϬϮ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϭϬ ϬϬϬ

ĐͿ ϰϬϮ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϭϲϬ ϮϬϯ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϴϬϬϬ ϱϯ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϭϱ ϯϱ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϭϮϱ ϱϯ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϴ

ĨͿ ϭϰ ϬϬϬϮ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϭϰ ϬϬϬ ϬϬϬ ϭϲϬϮ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϮϱϲϬ ϭϳϬϮ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ Ϯϴ ϵϬϬ ϱϱϮ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϮϱϮϱ

ĚͿ ϳϮ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ Ϯϳ ϳϮ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϭϰ ϳϮ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϰϵ ϳϮ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ Ϯ . ϳ ϳϮ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϳ . Ϯ

ŐͿ ϵϬϬϮ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϴϭϬ ϬϬϬ ϱϬϮ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϮϱϬϬ ϳϮϬϮ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϭϰ ϰϬϬ ϯϬϬϸ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϵϬϬϬ

21 ZĞƚƌŽƵǀĞ ůĞƐ ŶŽŵďƌĞƐ ĚŽŶƚ ǀŽŝĐŝ ůĂ ĚĠĐŽŵƉŽƐŝƚŝŽŶ ƐĂŶƐ ů͛ĂŝĚĞ ĚĞ ůĂ ĐĂůĐƵůĂƚƌŝĐĞ͘

ĂͿ Ϯϯ . ϱϯ с Ϯϱ . ϱϱ с Ϯϲ . ϱϲ с

ďͿ Ϯϯ . ϱϰ с Ϯϰ . ϱϯ с Ϯϲ . ϱϱ с

ĐͿ Ϯϳ . ϱϳ с Ϯϵ . ϱϴ с Ϯϭϳ . ϱϭϵ с

22 YƵĞů ĞƐƚ ůĞ ƉůƵƐ ƉĞƚŝƚ ĚĞƐ ĚĞƵǆ ŶŽŵďƌĞƐ ͗ Ϯϯ . ϱϯ . ϳ . ϭϭ ŽƵ Ϯϯ . ϱϯ . ϳ . ϭϭϮ ͍ :ƵƐƚŝĨŝĞ͘ 23 ^ŝ ϭϵϲϬ с Ϯϯ . ϱ . ϳϮ͕ ĂůŽƌƐ ĠĐƌŝƐ ƌĂƉŝĚĞŵĞŶƚ ůĂ ĚĠĐŽŵƉŽƐŝƚŝŽŶ ĞŶ ĨĂĐƚĞƵƌƐ ƉƌĞŵŝĞƌƐ ĚĞƐ

ŶŽŵďƌĞƐ ϯϵϮϬ͕ ϵϴϬϬ͕ ϭϵ ϲϬϬ Ğƚ ϭϵϲ͘ 24 ^ĂŶƐ ƌĞƚƌŽƵǀĞƌ ůĞ ŶŽŵďƌĞ ŵĂŝƐ ƵŶŝƋƵĞŵĞŶƚ ĞŶ ƵƚŝůŝƐĂŶƚ ƐĂ ĚĠĐŽŵƉŽƐŝƚŝŽŶ ĞŶ ƵŶ ƉƌŽĚƵŝƚ ĚĞ

ĨĂĐƚĞƵƌƐ ƉƌĞŵŝĞƌƐ͕ ƌĞƚƌŽƵǀĞ ƚŽƵƐ ƐĞƐ ĚŝǀŝƐĞƵƌƐ͘ ĂͿ Ϯϰ . ϱϯ

ďͿ Ϯϯ . ϯϮ . ϳ

25 sŽŝĐŝ ƋƵĂƚƌĞ ŶŽŵďƌĞƐ Ğƚ ůĞƵƌ ĚĠĐŽŵƉŽƐŝƚŝŽŶ ĞŶ ĨĂĐƚĞƵƌƐ ƉƌĞŵŝĞƌƐ͘ ZĞůŝĞ ƌĂƉŝĚĞŵĞŶƚ ĐŚĂƋƵĞ

ŶŽŵďƌĞ ă ƐĂ ĚĠĐŽŵƉŽƐŝƚŝŽŶ͘ ǆƉůŝƋƵĞ ƚŽŶ ƌĂŝƐŽŶŶĞŵĞŶƚ͘ ϯϳ ϭϰϱ ϮϬ ϬϭϬ Ϯϳ ϵϲϮ ϭϰ ϰϮϭ

ͻ ͻ ͻ ͻ

Ϯ . ϭϭ . ϯϭ . ϰϭ ϯ . ϭϭ . ϭϵ . Ϯϯ Ϯ . ϯ . ϱ . Ϯϯ . Ϯϵ ϱ . ϭϳ . ϭϵ . Ϯϯ

26 ĐƌŝƐ ůĞƐ ŐƌĂŶĚƐ ŶŽŵďƌĞƐ ƵƚŝůŝƐĠƐ ĚĂŶƐ ůĞƐ ƉŚƌĂƐĞƐ ĐŝͲĚĞƐƐŽƵƐ ƐŽƵƐ ůĂ ĨŽƌŵĞ Ě͛ƵŶ ƉƌŽĚƵŝƚ Ě͛ƵŶ

ŶŽŵďƌĞ ŶĂƚƵƌĞů ůĞ ƉůƵƐ ƉĞƚŝƚ ƉŽƐƐŝďůĞ Ğƚ Ě͛ƵŶĞ ƉƵŝƐƐĂŶĐĞ ĚĞ ϭϬ͘ ĂͿ >Ğ ^ŽůĞŝů ƐĞ ƚƌŽƵǀĞ ă ĞŶǀŝƌŽŶ ϭϱϬ ϬϬϬ ϬϬϬ Ŭŵ ĚĞ ůĂ dĞƌƌĞ͘ ďͿ Ŷ ϮϬϭϭ͕ ůĞ ƐĞƵŝů ĚĞƐ ϳ ϬϬϬ ϬϬϬ ϬϬϬ Ě͛ġƚƌĞƐ ŚƵŵĂŝŶƐ ƐƵƌ dĞƌƌĞ Ă ĠƚĠ ĨƌĂŶĐŚŝ͘ ĐͿ >Ğ ŶŽŵďƌĞ ĚĞ ĐĞůůƵůĞƐ ĚĂŶƐ ůĞ ĐŽƌƉƐ ŚƵŵĂŝŶ ĞƐƚ ĞƐƚŝŵĠ ă ĞŶǀŝƌŽŶ ϭϬ ϬϬϬ ϬϬϬ ϬϬϬ ϬϬϬ͘ ŚĂƋƵĞ ũŽƵƌ͕ ϮϬϬ ϬϬϬ ϬϬϬ ϬϬϬ ĚĞ ĐĞůůƵůĞƐ ŵĞƵƌĞŶƚ Ğƚ ƐĞ ƌĞŶŽƵǀĞůůĞŶƚ͘ ĚͿ ͛ĂƉƌğƐ ů͛KD^͕ Ϯϵ ϳϬϬ ϬϬϬ ůŝƚƌĞƐ ĚĞ ƐĂŶŐ ƐŽŶƚ ĐŽůůĞĐƚĠƐ ĐŚĂƋƵĞ ĂŶŶĠĞ͘ ĞͿ >Ğ ŶŽŵďƌĞ ƚŽƚĂů ĚĞ ƐŬŝĞƵƌƐ ƉĂƌ ĂŶ ĚĂŶƐ ůĞ ŵŽŶĚĞ ĞƐƚ ĞƐƚŝŵĠ ă ϭϭϬ ϬϬϬ ϬϬϬ͘ 27 WŽƵƌ ĐŚĂĐƵŶĞ ĚĞƐ ƐŝƚƵĂƚŝŽŶƐ ĚĠĐƌŝƚĞƐ ĐŝͲĚĞƐƐŽƵƐ͕ ĠĐƌŝƐ ůĞ ŶŽŵďƌĞ ŶĂƚƵƌĞů ĐŽƌƌĞƐƉŽŶĚĂŶƚ͘

ĂͿ dŽƵƚ ĂƵ ůŽŶŐ ĚĞ ůĂ ƋƵŝŶǌĂŝŶĞ ĚĞ ZŽůĂŶĚͲ'ĂƌƌŽƐ͕ ϲ . ϭϬϰ ďĂůůĞƐ ƐŽŶƚ ƵƚŝůŝƐĠĞƐ͘ ďͿ >Ă ƐƚĂƚŝŽŶ ĚĞ sĂů dŚŽƌĞŶƐ ĞƐƚ ů͛ƵŶĞ ĚĞƐ ƉůƵƐ ŝŵƉŽƌƚĂŶƚĞƐ ƐƚĂƚŝŽŶƐ ĚĞ ƐƉŽƌƚƐ Ě͛ŚŝǀĞƌ Žƶ ƐĞ ƌĞƚƌŽƵǀĞŶƚ ĐŚĂƋƵĞ ŚŝǀĞƌ ϯ . ϭϬϱ ǀĂĐĂŶĐŝĞƌƐ͘ ĐͿ ^Ƶƌ ůĞƐ ƌŽƵƚĞƐ ĚƵ dŽƵƌ ĚĞ &ƌĂŶĐĞ ϮϬϭϳ͕ ĞŶǀŝƌŽŶ ϭϰ . ϭϬϱ ͨ ŐŽŽĚŝĞƐ ͩ ;ƉĞƚŝƚƐ ĐĂĚĞĂƵǆͿ ŽŶƚ ĠƚĠ ĚŝƐƚƌŝďƵĠƐ͘

EXERCICES COMPLÉMENTAIRES

Chapitre 2 Diviseurs et multiples

28 ĂůĐƵůĞ ĞŶ ƵƚŝůŝƐĂŶƚ ůĞƐ ƌğŐůĞƐ ĚĞ ƉƌŝŽƌŝƚĠ͘ ^ŽƵůŝŐŶĞ ůĞ ĐĂůĐƵů ƉƌŝŽƌŝƚĂŝƌĞ ă ĐŚĂƋƵĞ ĠƚĂƉĞ͘

ĂͿ ϯ н ϰϸ с ;ϯ н ϰͿϸ с ϯϸ н ϰϸ с ;ϱ ʹ ϰͿϸ с ϱϸ ʹ ϰϸ с

ďͿ Ϯϸ н ϱϸ с ϭϬϸ ʹ ϭϳ с ;ϯ . ϮͿϸ с ϯ . Ϯϸ с ϯϸ . Ϯϸ с

ĨͿ ϰϮ ʹ ϭϬ с ϯϮ ʹ ϴ н ϭϬ с ;ϲ . ϮͿϮ с ϲϮ . ϮϮ с ϲ . ϮϮ с

ĐͿ ;ϰ ͘ ϱϸͿϸ с ϯϸ н ϯ . ϱ с ;ϯ н ϯͿϸ . ϱ с ϯ н ;ϯ . ϱͿϸ с ϯ н ϯϸ . ϱ с

ŐͿ ϰ . ϱ ʹ ϮϮ с ϵ н ϮϮ . ϯ с ϭϬ н Ϯϯ . ϳ с ϳ . Ϯ ʹ ϭϲ ͗ Ϯϯ с ϯ н ϯ . ϯ н ϯ . ϯϮ с

ĚͿ Ϯ н ϱϸ . ϰ н ϳ с ĞͿ ;Ϯ н ϯͿϸ . ϲ с ;Ϯ н ϱͿϸ . ϰ н ϳ с Ϯ н ϯϸ . ϲ с ;Ϯ н ϱͿϸ . ;ϰ н ϳͿ с ;ϲ н ϮͿ . ϯϸ с Ϯ н ϱϸ . ;ϰ н ϳͿ с ϲ н Ϯ . ϯϸ с ;Ϯ н ϱϸ . ϰͿ н ϳ с ϲ н ;Ϯ . ϯͿϸ с

ŚͿ ϰ . ;ϱ ʹ ϮͿϮ с Ϯ . ;ϰ н ϱͿϮ с ϰϮ ͗ ; ϵ н ϳͿ с ;ϵ н ϮϮͿ . ϯ с ;ϭϮ ʹ ϮϯͿ ͗ Ϯ с

ŝͿ ;ϯ н ϯͿϮ ͗ ϯ н ϯ . ϯ с ;ϯ . ϯ н ϯͿ ͗ ϯ ʹ ϯ с ;ϯϮ ʹ ϯ н ϯ . ϯͿ ͗ ϯ с Ϯ . ;ϭϰ ʹ Ϯ . ϲͿϮ с ;ϱϮ ʹ ϮϮ . ϱͿ . ϱ с

29 ĠƚĞƌŵŝŶĞ ůĞ ŶŽŵďƌĞ ĚĞ ĚŝǀŝƐĞƵƌƐ ŶĂƚƵƌĞůƐ ĚĞƐ ŶŽŵďƌĞƐ ĐŝͲĚĞƐƐŽƵƐ ĐŽŶŶĂŝƐƐĂŶƚ ůĞƵƌ

ĨĂĐƚŽƌŝƐĂƚŝŽŶ ƉƌĞŵŝğƌĞ͘ ĂͿ Ϯϴ ϯϲ ϱϭϬ

ďͿ Ϯϯ . ϱϮ с ϮϮ . ϳϮ с ϱϯ . ϳ с

ĐͿ ϯ . ϭϭϮ с ϱϯ . Ϯϰ с Ϯϱ . ϱϯ с

ĚͿ Ϯϯ . ϱϮ . ϳ с ϮϮ . ϱ . ϭϭ с ϮϮ . ϯϮ . ϱϮ с

Transférer 1

ĞƐ ĠůğǀĞƐ ŽŶƚ ĂŵĠŶĂŐĠ ƵŶ ƉŽƚĂŐĞƌ ĂƵ ƐĞŝŶ ĚĞ ůĞƵƌ ĠĐŽůĞ͘ /ůƐ ŽŶƚ ĚĠĐŽƵƉĠ ƵŶ ƚĞƌƌĂŝŶ ƌĞĐƚĂŶŐƵůĂŝƌĞ ĞŶ ƋƵĂƚƌĞ ƉĂƌĐĞůůĞƐ ĐŽŵŵĞ ůĞ ŵŽŶƚƌĞ ůĞ ƐĐŚĠŵĂ ĐŝͲĐŽŶƚƌĞ͘ >ĞƐ ĚŝŵĞŶƐŝŽŶƐ ĚĞ ĐŚĂƋƵĞ ƉĂƌĐĞůůĞ ƐŽŶƚ ĞǆƉƌŝŵĠĞƐ ĞŶ ŵğƚƌĞƐ Ğƚ ƐŽŶƚ ĚĞƐ ŶŽŵďƌĞƐ ŶĂƚƵƌĞůƐ͕ Ğƚ ůĞƵƌƐ ĂŝƌĞƐ ƐŽŶƚ ĚĞ ϴ ŵϮ͕ ϭϮ ŵϮ͕ ϭϰ ŵϮ Ğƚ Ϯϭ ŵϮ͘ ^ĂĐŚĂŶƚ ƋƵĞ ůĞƐ ĠůğǀĞƐ ƐŽƵŚĂŝƚĞŶƚ ĚĠůŝŵŝƚĞƌ ĐŚĂƋƵĞ ƉĂƌĐĞůůĞ ƉĂƌ ĚĞƐ ďŽƌĚƵƌĞƐ ĞŶ ďĠƚŽŶ ĚĞ ϭ ŵ ĚĞ ůŽŶŐ͕ ĚĠƚĞƌŵŝŶĞ ůĞ ŶŽŵďƌĞ ĚĞ ďŽƌĚƵƌĞƐ ă ƉůĂĐĞƌ͘

YƵĞůƐ ƐŽŶƚ ůĞƐ ŶŽŵďƌĞƐ ŶĂƚƵƌĞůƐ ƐƚƌŝĐƚĞŵĞŶƚ ƐƵƉĠƌŝĞƵƌƐ ă ϭϮ͕ ŵƵůƚŝƉůĞƐ ĚĞ ϯ Ğƚ ƋƵŝ ĚŝǀŝƐĞŶƚ ϭϮϬ ͍

YƵĞůƐ ƐŽŶƚ ůĞƐ ŶŽŵďƌĞƐ ŶĂƚƵƌĞůƐ ƋƵŝ ĚŝǀŝƐĞŶƚ ϴϰ͕ ƐŽŶƚ ŵƵůƚŝƉůĞƐ ĚĞ ϳ Ğƚ ƐƚƌŝĐƚĞŵĞŶƚ ŝŶĨĠƌŝĞƵƌƐ ă ϱϲ ͍

>Ă ĚĠĐŽŵƉŽƐŝƚŝŽŶ ƉƌĞŵŝğƌĞ Ě͛ƵŶ ŶŽŵďƌĞ ĞƐƚ Ϯ . ϱ . ϭϭ͘ YƵĞůƐ ƐŽŶƚ ůĞƐ ĚŝǀŝƐĞƵƌƐ͕ ŵƵůƚŝƉůĞƐ ĚĞ ϱ͕ ĚĞ ĐĞ ŶŽŵďƌĞ ͍

EĂƚŚĂŶ ĐŽůůĞĐƚŝŽŶŶĞ ůĞƐ ƉŝğĐĞƐ ĚĞ ůĂ ŵŽŶŶĂŝĞ ĚĞ WĂƌŝƐ͕ ŝů ĞŶ Ă ĞŶƚƌĞ ϭϬϬ Ğƚ ϮϬϬ͘ ĠƚĞƌŵŝŶĞ ůĞ ŶŽŵďƌĞ ĚĞ ƉŝğĐĞƐ ƋƵĞ EĂƚŚĂŶ ƉŽƐƐğĚĞ Ɛŝ ƚƵ ƐĂŝƐ ƋƵĞ ĐĞ ŶŽŵďƌĞ͕ ŵƵůƚŝƉůĞ ĚĞ ϭϳ͕ Ŷ͛ĞƐƚ ĚŝǀŝƐŝďůĞ Ŷŝ ƉĂƌ Ϯ͕ Ŷŝ ƉĂƌ ϯ͕ Ŷŝ ƉĂƌ ϭϭ͘

WŽƵƌ ƌĞůĞǀĞƌ ůĞ ͨ ĚĠĨŝ ĚĞ ůĂ ƐĞŵĂŝŶĞ ͩ ƉƌŽƉŽƐĠ ƉĂƌ ƐŽŶ ƉƌŽĨĞƐƐĞƵƌ ĚĞ ŵĂƚŚĠŵĂƚŝƋƵĞ͕ ,ƵŐŽ ĚŽŝƚ ƌĞƚƌŽƵǀĞƌ ƵŶ ĐŽĚĞ ĚĞ ŶĞƵĨ ĐŚŝĨĨƌĞƐ ĚŝĨĨĠƌĞŶƚƐ͘ Ğ ĐŽĚĞ ŶĞ ĐŽŶƚŝĞŶƚ ƉĂƐ ĚĞ ǌĠƌŽ͘ >Ğ ƉƌĞŵŝĞƌ ĐŚŝĨĨƌĞ ĞƐƚ ϭ Ğƚ ůĞ ƋƵĂƚƌŝğŵĞ ĞƐƚ Ϯ͘ >Ğ ŶŽŵďƌĞ ĨŽƌŵĠ ƉĂƌ ůĞƐ ϭĞƌ Ğƚ ϮĞ ĐŚŝĨĨƌĞƐ ĞƐƚ ƵŶ ŵƵůƚŝƉůĞ ĚĞ Ϯ͘ >Ğ ŶŽŵďƌĞ ĨŽƌŵĠ ƉĂƌ ůĞƐ ϮĞ Ğƚ ϯĞ ĐŚŝĨĨƌĞƐ ĞƐƚ ƵŶ ŵƵůƚŝƉůĞ ĚĞ ϯ͘ >Ğ ŶŽŵďƌĞ ĨŽƌŵĠ ƉĂƌ ůĞƐ ϯĞ Ğƚ ϰĞ ĐŚŝĨĨƌĞƐ ĞƐƚ ƵŶ ŵƵůƚŝƉůĞ ĚĞ ϰ͘ ƚ ĂŝŶƐŝ ĚĞ ƐƵŝƚĞ ũƵƐƋƵ͛ĂƵ ŶŽŵďƌĞ ĨŽƌŵĠ ƉĂƌ ůĞƐ ϴĞ Ğƚ ϵĞ ĐŚŝĨĨƌĞƐ ƋƵŝ ĞƐƚ ƵŶ ŵƵůƚŝƉůĞ ĚĞ ϵ͘ ŝĚĞ ,ƵŐŽ ĚĂŶƐ ƐĂ ƌĞĐŚĞƌĐŚĞ͘

EXERCICES COMPLÉMENTAIRES

Chapitre 2 Diviseurs et multiples

/ů ĞƐƚ ϭϬ Ś͕ WŝĞƌƌĞ ǀŝĞŶƚ Ě͛ĂƉƉƌĞŶĚƌĞ ůĂ ƐŽƌƚŝĞ Ě͛ƵŶĞ ŶŽƵǀĞůůĞ ĐŽŶƐŽůĞ ĚĞ ũĞƵ͘ ƵƐƐŝƚƀƚ͕ ŝů ĞŶǀŽŝĞ ƵŶ ^D^ ă ƚƌŽŝƐ ĚĞ ƐĞƐ ĂŵŝƐ ƉŽƵƌ ůĞƐ ĞŶ ŝŶĨŽƌŵĞƌ͘ hŶ ƋƵĂƌƚ Ě͛ŚĞƵƌĞ ƉůƵƐ ƚĂƌĚ͕ ĐŚĂĐƵŶ ĚĞ ƐĞƐ ƚƌŽŝƐ ĂŵŝƐ ĞŶǀŽŝĞ ƵŶ ^D^ ă ƚƌŽŝƐ ŶŽƵǀĞůůĞƐ ƉĞƌƐŽŶŶĞƐ͘ >Ă ĚŝĨĨƵƐŝŽŶ ĚĞ ů͛ŝŶĨŽƌŵĂƚŝŽŶ ƐĞ ƉŽƵƌƐƵŝƚ ĚĞ ůĂ ŵġŵĞ ŵĂŶŝğƌĞ͘ ğƐ ƋƵ͛ƵŶĞ ƉĞƌƐŽŶŶĞ ĞƐƚ ŝŶĨŽƌŵĠĞ͕ ĞůůĞ ĂƉƉƌĞŶĚ ůĂ ŶŽƵǀĞůůĞ͕ ƵŶ ƋƵĂƌƚ Ě͛ŚĞƵƌĞ ƉůƵƐ ƚĂƌĚ͕ ă ƚƌŽŝƐ ĂƵƚƌĞƐ ƉĞƌƐŽŶŶĞƐ Ğƚ ĂƵĐƵŶĞ ƉĞƌƐŽŶŶĞ Ŷ͛ĞƐƚ ŝŶĨŽƌŵĠĞ ƉůƵƐ Ě͛ƵŶĞ ĨŽŝƐ͘ Ŷ ƐƵƉƉŽƐĂŶƚ ƋƵĞ ůĞ ƚĞŵƉƐ ĚĞ ƚƌĂŶƐŵŝƐƐŝŽŶ Ě͛ƵŶ ^D^ ĞƐƚ ŶƵů͕ ͘͘͘ ĂͿ ĐŽŵďŝĞŶ ĚĞ ƉĞƌƐŽŶŶĞƐ ƌĞĐĞǀƌŽŶƚ ů͛ŝŶĨŽƌŵĂƚŝŽŶ ă ϭϬ Ś ϯϬ ͍ ϭϭ Ś ͍ ϭϮ Ś ϯϬ ͍ ďͿ ĠĐƌŝƐ ůĞ ĐĂůĐƵů ƉĞƌŵĞƚƚĂŶƚ ĚĞ ƚƌŽƵǀĞƌ ůĞ ŶŽŵďƌĞ ĚĞ ƉĞƌƐŽŶŶĞƐ ƋƵŝ ƌĞĐĞǀƌŽŶƚ ů͛ŝŶĨŽƌŵĂƚŝŽŶ ă ϮϬ Ś͘ ĐͿ ĠĐƌŝƐ ůĞ ĐĂůĐƵů ƉĞƌŵĞƚƚĂŶƚ ĚĞ ƚƌŽƵǀĞƌ ůĞ ŶŽŵďƌĞ ĚĞ ƉĞƌƐŽŶŶĞƐ ƋƵŝ ƌĞĐĞǀƌŽŶƚ ů͛ŝŶĨŽƌŵĂƚŝŽŶ Ŷ ŚĞƵƌĞƐ ƉůƵƐ ƚĂƌĚ͘

Ŷ ŽďƐĞƌǀĂŶƚ ĂƚƚĞŶƚŝǀĞŵĞŶƚ ůĂ ƚĞĐŚŶŝƋƵĞ ĚĞ ĐŽŶƐƚƌƵĐƚŝŽŶ ĚĞƐ ƚƌŽŝƐ ƉƌĞŵŝğƌĞƐ ĨŝŐƵƌĞƐ ĚĞ ůĂ ƐƵŝƚĞ͕ ĚĞƐƐŝŶĞ ůĞƐ ĚĞƵǆ ĨŝŐƵƌĞƐ ƐƵŝǀĂŶƚĞƐ͘ Fig. 1 Fig. 2 Fig. 3 Fig. 4 Fig. 5

ĂͿ ĠƚĞƌŵŝŶĞ ůĞ ŶŽŵďƌĞ ĚĞ ĐĂƌƌĠƐ ŶĠĐĞƐƐĂŝƌĞƐ ă ůĂ ĐŽŶƐƚƌƵĐƚŝŽŶ ĚĞ ĐŚĂƋƵĞ ĨŝŐƵƌĞ͘ ďͿ ĠƚĞƌŵŝŶĞ ƵŶĞ ĨŽƌŵƵůĞ ƋƵŝ ƉĞƌŵĞƚ ĚĞ ƚƌŽƵǀĞƌ ůĞ ŶŽŵďƌĞ ĚĞ ĐĂƌƌĠƐ ĚĞ ůĂ ŶŝğŵĞ ĨŝŐƵƌĞ͘ ĐͿ hƚŝůŝƐĞ ĐĞƚƚĞ ĨŽƌŵƵůĞ ƉŽƵƌ ĚĠƚĞƌŵŝŶĞƌ ůĞ ŶŽŵďƌĞ ĚĞ ĐĂƌƌĠƐ ĚĞ ůĂ ϮϱĞ ĨŝŐƵƌĞ͕ ĚĞ ůĂ ϭϬϬĞ ĨŝŐƵƌĞ͘ ĚͿ hƚŝůŝƐĞ ĐĞƚƚĞ ĨŽƌŵƵůĞ ƉŽƵƌ ĚĠƚĞƌŵŝŶĞƌ ůĞ ƌĂŶŐ ĚĞ ůĂ ĨŝŐƵƌĞ ĐŽŵƉƌĞŶĂŶƚ ϰϴ ĐĂƌƌĠƐ͕ ϭϬϮ ĐĂƌƌĠƐ͘ CE

1D 9 17

KďƐĞƌǀĞ ĐĞƚƚĞ ƐƵŝƚĞ Ě͛ĂƐƐĞŵďůĂŐĞƐ ĚĞ ĐƵďĞƐ͘ ﬁgure 1 ﬁgure 2

ﬁgure 3

COMPLÈTE ůĞ ƚĂďůĞĂƵ ƐƵŝǀĂŶƚ ͗ EƵŵĠƌŽ ĚĞ ůĂ ĨŝŐƵƌĞ

EŽŵďƌĞ ĚĞ ĐƵďĞƐ ;ŵġŵĞ ŝŶǀŝƐŝďůĞƐͿ

͙͙

DÉTERMINE ůĞ ŶƵŵĠƌŽ ĚĞ ůĂ ĨŝŐƵƌĞ ƋƵŝ ĐŽŵƉŽƌƚĞ ϯϲ ĐƵďĞƐ͘ DÉTERMINE ůĞ ŶŽŵďƌĞ ĚĞ ĐƵďĞƐ ĚĞ ůĂ ĨŝŐƵƌĞ ŶΣϭϬ͘

Chapitre 3 Traitement de données et pourcentages Tableaux de compétences Libre EŽŵďƌĞƐ ƌĂƟ ŽŶŶĞůƐ 11

DĂŠƚƌŝƐĞƌ ůĞƐ ĐŽŶǀĞŶƟ ŽŶƐ Ě͛ĠĐƌŝƚƵƌĞ ŵĂƚŚĠŵĂƟ ƋƵĞ ĚĞƐ ŽƉĠƌĂƟ ŽŶƐ ĂǀĞĐ ĚĞƐ ĞŶƟ ĞƌƐ͘

sĠƌŝĮ Ğƌ ĂǀĞĐ ƵŶĞ ĐĂůĐƵůĂƚƌŝĐĞ ůĂ ƉůĂƵƐŝďŝůŝƚĠ Ě͛ƵŶ ƌĠƐƵůƚĂƚ͘

Les mouvements du plan 42

ƐƐŽĐŝĞƌ ƵŶ ƉŽŝŶƚ Ğƚ ƐŽŶ ĂďƐĐŝƐƐĞ ƐƵƌ ƵŶ ĂǆĞ͘

ƐƐŽĐŝĞƌ ƵŶ ƉŽŝŶƚ Ğƚ ƐĞƐ ĐŽŽƌĚŽŶŶĠĞƐ ƐƵƌ ƵŶ ƋƵĂĚƌŝůůĂŐĞ͘

Mesurer des angles 71

DĞƐƵƌĞƌ ů͛ĂŵƉůŝƚƵĚĞ Ě͛ƵŶ ĂŶŐůĞ ĂǀĞĐ ƵŶ ƌĂƉƉŽƌƚĞƵƌ͘

dƌĂĐĞƌ ƵŶ ĂŶŐůĞ Ě͛ĂŵƉůŝƚƵĚĞ ĚŽŶŶĠĞ͘

ZĞƉŽƌƚĞƌ ĚĞƐ ĂŶŐůĞƐ͘

'ƌĂŶĚĞƵƌƐ ƉƌŽƉŽƌƟ ŽŶŶĞůůĞƐ 77

:ƵƐƟ Į Ğƌ ů͛ƵƐĂŐĞ Ě͛ƵŶ ƉŽƵƌĐĞŶƚĂŐĞ ĚĂŶƐ ƵŶ ĐĂůĐƵů͘

ŽŵƉůĠƚĞƌ ƵŶ ƚĂďůĞĂƵ ĚĞ ƉƌŽƉŽƌƟ ŽŶŶĂůŝƚĠ͘

hƟ ůŝƐĞƌ ůĞƐ ƉŽƵƌĐĞŶƚĂŐĞƐ ĐŽŵŵĞ ƵŶ ƌĂƉƉŽƌƚ ƉĂƌƟ ĐƵůŝĞƌ͘

ĂŶƐ ƵŶĞ ƐŝƚƵĂƟ ŽŶ ĚĞ ƉƌŽƉŽƌƟ ŽŶŶĂůŝƚĠ ĚŝƌĞĐƚĞ͕ ĐŽŵƉůĠƚĞƌ͕ ĐŽŶƐƚƌƵŝƌĞ͕ ĠƚĞŶĚƌĞ͕ ĞǆƉůŽŝƚĞƌ ƵŶ ƚĂďůĞĂƵ ĚĞ ŶŽŵďƌĞƐ͘

ACTIVITÉS

Chapitre 3 Traitement de données et pourcentages

>ĞƐ ƌĞƉƌĠƐĞŶƚĂƟ ŽŶƐ ĚĞ ĚŽŶŶĠĞƐ

/ŶƚĞƌƉƌĠƚĞƌ ƵŶ ƚĂďůĞĂƵ ĚĞ ŶŽŵďƌĞƐ͕ ƵŶ ŐƌĂƉŚŝƋƵĞ͕ ƵŶ ĚŝĂŐƌĂŵŵĞ͘

WƌĠƐĞŶƚĞƌ ĚĞƐ ĚŽŶŶĠĞƐ ŶƵŵĠƌŝƋƵĞƐ ƐŽƵƐ ĨŽƌŵĞ Ě͛ƵŶ ĚŝĂŐƌĂŵŵĞ ĞŶ ďąƚŽŶƐ͕ ĐŝƌĐƵůĂŝƌĞ ŽƵ ĠǀŽůƵƟ Ĩ͘

ƚĂďůŝƌ ƵŶ ůŝĞŶ ĞŶƚƌĞ ůĞƐ ŝŶĨŽƌŵĂƟ ŽŶƐ ĨŽƵƌŶŝĞƐ ƉĂƌ ƵŶ ƚĂďůĞĂƵ ĚĞ ŶŽŵďƌĞƐ Ğƚ ƵŶ ĚŝĂŐƌĂŵŵĞ ĞǆƉůŽŝƚĂŶƚ ůĞ ŵġŵĞ ĞŶƐĞŵďůĞ ĚĞ ĚŽŶŶĠĞƐ͘

Kĸ ĐŝĞů Lire et écrire des nombres 2

ĐƌŝƌĞ Ğƚ ƌĞĐŽŶŶĂŠƚƌĞ ƵŶ ŵġŵĞ ŶŽŵďƌĞ ƐŽƵƐ Ěŝī ĠƌĞŶƚĞƐ ĨŽƌŵĞƐ͘

ƌƌŽŶĚŝƌ ƵŶ ŶŽŵďƌĞ ĚĠĐŝŵĂů͕ ĞŶ ĚŽŶŶĞƌ ƵŶĞ ǀĂůĞƵƌ ĂƉƉƌŽĐŚĠĞ ƉĂƌ ĚĠĨĂƵƚ Ğƚ ƉĂƌ ĞǆĐğƐ͘

Repérer et classer 7

WůĂĐĞƌ ƐƵƌ ƵŶĞ ĚƌŽŝƚĞ ŐƌĂĚƵĠĞ ;ĂǆĞͿ ĚĞƐ ŶŽŵďƌĞƐ ŶĂƚƵƌĞůƐ Ğƚ ĚĞƐ ŶŽŵďƌĞƐ ĚĠĐŝŵĂƵǆ ƉŽƐŝƟ ĨƐ͘

>ŝƌĞ ů͛ĂďƐĐŝƐƐĞ Ě͛ƵŶ ƉŽŝŶƚ͘

WůĂĐĞƌ ƵŶ ĐŽƵƉůĞ ĚĞ ŶŽŵďƌĞƐ ĚĂŶƐ ƵŶ ƌĞƉğƌĞ ĐĂƌƚĠƐŝĞŶ͘

ī ĞĐƚƵĞƌ ĚĞƐ ŽƉĠƌĂƟ ŽŶƐ 25

ƐƟ ŵĞƌ ů͛ŽƌĚƌĞ ĚĞ ŐƌĂŶĚĞƵƌ Ğƚ ǀĠƌŝĮ Ğƌ ă ůĂ ĐĂůĐƵůĂƚƌŝĐĞ ůĂ ƉůĂƵƐŝďŝůŝƚĠ Ě͛ƵŶ ƌĠƐƵůƚĂƚ͘

Résoudre des problèmes et représenter des données 36

ZĠƐŽƵĚƌĞ ĚĞƐ ƉƌŽďůğŵĞƐ ŵĞƩ ĂŶƚ ĞŶ ƈƵǀƌĞ ĚĞƐ ƉŽƵƌĐĞŶƚĂŐĞƐ͘

/ŶƚĞƌƉƌĠƚĞƌ ƵŶ ƚĂďůĞĂƵ ĚĞ ŶŽŵďƌĞƐ͕ ƵŶ ŐƌĂƉŚŝƋƵĞ͕ ƵŶ ĚŝĂŐƌĂŵŵĞ͘

ZĞƉƌĠƐĞŶƚĞƌ ĚĞƐ ĚŽŶŶĠĞƐ ƉĂƌ ƵŶ ŐƌĂƉŚŝƋƵĞ͕ ƵŶ ĚŝĂŐƌĂŵŵĞ ĞŶ ďąƚŽŶƐ͕ ƵŶ ĚŝĂŐƌĂŵŵĞ ĐŝƌĐƵůĂŝƌĞ͘

Figures géométriques élémentaires et distances 79

DĞƐƵƌĞƌ ƵŶ ĂŶŐůĞ͘

ZĞƉŽƌƚĞƌ ƵŶ ĂŶŐůĞ ĚŽŶŶĠ͘

ACTIVITÉS

Chapitre 3 Traitement de données et pourcentages

ĐƚŝǀŝƚĠ ϭ Graphiques de toutes sortes 1 dŽƵƐ ůĞƐ ĞŶĨĂŶƚƐ Ě͛ƵŶ ŐƌŽƵƉĞ ŽŶƚ ƌĠƉŽŶĚƵ ă ƵŶ ƐŽŶĚĂŐĞ ůĞƵƌ ĚĞŵĂŶĚĂŶƚ ƋƵĞů ĠƚĂŝƚ ůĞƵƌ ĂŶŝŵĂů ƉƌĠĨĠƌĠ͘ >ĞƵƌƐ ƌĠƉŽŶƐĞƐ ƐŽŶƚ ŝůůƵƐƚƌĠĞƐ ƉĂƌ ůĞ ĚŝĂŐƌĂŵŵĞ ĞŶ ďąƚŽŶƐ ƋƵĞ ǀŽŝĐŝ͘ Nombre d’enfants 9 8 7 6 5 4 3 2 1 0

Répar on des enfants selon le choix de leur animal préféré

Chat Dauphin Chien Hamster Cheval Tortue Autre

ĂͿ YƵĞů ĞƐƚ ů͛ĂŶŝŵĂů ůĞ ƉůƵƐ ƐŽƵǀĞŶƚ ĐŝƚĠ ͍ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ďͿ ŽŵďŝĞŶ Ě͛ĞŶĨĂŶƚƐ ŽŶƚ ĐŚŽŝƐŝ ůĂ ƚŽƌƚƵĞ ĐŽŵŵĞ ĂŶŝŵĂů ƉƌĠĨĠƌĠ ͍ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ĐͿ ŽŵďŝĞŶ Ě͛ĞŶĨĂŶƚƐ Ǉ ĂͲƚͲŝů ĚĂŶƐ ĐĞ ŐƌŽƵƉĞ ͍ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ĚͿ sƌĂŝ ŽƵ ĨĂƵǆ ͍ /ů Ǉ Ă ĂƵƚĂŶƚ Ě͛ĞŶĨĂŶƚƐ ƋƵŝ ƉƌĠĨğƌĞŶƚ ůĞ ĐŚĂƚ ƋƵĞ ůĞ ĐŚĞǀĂů͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ >Ğ ĐŚŝĞŶ ĞƐƚ ů͛ĂŶŝŵĂů ƉƌĠĨĠƌĠ ĚĞ Ϯϱ й ĚĞƐ ĞŶĨĂŶƚƐ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ DŽŝŶƐ ĚĞ ϭϱ й ĚĞƐ ĞŶĨĂŶƚƐ ƉƌĠĨğƌĞŶƚ ůĞ ĚĂƵƉŚŝŶ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ 2 >Ğ ŐƌĂƉŚŝƋƵĞ ĐŝͲĚĞƐƐŽƵƐ ŵŽŶƚƌĞ ů͛ĠǀŽůƵƚŝŽŶ ĚƵ ŶŽŵďƌĞ Ě͛ĂĨĨŝůŝĠƐ ĚĂŶƐ ƵŶ ĐůƵď ĚĞ ĚĂŶƐĞ ŵŽĚĞƌŶĞ ĚĞƉƵŝƐ ƐĂ ĐƌĠĂƚŝŽŶ͕ ůĞ ϭer ũĂŶǀŝĞƌ ϮϬϬϵ͕ ũƵƐƋƵ͛ĂƵ ϭer ũĂŶǀŝĞƌ ϮϬϭϳ͘ ǀŽůƵƚŝŽŶ ĚƵ ŶŽŵďƌĞ Ě͛ĂĨĨŝůŝĠƐ Nombre d'aﬃliés 160 140 120 100 80 60 40 20 Date 0

01-01 01-01 01-01 01-01 01-01 01-01 01-01 01-01 01-01 2009 2010 2011 2012 2013 2014 2015 2016 2017

sƌĂŝ ŽƵ &ĂƵǆ ͍ >Ğ ŶŽŵďƌĞ Ě͛ĂĨĨŝůŝĠƐ Ă ƚŽƵũŽƵƌƐ ĂƵŐŵĞŶƚĠ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ >͛ĂƵŐŵĞŶƚĂƚŝŽŶ ĚƵƌĂŶƚ ůĂ ϭre ĂŶŶĠĞ ĞƐƚ ĚĞ ϮϬ ŵĞŵďƌĞƐ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ >Ğ ŶŽŵďƌĞ Ě͛ĂĨĨŝůŝĠƐ Ă ƋƵŝŶƚƵƉůĠ ĚƵ ϭer ũĂŶǀŝĞƌ ϮϬϭϭ ĂƵ ϭer ũĂŶǀŝĞƌ ϮϬϭϰ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

>Ă ƉůƵƐ ŝŵƉŽƌƚĂŶƚĞ ĂƵŐŵĞŶƚĂƚŝŽŶ ĚƵ ŶŽŵďƌĞ Ě͛ĂĨĨŝůŝĠƐ Ă ĞƵ ůŝĞƵ ĚƵƌĂŶƚ ů͛ĂŶŶĠĞ ϮϬϭϭ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ACTIVITÉS

Chapitre 3 Traitement de données et pourcentages

3 sŽŝĐŝ ůĂ ƌĠƉĂƌƚŝƚŝŽŶ͕ ƐĞůŽŶ ůĞƵƌ ąŐĞ͕ ĚΖƵŶ ŐƌŽƵƉĞ ĚĞ Ϯϰ ĞŶĨĂŶƚƐ ƉĂƌƚŝĐŝƉĂŶƚ ă ƵŶ ĂƚĞůŝĞƌ ŵĂƚŚĠŵĂƚŝƋƵĞ͘ ŐĞ ;ĂŶƐͿ EŽŵďƌĞ ĚΖĞŶĨĂŶƚƐ

ϭϬ 6

ϭϭ ϭϮ

ϭϮ ϰ

ϭϯ Ϯ

>Ğ ƉƌŽĨĞƐƐĞƵƌ Ă ĚĞŵĂŶĚĠ ĂƵǆ ĠůğǀĞƐ ĚĞ ƌĞƉƌĠƐĞŶƚĞƌ ĐĞƚƚĞ ƐŝƚƵĂƚŝŽŶ ƉĂƌ ƵŶ ĚŝĂŐƌĂŵŵĞ ĐŝƌĐƵůĂŝƌĞ͘ sŽŝĐŝ ůĞƵƌƐ ŐƌĂƉŚŝƋƵĞƐ͘ Marc EŽĂŚ >ƵĐŝĞ :ƵůŝĞ

10 ans

11 ans

12 ans

13 ans

ZĞƚƌŽƵǀĞ ĐĞůƵŝ ƋƵŝ ĞƐƚ ĐŽƌƌĞĐƚ Ğƚ ũƵƐƚŝĨŝĞ ƚŽŶ ĐŚŽŝǆ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

4 sŽŝĐŝ ƵŶ ŐƌĂƉŚŝƋƵĞ ŝůůƵƐƚƌĂŶƚ ůĞƐ ƌĠƐƵůƚĂƚƐ Ě͛ƵŶĞ ĞŶƋƵġƚĞ ƐƵƌ ůĞƐ ůŽŝƐŝƌƐ ŵĞŶĠĞ ĚĂŶƐ ƵŶ ŐƌŽƵƉĞ ĚĞ ũĞƵŶĞƐ ĨƌĠƋƵĞŶƚĂŶƚ ƵŶĞ ƉůĂŝŶĞ ĚĞ ũĞƵǆ͘ ^ĂĐŚĂŶƚ ƋƵĞ ĐŚĂƋƵĞ ũĞƵŶĞ Ă ĐŚŽŝƐŝ ƵŶ ƐĞƵů ůŽŝƐŝƌ͕ ĐŽŵƉůğƚĞ ůĞ ƚĂďůĞĂƵ͘

>ŽŝƐŝƌ

&ƌĂĐƚŝŽŶ ĚƵ ŶŽŵďƌĞ ĚĞ ũĞƵŶĞƐ

ŵƉůŝƚƵĚĞ ĚĞ ů͛ĂŶŐůĞ ĂƵ ĐĞŶƚƌĞ ĞŶ ĚĞŐƌĠƐ

EŽŵďƌĞ ĚĞ ũĞƵŶĞƐ

ZĠƉĂƌƚŝƚŝŽŶ ĚĞƐ ůŽŝƐŝƌƐ

:ĞƵǆ ǀŝĚĠŽ ^ƉŽƌƚƐ DƵƐŝƋƵĞ Jeux vidéo

>ĞĐƚƵƌĞ

Ϯϰ

Sports Musique

ŝŶĠŵĂ TOTAUX

Lecture Cinéma

ACTIVITÉS

Chapitre 3 Traitement de données et pourcentages

ĐƚŝǀŝƚĠ Ϯ Calculs de pourcentages 1 ĂͿ sŽŝĐŝ ůĞƐ ƌĠƐƵůƚĂƚƐ ŽďƚĞŶƵƐ ƉĂƌ ĐŝŶƋ ĠůğǀĞƐ Ě͛ƵŶĞ ŵġŵĞ ĐůĂƐƐĞ ĂƵ ďŝůĂŶ ĚĞ ƐĐŝĞŶĐĞƐ͘ ŝĚĞͲůĞƐ ă ĐĂůĐƵůĞƌ ůĞƵƌ ƉŽƵƌĐĞŶƚĂŐĞ͘

EŽŵ

WŽŝŶƚƐ ƐƵƌ ϭϮϬ

dŽŵ

ϲϬ

ŶĂģůůĞ

ϵϬ

WĂƵů

ϭϬϴ

EĂĚŝĂ

ϵϲ

>ǇŶĚĂ

ϭϬϮ

ĠŵĂƌĐŚĞ

WŽƵƌĐĞŶƚĂŐĞ

ďͿ ĂůĐƵůĞ ůĞ ƉŽƵƌĐĞŶƚĂŐĞ͕ ĂƌƌŽŶĚŝ ă ů͛ƵŶŝƚĠ ƉƌğƐ͕ ŽďƚĞŶƵ ĞŶ ĨƌĂŶĕĂŝƐ ƉĂƌ ĐŚĂƋƵĞ ĠůğǀĞ ă ůĂ ĨŝŶ ĚĞ ůĂ ƉĠƌŝŽĚĞ͘

EŽŵ

/ŶƚĞƌƌŽ ϭ /ŶƚĞƌƌŽ Ϯ /ŶƚĞƌƌŽ ϯ /ŶƚĞƌƌŽ ϰ

>ŝƐĂ

ϵͬϭϬ

ϮϬͬϯϬ

ϭϮͬϮϬ

ϮϭͬϰϬ

Pierre

ϴͬϭϬ

ϮϭͬϯϬ

ďƐ͘

ϯϮͬϰϬ

^ŽƉŚŝĞ

ďƐ͘

ϭϲͬϯϬ

ďƐ͘

ϮϱͬϰϬ

dŽƚĂů

WŽƵƌĐĞŶƚĂŐĞ

p.41 A2a

2 ĂͿ ĂůĐƵůĞ ŵĞŶƚĂůĞŵĞŶƚ͘ ϭϬ й ĚĞ ϮϬϬ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϱ й ĚĞ ϴϬϬϬ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϱϬ й ĚĞ Ϯϰ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϮϬ й ĚĞ ϯϮϱϬ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Ϯϱ й ĚĞ ϴϮϰ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϳϱ й ĚĞ ϰϲϬ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ďͿ EŽƚĞ ĚĞ ƉůƵƐŝĞƵƌƐ ŵĂŶŝğƌĞƐ ůĞ ĐĂůĐƵů ƋƵŝ ƚĞ ƉĞƌŵĞƚ Ě͛ĞĨĨĞĐƚƵĞƌ ůĞ ƉŽƵƌĐĞŶƚĂŐĞ ĚĞŵĂŶĚĠ ă ůĂ ĐĂůĐƵůĂƚƌŝĐĞ͘ ϯϰ й ĚĞ ϰϳϬϬ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϯϰ й ĚĞ ϰϳϬϬ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϯϰ й ĚĞ ϰϳϬϬ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϳ й ĚĞ ϮϭϯϬ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϳ й ĚĞ ϮϭϯϬ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ p.41 A2b

ϳ й ĚĞ ϮϭϯϬ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ACTIVITÉS

Chapitre 3 Traitement de données et pourcentages

3 ĂͿ WŽƵƌ ůĂ ĨġƚĞ ĂŶŶƵĞůůĞ ĚĞ ů͛ĠĐŽůĞ͕ ƵŶ ĐŚĂƉŝƚĞĂƵ Ă ĠƚĠ ĚƌĞƐƐĠ ĚĂŶƐ ůĂ ĐŽƵƌ ĚĞ ƌĠĐƌĠĂƚŝŽŶ͘ /ů Ă ĠƚĠ ĂŵĠŶĂŐĠ ĂĨŝŶ ĚĞ ƌĞĐĞǀŽŝƌ ĂƵ ŵĂǆŝŵƵŵ ϯϮϬ ƐƉĞĐƚĂƚĞƵƌƐ͘ ^ĂĐŚĂŶƚ ƋƵ͛ŝů ĠƚĂŝƚ ƌĞŵƉůŝ ă ϴϬ й ĚĞ ƐĂ ĐĂƉĂĐŝƚĠ͕ ĚĠƚĞƌŵŝŶĞ ůĞ ŶŽŵďƌĞ ĚĞ ƉůĂĐĞƐ ŝŶŽĐĐƵƉĠĞƐ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ďͿ ^Ƶƌ ůĞƐ ϲϱϳ ĠůğǀĞƐ ŝŶƐĐƌŝƚƐ ĚĂŶƐ ƵŶĞ ĠĐŽůĞ͕ ϯϮ ŶĞ ƐĞ ƐŽŶƚ ƉůƵƐ ƌĠŝŶƐĐƌŝƚƐ ů͛ĂŶŶĠĞ ƐĐŽůĂŝƌĞ ƐƵŝǀĂŶƚĞ͘

^ĂŶƐ ĐĂůĐƵůĂƚƌŝĐĞ͕ ĚĠƚĞƌŵŝŶĞ Ɛŝ ůĞ ƉŽƵƌĐĞŶƚĂŐĞ Ě͛ĠůğǀĞƐ ŶŽŶ ƌĠŝŶƐĐƌŝƚƐ ĞƐƚ ŝŶĨĠƌŝĞƵƌ ŽƵ ƐƵƉĠƌŝĞƵƌ ă ϱ й͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

hƚŝůŝƐĞ ƚĂ ĐĂůĐƵůĂƚƌŝĐĞ ƉŽƵƌ ĚĠƚĞƌŵŝŶĞƌ ůĞ ƉŽƵƌĐĞŶƚĂŐĞ ĞǆĂĐƚ Ě͛ĠůğǀĞƐ ŶŽŶ ƌĠŝŶƐĐƌŝƚƐ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ĐͿ >ŽƌƐ ĚĞ ƐŽŶ ǀŽǇĂŐĞ ĂƵ WĠƌŽƵ͕ ŚĂƌůĞƐ Ă ƉƌŝƐ ĚĞƐ ƉŚŽƚŽƐ ĂǀĞĐ ƐŽŶ ĂƉƉĂƌĞŝů ŶƵŵĠƌŝƋƵĞ ĚŽŶƚ ůĂ ĐĂƌƚĞ ŵĠŵŽŝƌĞ ƉĞƌŵĞƚ ĚĞ ƐƚŽĐŬĞƌ ϯϱϬ ƉƌŝƐĞƐ ĚĞ ǀƵĞ͘ ůĂ ĨŝŶ ĚĞ ƐĞƐ ǀĂĐĂŶĐĞƐ͕ ů͛ĂƉƉĂƌĞŝů ůƵŝ ŝŶĚŝƋƵĞ ƋƵĞ ϯϬ й ĚĞ ůĂ ŵĠŵŽŝƌĞ Ŷ͛ŽŶƚ ƉĂƐ ĠƚĠ ƵƚŝůŝƐĠƐ͘ /ů ĨĂŝƚ ĚĠǀĞůŽƉƉĞƌ ϰϬ й ĚĞƐ ƉŚŽƚŽƐ ƌĠĂůŝƐĠĞƐ ĂĨŝŶ ĚĞ ĐŽŶƐƚŝƚƵĞƌ ƵŶ ĂůďƵŵ ĚĞ ǀĂĐĂŶĐĞƐ͘ ŽŵďŝĞŶ ĚĞ ƉŚŽƚŽƐ ŚĂƌůĞƐ ǀĂͲƚͲŝů ĐŽůůĞƌ ĚĂŶƐ ƐŽŶ ĂůďƵŵ ͍ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ĚͿ DĂƌŝĞ Ğƚ ƌŶĂƵĚ ƉŽƐƐğĚĞŶƚ ƚŽƵƐ ĚĞƵǆ ƵŶ ƐŵĂƌƚƉŚŽŶĞ͕ ĚĞ ŵĂƌƋƵĞƐ ĚŝĨĨĠƌĞŶƚĞƐ͕ ƋƵΖŝůƐ ŽŶƚ ƌĞĐŚĂƌŐĠ ĞŶ ĚĠďƵƚ ĚĞ ǁĞĞŬͲĞŶĚ͘ >ƵŶĚŝ ŵĂƚŝŶ͕ ĂǀĂŶƚ ĚĞ ƉĂƌƚŝƌ ĞŶ ĞǆĐƵƌƐŝŽŶ͕ ŝůƐ ƌĞŐĂƌĚĞŶƚ ůĞƐ ƚĠŵŽŝŶƐ ĚĞ ĐŚĂƌŐĞ ĚĞ ůĞƵƌ ƚĠůĠƉŚŽŶĞ ŵŽďŝůĞ͘ ^ŵĂƌƚƉŚŽŶĞ ĚĞ DĂƌŝĞ ͗ ^ŵĂƌƚƉŚŽŶĞ Ě͛ ƌŶĂƵĚ ͗ YƵĞů ƉŽƵƌĐĞŶƚĂŐĞ ĚƵ ĐŚĂƌŐĞŵĞŶƚ ĚĞ ůĂ ďĂƚƚĞƌŝĞ ƌĞƐƚĞͲƚͲŝů ă ĐŚĂĐƵŶ Ě͛ĞƵǆ ͍ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

^ĂĐŚĂŶƚ ƋƵĞ ů͛ĂƵƚŽŶŽŵŝĞ ŵĂǆŝŵĂůĞ ĞŶ ĐŽŵŵƵŶŝĐĂƚŝŽŶ ĚĞ ůĂ ďĂƚƚĞƌŝĞ ĚĞ ĐŚĂƋƵĞ ŵŽďŝůĞ ĞƐƚ ĚĞ ϴ ŚĞƵƌĞƐ͕ ĚĠƚĞƌŵŝŶĞ ůĞ ƚĞŵƉƐ ƌĞƐƚĂŶƚ ĚĞ ĐŽŵŵƵŶŝĐĂƚŝŽŶ ă DĂƌŝĞ Ğƚ ă ƌŶĂƵĚ͘ ǆƉƌŝŵĞ ƚĞƐ ƌĠƉŽŶƐĞƐ ĞŶ ŚĞƵƌĞƐ Ğƚ ĞŶ ŵŝŶƵƚĞƐ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ACTIVITÉS

Chapitre 3 Traitement de données et pourcentages

ĞͿ >Ğ ƚĂďůĞĂƵ ĐŝͲĚĞƐƐŽƵƐ ĚŽŶŶĞ ůĂ ƌĠƉĂƌƚŝƚŝŽŶ ĚĞƐ ϳϮϱ ĠůğǀĞƐ Ě͛ƵŶĞ ĠĐŽůĞ Ě͛ĞŶƐĞŝŐŶĞŵĞŶƚ ŐĠŶĠƌĂů ĞŶ ĨŽŶĐƚŝŽŶ ĚĞ ůĞƵƌ ĂŶŶĠĞ Ě͛ĠƚƵĚĞ͘ ĂůĐƵůĞ͕ ă ů͛ƵŶŝƚĠ ƉƌğƐ͕ ůĞƐ ƉŽƵƌĐĞŶƚĂŐĞƐ Ě͛ĠůğǀĞƐ ĚĂŶƐ ĐŚĂƋƵĞ ĂŶŶĠĞ Ě͛ĠƚƵĚĞ͘ ŶŶĠĞ

EŽŵďƌĞ Ě͛ĠůğǀĞƐ

ϭre

ϭϴϭ

Ϯe

ϭϲϳ

ϯe

ϭϮϬ

ϰe

ϭϬϵ

ϴϵ

ϱϵ

WŽƵƌĐĞŶƚĂŐĞ

TOTAUX 4 ĂͿ ŽŵƉůğƚĞ ůĞƐ ĂĨĨŝĐŚĞƐ ƐƵŝǀĂŶƚĞƐ͘ sĠƌŝĨŝĞ ƚĞƐ ƌĠƐƵůƚĂƚƐ ă ůĂ ĐĂůĐƵůĂƚƌŝĐĞ͘

p.41 A2c

Wƌŝǆ ,ds

ϱϬϬ €

Wƌŝǆ ,ds

ϯϮϬ €

ds Ϯϭ й

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ds ϲ й

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Wƌŝǆ ds

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Wƌŝǆ ds

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

WŽƵƌ ĐŚĂƋƵĞ ĂĨĨŝĐŚĞ͕ ƚƌŽƵǀĞ ƵŶ ĐĂůĐƵů ƵŶŝƋƵĞ ƋƵŝ ƉĞƌŵĞƚ ĚĞ ĚĠƚĞƌŵŝŶĞƌ ůĞ Ɖƌŝǆ ds ă ƉĂƌƚŝƌ ĚƵ Ɖƌŝǆ ,ds ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ďͿ sĠƌŝĨŝĞ ĚĞ ĚĞƵǆ ŵĂŶŝğƌĞƐ ĚŝĨĨĠƌĞŶƚĞƐ ůΖĞǆĂĐƚŝƚƵĚĞ ĚĞƐ ĠƚŝƋƵĞƚƚĞƐ ĐŝͲĚĞƐƐŽƵƐ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϱϲϬ € ZŝƐƚŽƵƌŶĞ ϭϬ й ϰϱϬ €

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

p.41 A2d

ϵϰϬ € ZŝƐƚŽƵƌŶĞ ϱ й ϴϵϯ €

ACTIVITÉS

Chapitre 3 Traitement de données et pourcentages

ĐͿ Ŷ ǀƵĞ ĚĞƐ ƉƌŽĐŚĂŝŶĞƐ ĐůĂƐƐĞƐ ĚĞ ŶĞŝŐĞ͕ ƵŶĞ ĠĐŽůĞ Ă ĚĠĐŝĚĠ ĚĞ ƌĞŶŽƵǀĞůĞƌ ƐŽŶ ƐƚŽĐŬ ĚĞ ŵĂƚĠƌŝĞů ĚĞ ƐŬŝ͘ ůůĞ ĂĐŚğƚĞ ůĞƐ ĂƌƚŝĐůĞƐ ƐƵŝǀĂŶƚƐ ͗ ϭϬ ƌĂƋƵĞƚƚĞƐ ă ŶĞŝŐĞ ă ϵϱ Φ ƉŝğĐĞ͕ ϭϱ ƉĂŝƌĞƐ ĚĞ ƐŬŝ ă ϯϳϱ Φ ůĂ ƉĂŝƌĞ Ğƚ ϭϱ ƉĂŝƌĞƐ ĚĞ ďąƚŽŶƐ ă Ϯϱ Φ ůĂ ƉĂŝƌĞ͘ ^ĂĐŚĂŶƚ ƋƵĞ ůĂ ds ĞƐƚ ĚĞ Ϯϭ й͕ ĚĠƚĞƌŵŝŶĞ͙ ůĞ Ɖƌŝǆ ƚŽƚĂů ,ds ĚĞ ĐĞƐ ĂĐŚĂƚƐ ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ůĞ Ɖƌŝǆ ds ĞŶ ƵƚŝůŝƐĂŶƚ ƵŶ ƐĞƵů ĐĂůĐƵů ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ĚͿ DĂĚĂŵĞ EŝĐĂŝƐĞ Ă ƵŶ ƐĂůĂŝƌĞ ďƌƵƚ ŵĞŶƐƵĞů ĚĞ ϮϰϳϬ Φ͘ ^ŽŶ ĚŝƌĞĐƚĞƵƌ ůƵŝ ĂŶŶŽŶĐĞ ƋƵ͛ă ƉĂƌƚŝƌ ĚƵ ŵŽŝƐ ƉƌŽĐŚĂŝŶ͕ ĞůůĞ ĐŚĂŶŐĞƌĂ ĚĞ ĨŽŶĐƚŝŽŶ Ğƚ ĂƵƌĂ ƵŶĞ ĂƵŐŵĞŶƚĂƚŝŽŶ ĚĞ ϴ й͘ ůůĞ ƉƌĞŶĚ ĂůŽƌƐ ƐĂ ĐĂůĐƵůĂƚƌŝĐĞ Ğƚ ĚĠƚĞƌŵŝŶĞ ƐŽŶ ŶŽƵǀĞĂƵ ƐĂůĂŝƌĞ ĞŶ ĞĨĨĞĐƚƵĂŶƚ ƵŶ ƐĞƵů ĐĂůĐƵů͘ dƌŽƵǀĞ ĐĞ ĐĂůĐƵů͘

ĞͿ WĞŶĚĂŶƚ ůĞƐ ƐŽůĚĞƐ͕ DĂƌĐ Ă ƚƌŽƵǀĠ ĚĞƐ ďĂƐŬĞƚƐ ĂĨĨŝĐŚĠƐ ă ϱϰ Φ ĂƵ ůŝĞƵ ĚĞ ϵϬ Φ͘ ĂůĐƵůĞ ůĞ ƉŽƵƌĐĞŶƚĂŐĞ ĚĞ ůĂ ƌĠĚƵĐƚŝŽŶ ƉĂƌ ƌĂƉƉŽƌƚ ĂƵ Ɖƌŝǆ ŝŶŝƚŝĂů͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ĨͿ hŶ ŵĂŐĂƐŝŶ ƉƌŽƉŽƐĞ ůĞƐ ƌĠĚƵĐƚŝŽŶƐ ƐƵŝǀĂŶƚĞƐ ͗ ʹϮϬ й ă ůΖĂĐŚĂƚ ĚĞ Ϯ ĂƌƚŝĐůĞƐ͕ ʹϯϬ й ă ůΖĂĐŚĂƚ ĚĞ ϯ ĂƌƚŝĐůĞƐ͕ ʹϰϬ й ă ůΖĂĐŚĂƚ ĚĞ ϰ ĂƌƚŝĐůĞƐ ŽƵ ƉůƵƐ͘

DĂƌŝŶĞ ĂĐŚğƚĞ ƵŶĞ ƉĂŝƌĞ ĚĞ ĐŚĂƵƐƐƵƌĞƐ ă ϰϬ Φ Ğƚ ĚĞƵǆ ĨŽƵůĂƌĚƐ ă ϭϬ Φ ƉŝğĐĞ͘ KĐĠĂŶĞ ĂĐŚğƚĞ ƵŶĞ ƉĂŝƌĞ ĚĞ ĐŚĂƵƐƐƵƌĞƐ ă ϰϬ Φ Ğƚ ƚƌŽŝƐ ĨŽƵůĂƌĚƐ ă ϭϬ Φ ƉŝğĐĞ͘ JUSTIFIE ƉŽƵƌƋƵŽŝ KĐĠĂŶĞ Ă ĨĂŝƚ ƵŶĞ ŵĞŝůůĞƵƌĞ ĂĨĨĂŝƌĞ ƋƵĞ DĂƌŝŶĞ͘ ÉCRIS ƚŽƵƐ ƚĞƐ ĐĂůĐƵůƐ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ĐƚŝǀŝƚĠ ϯ Notion de repérage 1 WŽƵƌ ůĞ ĐŽƵƌƐ ĚĞ ƐĐŝĞŶĐĞƐ͕ DĂƚŚŝĞƵ Ă ƌĞůĞǀĠ ůĞƐ ƚĞŵƉĠƌĂƚƵƌĞƐ ĞǆƚĠƌŝĞƵƌĞƐ ă ƉůƵƐŝĞƵƌƐ ŵŽŵĞŶƚƐ Ě͛ƵŶĞ ũŽƵƌŶĠĞ͘ /ů Ă ŶŽƚĠ ůĞƐ ƌĠƐƵůƚĂƚƐ ĚĂŶƐ ůĞ ƚĂďůĞĂƵ ĐŝͲĚĞƐƐŽƵƐ͘ ϭ Ś ϭΣ

ϯ Ś ϯΣ

ϴ Ś ϱΣ

ϭϮ Ś ϵΣ

ϭϱ Ś ϭϬΣ

ϮϬ Ś ϲΣ

Ϯϰ Ś ϮΣ

Ŷ ĐůĂƐƐĞ͕ ůĞ ƉƌŽĨĞƐƐĞƵƌ ŝŶǀŝƚĞ ůĞƐ ĠůğǀĞƐ ă ƉŽƌƚĞƌ ĐĞƐ ĚŽŶŶĠĞƐ ƐƵƌ ƵŶ ŐƌĂƉŚŝƋƵĞ͘ WŽƵƌ ĐĞůĂ͕ ŝů ůĞƵƌ ĚĞŵĂŶĚĞ ĚĞ ƚƌĂĐĞƌ ĚĞƵǆ ĚƌŽŝƚĞƐ ƉĞƌƉĞŶĚŝĐƵůĂŝƌĞƐ ͗ ƵŶĞ ĚƌŽŝƚĞ ŚŽƌŝǌŽŶƚĂůĞ ƐƵƌ ůĂƋƵĞůůĞ ƐŽŶƚ ŶŽƚĠĞƐ ůĞƐ ŚĞƵƌĞƐ ;ϱ ŵŵ ƉŽƵƌ ϭ ŚͿ Ğƚ ƵŶĞ ĚƌŽŝƚĞ ǀĞƌƚŝĐĂůĞ ƐƵƌ ůĂƋƵĞůůĞ ƐŽŶƚ ƌĞƉŽƌƚĠĞƐ ůĞƐ ƚĞŵƉĠƌĂƚƵƌĞƐ ;ϭϬ ŵŵ ƉŽƵƌ ϭΣ Ϳ͘ 64

ACTIVITÉS

Chapitre 3 Traitement de données et pourcentages ǀŽůƵƟ ŽŶ ĚĞ ůĂ ƚĞŵƉĠƌĂƚƵƌĞ ƉĞŶĚĂŶƚ ƵŶĞ ũŽƵƌŶĠĞ Température (°C)

1 Temps (h) 0

ĂͿ ĐŚğǀĞ ůĂ ŐƌĂĚƵĂƚŝŽŶ ĚĞƐ ĚĞƵǆ ĂǆĞƐ͘ ďͿ ^ĂĐŚĂŶƚ ƋƵĞ ůĞ ƉŽŝŶƚ ƌĞƉƌĠƐĞŶƚĠ ƐŝŐŶŝĨŝĞ ƋƵ͛ă ϴ Ś ĚƵ ŵĂƚŝŶ͕ ůĂ ƚĞŵƉĠƌĂƚƵƌĞ ĠƚĂŝƚ ĚĞ ϱΣ ͕ ƌĞƉğƌĞ ƐƵƌ ůĞ ƋƵĂĚƌŝůůĂŐĞ ĐŝͲĚĞƐƐƵƐ ůĞƐ Ɛŝǆ ĂƵƚƌĞƐ ƉŽŝŶƚƐ ƌĞƉƌĠƐĞŶƚĂŶƚ ůĂ ƚĞŵƉĠƌĂƚƵƌĞ ŽďƐĞƌǀĠĞ ĂƵǆ ĚŝĨĨĠƌĞŶƚĞƐ ŚĞƵƌĞƐ͘ ĐͿ ůĂ ůĂƚƚĞ͕ ƌĞůŝĞ ůĞƐ ƐĞƉƚ ƉŽŝŶƚƐ ƉŽƵƌ ŵŽŶƚƌĞƌ ů͛ĠǀŽůƵƚŝŽŶ ĚĞ ůĂ ƚĞŵƉĠƌĂƚƵƌĞ ĚƵƌĂŶƚ ůĂ ũŽƵƌŶĠĞ͘ ĚͿ hƚŝůŝƐĞ ůĞ ŐƌĂƉŚŝƋƵĞ ƉŽƵƌ ĞƐƚŝŵĞƌ ůĞƐ ƚĞŵƉĠƌĂƚƵƌĞƐ ă Ϯ Ś͕ ϭϬ Ś Ğƚ ϮϮ Ś͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

2 ĂͿ ĠƚĞƌŵŝŶĞ ůĞƐ ĐŽŽƌĚŽŶŶĠĞƐ ĚĞƐ ƉŽŝŶƚƐ ƌĞƉƌĠƐĞŶƚĠƐ ĚĂŶƐ ůĞ ƌĞƉğƌĞ ĐĂƌƚĠƐŝĞŶ ĐŝͲĐŽŶƚƌĞ͘ A ; ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ; ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ Ϳ

G ; ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ; ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ Ϳ

, ; ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ; ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ Ϳ

I ; ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ; ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ Ϳ

J ; ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ; ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ Ϳ

O ; ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ; ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ Ϳ

^Ƶƌ ůĞ ŵġŵĞ ƌĞƉğƌĞ ĐĂƌƚĠƐŝĞŶ͕ ƉůĂĐĞ ůĞƐ ƉŽŝŶƚƐ ĚŽŶƚ ǀŽŝĐŝ ůĞƐ ĐŽŽƌĚŽŶŶĠĞƐ ͗ ;Ϯ ͖ ϵͿപ ;Ϯ ͖ ϭϱͿപ ;ϯ ͖ ϭϴͿപ ;ϰ ͖ ϭϱͿപ& ;ϰ ͖ ϵͿ ZĞůŝĞ͕ ĚĂŶƐ ů͛ŽƌĚƌĞ͕ ůĞƐ ƉŽŝŶƚƐ K͕ ͕ ͕ ͕ ͕ ͕ &͕ '͕ ,͕ /͕ : Ğƚ K͘ p.42 B

YƵ͛ŽďƚŝĞŶƐͲƚƵ ͍ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ J

1 0

H 1

ACTIVITÉS

Chapitre 3 Traitement de données et pourcentages

3 Ğ ϴ Ś ă ϵ Ś ĚƵ ŵĂƚŝŶ͕ ůĞ ƉĂƐƐĂŐĞƌ Ě͛ƵŶ ŵŽďŝů ŚŽŵĞ ƌŽƵůĂŶƚ ĞŶ ŵŽŶƚĂŐŶĞ Ă ŶŽƚĠ ƚŽƵƚĞƐ ůĞƐ ϭϬ ŵŝŶƵƚĞƐ ůĞƐ ƚĞŵƉĠƌĂƚƵƌĞƐ ĞǆƚĠƌŝĞƵƌĞƐ ŝŶĚŝƋƵĠĞƐ ƐƵƌ ůĞ ƚŚĞƌŵŽŵğƚƌĞ ĚĞ ƐŽŶ ǀĠŚŝĐƵůĞ͘ dĞŵƉƐ ;ŵŝŶͿ dĞŵƉĠƌĂƚƵƌĞ ;Σ Ϳ

Ϭ ϭ

ϭϬ Ϯ͕ϱ

ϮϬ ϯ͕ϯ

ϯϬ ϰ

ϰϬ ϰ͕Ϯ

ϱϬ ϯ͕ϴ

ϲϬ Ϯ͕ϱ

ĂŶƐ ůĞ ƌĞƉğƌĞ ĐĂƌƚĠƐŝĞŶ ĐŝͲĚĞƐƐŽƵƐ͕ ƉůĂĐĞ ůĞƐ ƐĞƉƚ ƉŽŝŶƚƐ ƌĞƉƌĠƐĞŶƚĂŶƚ ůĞƐ ŝŶĨŽƌŵĂƚŝŽŶƐ ĚƵ ƚĂďůĞĂƵ͘ ŶƐƵŝƚĞ͕ ƌĞůŝĞͲůĞƐ ĂĨŝŶ ĚĞ ŵŽŶƚƌĞƌ ů͛ĠǀŽůƵƚŝŽŶ ĚĞ ůĂ ƚĞŵƉĠƌĂƚƵƌĞ͘

ǀŽůƵƚŝŽŶ ĚĞ ůĂ ƚĞŵƉĠƌĂƚƵƌĞ ĞŶƚƌĞ ϴ Ś Ğƚ ϵ Ś y

ŽŵƉůğƚĞ ůĞƐ ĐŽƵƉůĞƐ ƉŽƵƌ ƋƵ͛ŝůƐ ƌĠƉŽŶĚĞŶƚ ă ůĂ ĐŽŶĚŝƟ ŽŶ ĠŶŽŶĐĠĞ͘ ĂͿ >͛ĂďƐĐŝƐƐĞ ǀĂƵƚ ϯ ĚĞ ƉůƵƐ ƋƵĞ ů͛ŽƌĚŽŶŶĠĞ͘ ; ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͖ ϰͿ

;ϱ ͖ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ Ϳ

;ϯ ͖ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ Ϳ

;ϰ͕ϱ ͖ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ Ϳ

; ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͖ ϲͿ

; ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͖ ϰ͕ϯͿ

;ϱ͕ϰ ͖ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ Ϳ

; ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͖ ϳ͕ϮͿ

;Ϭ ͖ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ Ϳ

;Ϯ͕ϲ ͖ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ Ϳ

; ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͖ ϱ͕ϴͿ

; ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͖ ϯ͕ϲͿ

;ϱ͕ϭ ͖ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ Ϳ

ďͿ >͛ŽƌĚŽŶŶĠĞ ǀĂƵƚ Ϯ͕ϱ ĚĞ ŵŽŝŶƐ ƋƵĞ ů͛ĂďƐĐŝƐƐĞ͘ ;ϳ ͖ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ Ϳ

; ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͖ Ϯ͕ϱͿ

;ϯ͕ϲ ͖ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ Ϳ

ĐͿ >͛ĂďƐĐŝƐƐĞ ǀĂƵƚ ůĞ Ɵ ĞƌƐ ĚĞ ů͛ŽƌĚŽŶŶĠĞ͘ ; ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͖ ϲͿ

;ϯ ͖ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ Ϳ

;Ϯ͕ϭ ͖ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ Ϳ

ĚͿ >͛ŽƌĚŽŶŶĠĞ ǀĂƵƚ ůĞ ĚŽƵďůĞ ĚĞ ů͛ĂďƐĐŝƐƐĞ͘ ;ϱ ͖ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ Ϳ

; ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͖ ϴͿ

; ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͖ ϵͿ

ĞͿ >Ă ƐŽŵŵĞ ĚĞƐ ĐŽŽƌĚŽŶŶĠĞƐ ǀĂƵƚ ϭϮ͘ ;ϳ ͖ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ Ϳ

; ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͖ ϲͿ

;ϳ͕ϱ ͖ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ Ϳ

Chapitre 3 Traitement de données et pourcentages

ACTIVITÉS

ĐƚŝǀŝƚĠ ϰ Utilisation du rapporteur ĂŶƐ ĐŚĂĐƵŶ ĚĞƐ ĐĂƐ ƐƵŝǀĂŶƚƐ͕ ƚƵ ƵƚŝůŝƐĞƌĂƐ ƚŽŶ ƌĂƉƉŽƌƚĞƵƌ ƉŽƵƌ ƌĠĂůŝƐĞƌ ůĞƐ ĐŽŶƐƚƌƵĐƚŝŽŶƐ ĚĞŵĂŶĚĠĞƐ͘ 1 ZĞƉŽƌƚĞ ĚĂŶƐ ůĞ ĐĞƌĐůĞ ůĞƐ ƚƌŽŝƐ ƐĞĐƚĞƵƌƐ ĚŽŶƚ ůĞƐ ĂŵƉůŝƚƵĚĞƐ ƐŽŶƚ ĚŽŶŶĠĞƐ ĚĂŶƐ ůĞ ƚĂďůĞĂƵ͘ ŶƐƵŝƚĞ͕ ŵĞƐƵƌĞ ůΖĂŵƉůŝƚƵĚĞ ĚƵ ĚĞƌŶŝĞƌ ƐĞĐƚĞƵƌ͕ ŶŽƚĞͲůĂ ĚĂŶƐ ůĞ ƚĂďůĞĂƵ Ğƚ ǀĠƌŝĨŝĞ ƋƵĞ ůĂ ƐŽŵŵĞ ĚĞƐ ĂŵƉůŝƚƵĚĞƐ ǀĂƵƚ ϯϲϬΣ͘

^ĞĐƚĞƵƌ

ŵƉůŝƚƵĚĞ

ϴϱΣ

ϳϬΣ

ϭϰϴΣ

ϰ Total

ϯϲϬΣ

2 ZĞƉŽƌƚĞ ĚĂŶƐ ůĞ ĐĞƌĐůĞ͕ ă ƉĂƌƚŝƌ ĚƵ ƉŽŝŶƚ ͕ ůĞƐ ƋƵĂƚƌĞ ƐĞĐƚĞƵƌƐ ĚŽŶƚ ůĞƐ ĂŵƉůŝƚƵĚĞƐ ƐŽŶƚ ĚŽŶŶĠĞƐ ĚĂŶƐ ůĞ ƚĂďůĞĂƵ͘ ZĞƐƉĞĐƚĞ ďŝĞŶ ůΖŽƌĚƌĞ ĚĞ ĐĞƵǆͲĐŝ Ğƚ ĂƐƐƵƌĞͲƚŽŝ ƋƵΖŝůƐ ƌĞŵƉůŝƐƐĞŶƚ ĞǆĂĐƚĞŵĞŶƚ ůĞ ĐĞƌĐůĞ͘

^ĞĐƚĞƵƌ

ŵƉůŝƚƵĚĞ

ϮϭϬΣ

ϮϮΣ

ϳϴΣ

ϱϬΣ

Total

ϯϲϬΣ

p.45 D

ACTIVITÉS

Chapitre 3 Traitement de données et pourcentages

ĐƚŝǀŝƚĠ ϱ Représentation de données numériques 1 sŽŝĐŝ ůĂ ƌĠƉĂƌƚŝƚŝŽŶ ĚĞƐ ĚĠƉĞŶƐĞƐ ĂŶŶƵĞůůĞƐ ĐŽŶƐĂĐƌĠĞƐ ĂƵǆ ůŽŝƐŝƌƐ ĚĞ ůĂ ĨĂŵŝůůĞ ƵƉŽŶƚ͘ ^ƉĞĐƚĂĐůĞƐ ͗ ϮϬ й sĂĐĂŶĐĞƐ ͗ ϯϱ й

ƌƚƐ ͗ ϱ й ^ƉŽƌƚƐ ͗ Ϯϱ й

>ĞĐƚƵƌĞƐ ͗ ϭϱ й

ŽŵƉůğƚĞ ůĞ ƚĂďůĞĂƵ Ğƚ ƌĞƉƌĠƐĞŶƚĞ ĐĞƐ ĚŽŶŶĠĞƐ ă ů͛ĂŝĚĞ Ě͛ƵŶ ĚŝĂŐƌĂŵŵĞ ĐŝƌĐƵůĂŝƌĞ͘

ĠƉĞŶƐĞƐ WŽƵƌĐĞŶƚĂŐĞ ŵƉůŝƚƵĚĞ

ZĠƉĂƌƚŝƚŝŽŶ ĚĞƐ ĚĠƉĞŶƐĞƐ

^ƉĞĐƚĂĐůĞƐ Arts >ĞĐƚƵƌĞƐ Vacances ^ƉŽƌƚƐ p.44 C3

dŽƚĂƵǆ

ϭϬϬ й

ϯϲϬΣ

2 >Ğ ƚĂďůĞĂƵ ĐŝͲĚĞƐƐŽƵƐ ĐŽŶƚŝĞŶƚ ůĂ ƌĠƉĂƌƚŝƚŝŽŶ ĚĞƐ ϭϲϬ ůŝĐĞŶĐŝĠƐ ĚĞƐ ĐůƵďƐ ƐƉŽƌƚŝĨƐ Ě͛ƵŶ ǀŝůůĂŐĞ ǁĂůůŽŶ ĞŶ ĨŽŶĐƚŝŽŶ ĚĞ ůĞƵƌ ĚŝƐĐŝƉůŝŶĞ ƐƉŽƌƚŝǀĞ͘ hƚŝůŝƐĞ ƚĂ ĐĂůĐƵůĂƚƌŝĐĞ ƉŽƵƌ ĐŽŵƉůĠƚĞƌ ůĞ ƚĂďůĞĂƵ͘ ŶƐƵŝƚĞ͕ ŝůůƵƐƚƌĞ ĐĞƚƚĞ ƌĠƉĂƌƚŝƚŝŽŶ ƉĂƌ ƵŶ ĚŝĂŐƌĂŵŵĞ ĐŝƌĐƵůĂŝƌĞ͘

^ƉŽƌƚ ĂƐŬĞƚ

ϭϳ

&ŽŽƚďĂůů

Tennis

ϮϬ

sŽůůĞǇ

ϭϵ

Natation

ϯϴ

dŽƚĂƵǆ

EŽŵďƌĞ Ě͛ĂĨĨŝůŝĠƐ

ŵƉůŝƚƵĚĞ % ĞŐƌĠƐ

ĞŐƌĠƐ ĂƌƌŽŶĚŝƐ

ZĠƉĂƌƚŝƚŝŽŶ ĚĞƐ ƐƉŽƌƚƐ

ACTIVITÉS

Chapitre 3 Traitement de données et pourcentages

ZĠƉĂƌƟ Ɵ ŽŶ ĚĞƐ ůŝǀƌĞƐ ĚĞ ůĂ ďŝďůŝŽƚŚğƋƵĞ

>Ă ďŝďůŝŽƚŚĠĐĂŝƌĞ Ě͛ƵŶĞ ĠĐŽůĞ Ă ƌĞĐĞŶƐĠ ůĞ ŶŽŵďƌĞ ĚĞ ůŝǀƌĞƐ ĚĞ ůĂ ďŝďůŝŽƚŚğƋƵĞ ƉĂƌ ĐĂƚĠŐŽƌŝĞƐ͘

Nombre de livres

ŽŶƐƚƌƵŝƐ ƵŶ ĚŝĂŐƌĂŵŵĞ ĞŶ ďąƚŽŶƐ ŝůůƵƐƚƌĂŶƚ ĐĞƚƚĞ ƐŝƚƵĂƚŝŽŶ͘ ^ƉŽƌƚƐ

EĂƚƵƌĞ

ϮϲϬ ϮϯϬ ϭϱϬ

WŽĠƐŝĞ

ZĞǀƵĞ

ZŽŵĂŶ

p.43 C2

ϲϬ

ϵϬ

ϴϬ

3 50

0 Catégories

4 sŽŝĐŝ ůĞƐ ƌĠƐƵůƚĂƚƐ ĚΖƵŶĞ ĞŶƋƵġƚĞ ƌĠĂůŝƐĠĞ ĂƵƉƌğƐ ĚĞƐ ϭϮϬ ũĞƵŶĞƐ͕ ƉŽƌƚĂŶƚ ƐƵƌ ůΖĂĐƚŝǀŝƚĠ ĐŚŽŝƐŝĞ ůŽƌƐ ĚĞ ƐƚĂŐĞƐ ĚΖĠƚĠ ͗ ƵŶ ũĞƵŶĞ ƐƵƌ ϲ ƐĞ ƌĞŶĚ ă ůĂ ƐĂůůĞ ĚΖŝŶĨŽƌŵĂƟ ƋƵĞ͕ ƵŶ Ɵ ĞƌƐ ĚĞƐ ũĞƵŶĞƐ ĨĂŝƚ ĚƵ ďƌŝĐŽůĂŐĞ͕ ϱ й ĚĞƐ ũĞƵŶĞƐ ǀŽŶƚ ă ůĂ ďŝďůŝŽƚŚğƋƵĞ͕ ƵŶ ũĞƵŶĞ ƐƵƌ ϴ ƐĞ ƌĞŶĚ ă ůΖĂƚĞůŝĞƌ ƉŚŽƚŽ͕ ůĞ ƌĞƐƚĞ ĚĞƐ ũĞƵŶĞƐ ƉƌĂƟ ƋƵĞ ƵŶ ƐƉŽƌƚ͘ ƉƌğƐ ĂǀŽŝƌ ĐŽŵƉůĠƚĠ ůĞ ƚĂďůĞĂƵ͕ ĐŽŶƐƚƌƵŝƐ ƵŶ ĚŝĂŐƌĂŵŵĞ ĞŶ ďąƚŽŶƐ ŝůůƵƐƚƌĂŶƚ ĐĞƚƚĞ ƐŝƚƵĂƚŝŽŶ͘ Répar on des ac vités ĐƚŝǀŝƚĠ

Nombre de jeunes

EŽŵďƌĞ ĚĞ ũĞƵŶĞƐ

/ŶĨŽƌŵĂƚŝƋƵĞ ƌŝĐŽůĂŐĞ ŝďůŝŽƚŚğƋƵĞ

WŚŽƚŽ ^ƉŽƌƚ

Ac vités

p.43 C1

>ĞƐ ƉĂƌĞŶƚƐ ĚĞ EŝĐŽůĂƐ ů͛ŽŶƚ ƉĞƐĠ ƵŶĞ ĨŽŝƐ ƉĂƌ ĂŶ ĚĞƉƵŝƐ ƐĂ ŶĂŝƐƐĂŶĐĞ ũƵƐƋƵ͛ă ϲ ĂŶƐ͘ ŽŶƐƚƌƵŝƐ ƵŶ ŐƌĂƉŚŝƋƵĞ ŵŽŶƚƌĂŶƚ ǀŽůƵƟ ŽŶ ĚĞ ůĂ ŵĂƐƐĞ ĚĞ EŝĐŽůĂƐ ů͛ĠǀŽůƵƚŝŽŶ ĚĞ ůĂ ŵĂƐƐĞ ĚĞ EŝĐŽůĂƐ ĞŶ ĨŽŶĐƚŝŽŶ ĚĞ ƐŽŶ ąŐĞ͘ ŐĞ ;ĂŶƐͿ DĂƐƐĞ ;ŬŐͿ Ϭ ϰ ϭ ϭϭ Ϯ ϭϯ ϯ ϭϱ ϰ ϭϴ ϱ Ϯϭ 6 Ϯϱ 69

ACTIVITÉS

Chapitre 3 Traitement de données et pourcentages

ĐƚŝǀŝƚĠ ϲ Analyse de graphiques et de diagrammes 1 hŶ ƉƌŽĨĞƐƐĞƵƌ Ă ƚƌĂĚƵŝƚ ůĞƐ ƌĠƐƵůƚĂƚƐ ĚΖƵŶ ƚĞƐƚ ŶŽƚĠ ƐƵƌ ϭϬ ƉĂƌ ůĞ ĚŝĂŐƌĂŵŵĞ ĞŶ ďąƚŽŶƐ ƋƵĞ ǀŽŝĐŝ͘ Nombre d’élèves 6

Résultats d’un test noté sur 10

4 3 2 1 Cote sur 10

0 1

hƚŝůŝƐĞ ůĞ ŐƌĂƉŚŝƋƵĞ ƉŽƵƌ ƌĠƉŽŶĚƌĞ ĂƵǆ ƋƵĞƐƚŝŽŶƐ ƐƵŝǀĂŶƚĞƐ͘ ĂͿ YƵĞů ĞƐƚ ůĞ ŶŽŵďƌĞ ĚΖĠůğǀĞƐ ƋƵŝ͙ ŽŶƚ ƉĂƌƚŝĐŝƉĠ ĂƵ ƚĞƐƚ ͍ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ŽŶƚ ŽďƚĞŶƵ ůĂ ŶŽƚĞ ŵĂǆŝŵĂůĞ ͍ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ƐŽŶƚ ĞŶ ĠĐŚĞĐ ͍ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ŽŶƚ ƉůƵƐ ĚĞ ϴϬ й ͍ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ďͿ ĂůĐƵůĞ ůĞ ƉŽƵƌĐĞŶƚĂŐĞ ĚΖĠůğǀĞƐ ƋƵŝ ŽŶƚ ŽďƚĞŶƵ ĞǆĂĐƚĞŵĞŶƚ ϱ ƐƵƌ ϭϬ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ĐͿ >Ğ ƉƌŽĨĞƐƐĞƵƌ Ă ĚĠĐŝĚĠ ĚĞ ƌĠĐŽŵƉĞŶƐĞƌ ůĞƐ ĠůğǀĞƐ ƋƵŝ ŽŶƚ ŽďƚĞŶƵ ĂƵ ŵŽŝŶƐ ϳ ƐƵƌ ϭϬ͘ ŽŵďŝĞŶ ƐŽŶƚͲŝůƐ ͍ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

2 sŽŝĐŝ ƵŶ ŐƌĂƉŚŝƋƵĞ ŝůůƵƐƚƌĂŶƚ ůĞƐ ďĞƐŽŝŶƐ ŵŽǇĞŶƐ ũŽƵƌŶĂůŝĞƌƐ ĞŶ ŬŝůŽĐĂůŽƌŝĞƐ ĚĞƐ ĨŝůůĞƐ Ğƚ ĚĞƐ ŐĂƌĕŽŶƐ͘ Kilocalories 3500 3000 2500 2000 1500 1000 500 0

Besoins journaliers en kilocalories

10-12 ans Filles

13-15 ans Garçons

16-19 ans

ACTIVITÉS

Chapitre 3 Traitement de données et pourcentages

hƚŝůŝƐĞ ĐĞ ŐƌĂƉŚŝƋƵĞ ƉŽƵƌ ƌĠƉŽŶĚƌĞ ĂƵǆ ƋƵĞƐƚŝŽŶƐ ĐŝͲĚĞƐƐŽƵƐ͘ ĂͿ >ƵĐŝĞ Ă ϭϭ ĂŶƐ͘ ŽŵďŝĞŶ ůƵŝ ĨĂƵƚͲŝů ĚĞ ŬŝůŽĐĂůŽƌŝĞƐ ƉĂƌ ũŽƵƌ ͍ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ďͿ ƌŶĂƵĚ ĞƐƚ ƵŶ ŐƌĂŶĚ ƐƉŽƌƚŝĨ ąŐĠ ĚĞ ϭϭ ĂŶƐ Ğƚ ŝů ĂďƐŽƌďĞ ϮϱϱϬ ŬŝůŽĐĂůŽƌŝĞƐ ƉĂƌ ũŽƵƌ͘ ͲƚͲŝů ůĂ ƌĂƚŝŽŶ ĚŽŶƚ ŝů Ă ďĞƐŽŝŶ ͍ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ĐͿ ĂŶƐ ƵŶ ĐĂŵƉ ƐĐŽƵƚ ĐŽŵƉŽƐĠ ƵŶŝƋƵĞŵĞŶƚ ĚĞ ĨŝůůĞƐ ĚĞ ĚŝĨĨĠƌĞŶƚƐ ąŐĞƐ͕ ƋƵĞůůĞ ƌĂƚŝŽŶ ĨĂƵƚͲŝů ĨŽƵƌŶŝƌ ƉŽƵƌ ġƚƌĞ ĐĞƌƚĂŝŶ ƋƵ͛ĞůůĞƐ ĂŝĞŶƚ ƚŽƵƚĞƐ ƵŶĞ ƌĂƚŝŽŶ ĐŽƌƌĞƐƉŽŶĚĂŶƚ ă ůĞƵƌƐ ďĞƐŽŝŶƐ ũŽƵƌŶĂůŝĞƌƐ ͍ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ĚͿ ĠƚĞƌŵŝŶĞ ůĞ ŶŽŵďƌĞ ĚĞ ŬŝůŽĐĂůŽƌŝĞƐ ƐƵƉƉůĠŵĞŶƚĂŝƌĞƐ ĚŽŶƚ Ă ďĞƐŽŝŶ ƵŶ ŐĂƌĕŽŶ ĚĞ ϭϴ ĂŶƐ ƉĂƌ ƌĂƉƉŽƌƚ ă ƵŶĞ ĨŝůůĞ ĚƵ ŵġŵĞ ąŐĞ͕ ƉƵŝƐ ĞǆƉƌŝŵĞ ĐĞƚƚĞ ƋƵĂŶƚŝƚĠ ĞŶ ƉŽƵƌĐĞŶƚƐ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ĞͿ ŽŵŝŶŝƋƵĞ ƐĞ ŶŽƵƌƌŝƚ ĞŶ ƌĞƐƉĞĐƚĂŶƚ ůĞƐ ďĞƐŽŝŶƐ ũŽƵƌŶĂůŝĞƌƐ Ğƚ ĂďƐŽƌďĞ ϮϳϬϬ ŬĐĂů ƉĂƌ ũŽƵƌ͘ ^͛ĂŐŝƚͲŝů Ě͛ƵŶĞ ĨŝůůĞ ŽƵ Ě͛ƵŶ ŐĂƌĕŽŶ Ğƚ ĚĞ ƋƵĞůůĞ ƚƌĂŶĐŚĞ Ě͛ąŐĞƐ ĨĂŝƚ ƉĂƌƚŝĞ ŽŵŝŶŝƋƵĞ ͍ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

3 >Ğ ŐƌĂƉŚŝƋƵĞ ĐŝͲĐŽŶƚƌĞ ƌĞƉƌĠƐĞŶƚĞ ůĂ ƌĠƉĂƌƚŝƚŝŽŶ ĚĞƐ ŽƵǀƌŝĞƌƐ Ě͛ƵŶĞ WD ƐĞůŽŶ ůĞƵƌ ŐƌŽƵƉĞ ƐĂŶŐƵŝŶ͘

'ƌŽƵƉĞ ƐĂŶŐƵŝŶ ĚĞƐ ŽƵǀƌŝĞƌƐ Ě͛ƵŶĞ WD

ĂͿ >ĞƐ ĂĨĨŝƌŵĂƚŝŽŶƐ ƐƵŝǀĂŶƚĞƐ ƐŽŶƚͲĞůůĞƐ ǀƌĂŝĞƐ ŽƵ ĨĂƵƐƐĞƐ ͍ :ƵƐƚŝĨŝĞ͘ >Ğ ŐƌŽƵƉĞ ƐĂŶŐƵŝŶ ůĞ ƉůƵƐ ƌĞƉƌĠƐĞŶƚĠ ĞƐƚ ůĞ ŐƌŽƵƉĞ ͘

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

>Ğ ŐƌŽƵƉĞ ƐĂŶŐƵŝŶ ůĞ ŵŽŝŶƐ ƌĞƉƌĠƐĞŶƚĠ ĞƐƚ ůĞ ŐƌŽƵƉĞ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

WůƵƐ ĚĞ ůĂ ŵŽŝƚŝĠ ĚĞƐ ŽƵǀƌŝĞƌƐ ƐŽŶƚ ĚƵ ŐƌŽƵƉĞ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

DŽŝŶƐ ĚĞ ϳϱ й ĚĞƐ ŽƵǀƌŝĞƌƐ ƐŽŶƚ ĚƵ ŐƌŽƵƉĞ ŽƵ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ďͿ hƚŝůŝƐĞ ƚĂ ĐĂůĐƵůĂƚƌŝĐĞ ƉŽƵƌ ĐŽŵƉůĠƚĞƌ ůĞ ƚĂďůĞĂƵ ĐŝͲĚĞƐƐŽƵƐ͘ 'ƌŽƵƉĞ

ŵƉůŝƚƵĚĞ

WŽƵƌĐĞŶƚĂŐĞ

EŽŵďƌĞ Ě͛ŽƵǀƌŝĞƌƐ

A B AB O

ϮϰϬ

TOTAUX 71

ACTIVITÉS

Chapitre 3 Traitement de données et pourcentages

4 KŶ Ă ƌĞƉƌĠƐĞŶƚĠ ĐŝͲĐŽŶƚƌĞ ů͛ĠǀŽůƵƚŝŽŶ ĚĞ ůĂ ĚŝƐƚĂŶĐĞ ƉĂƌĐŽƵƌƵĞ ƉĂƌ ƵŶ ĂƵƚŽŵŽďŝůŝƐƚĞ ůŽƌƐ ĚĞ ƐŽŶ ĚĠƉĂƌƚ ĞŶ ǀĂĐĂŶĐĞƐ͘ hƚŝůŝƐĞ ĐĞ ŐƌĂƉŚŝƋƵĞ ƉŽƵƌ ƌĠƉŽŶĚƌĞ ĂƵǆ ƋƵĞƐƚŝŽŶƐ ƐƵŝǀĂŶƚĞƐ͘

ǀŽůƵƟ ŽŶ ĚĞ ůĂ ĚŝƐƚĂŶĐĞ ƉĂƌĐŽƵƌƵĞ Distance (km)

ĂͿ YƵĞůůĞ ĚŝƐƚĂŶĐĞ ůΖĂƵƚŽŵŽďŝůŝƐƚĞ ĂͲƚͲŝů ƉĂƌĐŽƵƌƵĞ Ğƚ ĞŶ ĐŽŵďŝĞŶ ĚĞ ƚĞŵƉƐ ͍ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

100 Durée (h)

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ďͿ YƵĞůůĞ ĚŝƐƚĂŶĐĞ ůΖĂƵƚŽŵŽďŝůŝƐƚĞ ĂͲƚͲŝů ƉĂƌĐŽƵƌƵĞ ĂƵ ďŽƵƚ ĚĞ͙ ϭ Ś ͍ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϯ Ś ͍ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ĐͿ Ƶ ďŽƵƚ ĚĞ ĐŽŵďŝĞŶ ĚĞ ƚĞŵƉƐ ĐĞƚ ĂƵƚŽŵŽďŝůŝƐƚĞ ĂͲƚͲŝů ƉĂƌĐŽƵƌƵ͘͘͘ ϭϬϬ Ŭŵ ͍ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϮϬϬ Ŭŵ ͍ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϰϳϱ Ŭŵ ͍ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϱϬϬ Ŭŵ ͍ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ĚͿ Ƶ ĐŽƵƌƐ ĚĞ ƐŽŶ ƚƌĂũĞƚ͕ ŝů Ă ĨĂŝƚ ƵŶĞ ƉĂƵƐĞ͘ WĞŶĚĂŶƚ ĐŽŵďŝĞŶ ĚĞ ƚĞŵƉƐ ͍ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ĞͿ ƋƵĞůůĞ ǀŝƚĞƐƐĞ ŵŽǇĞŶŶĞ ĂͲƚͲŝů ƌŽƵůĠ ͙ ƉĞŶĚĂŶƚ ůĂ ϭre ŚĞƵƌĞ ͍ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ƉĞŶĚĂŶƚ ůĞƐ ƚƌŽŝƐ ƉƌĞŵŝğƌĞƐ ŚĞƵƌĞƐ ͍ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ĚĞƉƵŝƐ ƐŽŶ ĚĠƉĂƌƚ ũƵƐƋƵ͛ĂƵ ŵŽŵĞŶƚ ĚĞ ůĂ ƉĂƵƐĞ ͍ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ 25 dƌŽŝƐ ĂŵŝƐ ĚĠĐŝĚĞŶƚ ĚĞ ĨĂŝƌĞ ƵŶĞ ĐŽƵƌƐĞ ă ƉŝĞĚ ĚĂŶƐ ůĂ ŐƌĂŶĚĞ ƉĞůŽƵƐĞ ĚĞ ůΖƵŶ ĚΖĞƵǆ͘ WŽƵƌ ĐĞůĂ͕ ŝůƐ ĚŽŝǀĞŶƚ ĐŽƵƌŝƌ ĞŶ ůŝŐŶĞ ĚƌŽŝƚĞ ũƵƐƋƵΖă ƵŶ ƐĂƉŝŶ ƐŝƚƵĠ ă ƵŶĞ ĚŝƐƚĂŶĐĞ ĚĞ ϴϬ ŵ͕ ůĞ ƚŽƵĐŚĞƌ ĚĞ ůĂ ŵĂŝŶ͕ ƉƵŝƐ ƌĞǀĞŶŝƌ ƐƵƌ ůĞƵƌƐ ƉĂƐ ă ůĞƵƌ ƉŽŝŶƚ ĚĞ ĚĠƉĂƌƚ͘ >Ğ ŐƌĂƉŚŝƋƵĞ ĐŝͲĐŽŶƚƌĞ ŝůůƵƐƚƌĞ ůĂ ĚŝƐƚĂŶĐĞ ĚĞ ĐŚĂĐƵŶ ƉĂƌ ƌĂƉƉŽƌƚ ă ůĞƵƌ ƉŽŝŶƚ ĚĞ ĚĠƉĂƌƚ͘

ŝƐƚĂŶĐĞ ƉĂƌĐŽƵƌƵĞ ƉĂƌ ƌĂƉƉŽƌƚ ĂƵ ƉŽŝŶƚ ĚĞ ĚĠƉĂƌƚ y Distance (m) Alex Claude Mar n

20 0

Temps (s)

hƚŝůŝƐĞ ůĞ ŐƌĂƉŚŝƋƵĞ ƉŽƵƌ ƌĠƉŽŶĚƌĞ ĂƵǆ ƋƵĞƐƚŝŽŶƐ ƐƵŝǀĂŶƚĞƐ͘ ĂͿ YƵŝ Ă ƚŽƵĐŚĠ ůĞ ƐĂƉŝŶ ůĞ ƉƌĞŵŝĞƌ Ğƚ ĞŶ ĐŽŵďŝĞŶ ĚĞ ƚĞŵƉƐ ͍ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ďͿ YƵŝ Ă ŐĂŐŶĠ ůĂ ĐŽƵƌƐĞ Ğƚ ĞŶ ĐŽŵďŝĞŶ ĚĞ ƚĞŵƉƐ ͍ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ĐͿ hŶ ĐŽƵƌĞƵƌ Ă ĐŚƵƚĠ ůŽƌƐ ĚƵ ƚƌĂũĞƚ ƌĞƚŽƵƌ͘ YƵŝ ͍ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ĐŽŵďŝĞŶ ĚĞ ŵğƚƌĞƐ ĚĞ ů͛ĂƌƌŝǀĠĞ ĐĞƚƚĞ ĐŚƵƚĞ Ɛ͛ĞƐƚͲĞůůĞ ƉƌŽĚƵŝƚĞ ͍ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ŽŵďŝĞŶ ĚĞ ƚĞŵƉƐ ĐĞ ĐŽƵƌĞƵƌ ĂͲƚͲŝů ƉĞƌĚƵ ĞŶ ĐŚƵƚĂŶƚ ͍ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ĚͿ YƵĞů Ăŵŝ Ă ƚƌŝĐŚĠ ͍ ǆƉůŝƋƵĞ ƉŽƵƌƋƵŽŝ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Chapitre 3 Traitement de données et pourcentages

EXERCICES COMPLÉMENTAIRES

Connaître 1

YƵĞů ƚǇƉĞ ĚĞ ŐƌĂƉŚŝƋƵĞ ĐŽŶǀŝĞŶƚ ůĞ ŵŝĞƵǆ ƉŽƵƌ ƌĞƉƌĠƐĞŶƚĞƌ ͗ ĂͿ ůĂ ƌĠƉĂƌƟ Ɵ ŽŶ ĚĞƐ ĂĐĐŝĚĞŶƚƐ ĚĞ ůĂ ƌŽƵƚĞ ƐĞůŽŶ ůĞ ƚǇƉĞ Ě͛ƵƐĂŐĞƌ ͍ ďͿ ůĞƐ ƌĠƐƵůƚĂƚƐ ŽďƚĞŶƵƐ ƉĂƌ ƵŶ ĠůğǀĞ ĚĂŶƐ ůĞƐ Ěŝī ĠƌĞŶƚƐ ĐŽƵƌƐ ͍ ĐͿ ů͛ĠǀŽůƵƟ ŽŶ ĚĞ ů͛ŝŶĚĞǆ ĚĞƐ Ɖƌŝǆ ă ůĂ ĐŽŶƐŽŵŵĂƟ ŽŶ ĐĞƐ Ěŝǆ ĚĞƌŶŝğƌĞƐ ĂŶŶĠĞƐ ͍ ĚͿ ůĂ ǀĂƌŝĂƟ ŽŶ ĚĞ ůĂ ĚƵƌĠĞ Ě͛ĞŶƐŽůĞŝůůĞŵĞŶƚ ĂƵ ĐŽƵƌƐ ĚƵ ŵŽŝƐ ĚĞ ũƵŝŶ ͍ ĞͿ ůĂ ƌĠƉĂƌƟ Ɵ ŽŶ ĚĞ ůĂ ƉŽƉƵůĂƟ ŽŶ ƐĐŽůĂŝƌĞ ƐĞůŽŶ ůĞ ƚǇƉĞ Ě͛ĞŶƐĞŝŐŶĞŵĞŶƚ ͍ ĨͿ ůĞ ŶŽŵďƌĞ Ě͛ŚĂďŝƚĂŶƚƐ ĞŶ ĞůŐŝƋƵĞ ƉĂƌ ĐůĂƐƐĞ Ě͛ąŐĞƐ ͍ ŐͿ ů͛ŚŝƐƚŽƌŝƋƵĞ ĚĞ ůĂ ĐŽŶƐŽŵŵĂƟ ŽŶ Ě͛ĞĂƵ Ě͛ƵŶ ŵĠŶĂŐĞ ĐĞƐ ĐŝŶƋ ĚĞƌŶŝğƌĞƐ ĂŶŶĠĞƐ ͍

>ĞƐ ƉƌŽƉŽƐŝƟ ŽŶƐ ƐƵŝǀĂŶƚĞƐ ƐŽŶƚͲĞůůĞƐ ǀƌĂŝĞƐ ŽƵ ĨĂƵƐƐĞƐ ͍ ĂͿ ĂůĐƵůĞƌ ϳϱ й Ě͛ƵŶ ŶŽŵďƌĞ ƌĞǀŝĞŶƚ ă ĞŶ ƉƌĞŶĚƌĞ ůĞƐ ϯͬϰ͘ ďͿ WŽƵƌ ĐĂůĐƵůĞƌ ϵ й Ě͛ƵŶ ŵŽŶƚĂŶƚ Ě͛ƵŶĞ ĨĂĐƚƵƌĞ͕ ŽŶ ůĞ ŵƵůƟ ƉůŝĞ ƉĂƌ Ϭ͕ϵ͘ ĐͿ hŶĞ ƌĞŵŝƐĞ ĚĞ ϮϬ € ƐƵƌ ƵŶ ĂƌƟ ĐůĞ ĐŽƸƚĂŶƚ ϴϬ € ĐŽƌƌĞƐƉŽŶĚ ă ƵŶĞ ƌĠĚƵĐƟ ŽŶ ĚĞ Ϯϱ й͘ ĚͿ ^ŝ ƵŶĞ ƉŽƉƵůĂƟ ŽŶ ƐĐŽůĂŝƌĞ ƉĂƐƐĞ ĚĞ ϭϬϬ ă ϭϯϮ ĠůğǀĞƐ͕ ĂůŽƌƐ ĞůůĞ ĂƵŐŵĞŶƚĞ ĚĞ ϯϮ й͘ ĞͿ ĂůĐƵůĞƌ ƵŶ ŵŽŶƚĂŶƚ ŵĂũŽƌĠ ĚĞ ϴ й ƌĞǀŝĞŶƚ ă ůĞ ŵƵůƟ ƉůŝĞƌ ƉĂƌ ϭ͕ϴ͘

>ĞƋƵĞů ĚĞ ĐĞƐ ďŝĞŶƐ ŝŵŵŽďŝůŝĞƌƐ Ă ǀƵ ƐŽŶ Ɖƌŝǆ ĚŝŵŝŶƵĞƌ ůĞ ƉůƵƐ ͍ :ƵƐƟ Į Ğ ƚŽŶ ĐŚŽŝǆ͘ ͗ ƵŶĞ ĚŝŵŝŶƵƟ ŽŶ ĚĞ ϭϬ й ƉƵŝƐ ƵŶĞ ĚŝŵŝŶƵƟ ŽŶ ĚĞ ϯϬ й ͗ ƵŶĞ ĚŝŵŝŶƵƟ ŽŶ ĚĞ ϯϬ й ƉƵŝƐ ƵŶĞ ĚŝŵŝŶƵƟ ŽŶ ĚĞ ϭϬ й ͗ ƵŶĞ ĚŝŵŝŶƵƟ ŽŶ ĚĞ ϮϬ й ƉƵŝƐ ƵŶĞ ĚŝŵŝŶƵƟ ŽŶ ĚĞ ϮϬ й ͗ ƵŶĞ ĚŝŵŝŶƵƟ ŽŶ ĚĞ ϰϬ й

ŽŵƉůğƚĞ ĂǀĞĐ ͕ ͕ ͕ ͕ ͕ & ŽƵ '͘ ĂͿ DŽŶ ĂďƐĐŝƐƐĞ ǀĂƵƚ Ϯ ĚĞ ƉůƵƐ ƋƵĞ ŵŽŶ ŽƌĚŽŶŶĠĞ͕ ũĞ ƐƵŝƐ ůĞ ƉŽŝŶƚ ͘͘͘ ďͿ DŽŶ ĂďƐĐŝƐƐĞ ĞƐƚ ĠŐĂůĞ ă ŵŽŶ ŽƌĚŽŶŶĠĞ͕ ũĞ ƐƵŝƐ ůĞ ƉŽŝŶƚ ͘͘͘ ĐͿ DŽŶ ŽƌĚŽŶŶĠĞ ǀĂƵƚ ůĂ ŵŽŝƟ Ġ ĚĞ ŵŽŶ ĂďƐĐŝƐƐĞ͕ ũĞ ƐƵŝƐ ůĞ ƉŽŝŶƚ ͘͘͘ ĚͿ DŽŶ ŽƌĚŽŶŶĠĞ ǀĂƵƚ ůĞ ƚƌŝƉůĞ ĚĞ ŵŽŶ ĂďƐĐŝƐƐĞ͕ ũĞ ƐƵŝƐ ůĞ ƉŽŝŶƚ ͘͘͘

D A

B G

1 0

Appliquer Les pourcentages 1

ĂůĐƵůĞ ŵĞŶƚĂůĞŵĞŶƚ͘ Ϯϱ й ĚĞ ϴϬ ϮϬ й ĚĞ ϭϱϬ ϱϬ й ĚĞ ϵϴ

ϮϬ й ĚĞ ϴϱϬϬ ϱϬ й ĚĞ ϮϳϰϬ ϳϱ й ĚĞ ϯϲϴϬ

ϭϬ й ĚĞ ϲϯϱ Ϯϱ й ĚĞ ϴϰϰ ϮϬ й ĚĞ ϭϮϱ

ĂůĐƵůĞ ĞŶ ƵƟ ůŝƐĂŶƚ ĠǀĞŶƚƵĞůůĞŵĞŶƚ ƵŶĞ ĐĂůĐƵůĂƚƌŝĐĞ͘ ϭϮ й ĚĞ ϭϰ ϱϬϬ ϭϱ й ĚĞ ϰϱϬ Ϯϭ й ĚĞ ϰϱ ϬϬϬ Ϯϭ й ĚĞ ϭϮϬ ϲ й ĚĞ ϭϮ ϬϬϬ ϵ й ĚĞ ϳϴϱϬ

ϲ й ĚĞ ϴϬ ϰ й ĚĞ ϰϱϬ ϭϭ й ĚĞ ϳϬϬ

ϭϭ й ĚĞ ϰϮϬϬ ϴ й ĚĞ ϭϮϱϬ ϭϱ й ĚĞ ϲϰϮϰ

Ϯϱ й ĚĞ ϭϰϱ Ϯϭ͕ϱ й ĚĞ ϰϱϬϬ ϳ͕ϱ й ĚĞ ϲϱϬ

EXERCICES COMPLÉMENTAIRES 3

ŽŵƉůğƚĞ ůĞƐ ƚĂďůĞĂƵǆ ĞŶ ƵƟ ůŝƐĂŶƚ ĠǀĞŶƚƵĞůůĞŵĞŶƚ ƚĂ ĐĂůĐƵůĂƚƌŝĐĞ͘ Wƌŝǆ ĂǀĂŶƚ ƌĠĚƵĐƟ ŽŶ

ZĠĚƵĐƟ ŽŶ

ϯϬϬ Φ ϭϰϬϬ Φ ϰϮ͕ϲϬ Φ ϯϭ Φ ϭϴ Φ

ϮϬ й ϯϬ й ϭϱ й ϭϬ й ϯϱ й

Wƌŝǆ ĂƉƌğƐ ƌĠĚƵĐƟ ŽŶ

Wƌŝǆ ĂǀĂŶƚ Wƌŝǆ ĂƉƌğƐ ƵŐŵĞŶƚĂƟ ŽŶ ĂƵŐŵĞŶƚĂƟ ŽŶ ĂƵŐŵĞŶƚĂƟ ŽŶ ϯϮ͕ϱϬ Φ ϭϰ͕ϰϱ Φ ϰϮϰ Φ ϰϱ Φ ϯϭϬ Φ

ϭϬ й ϱ й Ϯϱ й ϲ й Ϯϭ й

Ŷ ƐŽůĚĂŶƚ ƐĞƐ Ɖƌŝǆ͕ ƵŶ ĐŽŵŵĞƌĕĂŶƚ Ă ĐŽŵŵŝƐ ƵŶĞ ĞƌƌĞƵƌ͘ ZĞƚƌŽƵǀĞͲůĂ͘ ϮϬϬ € ʹϭϬ й ϭϴϬ €

Chapitre 3 Traitement de données et pourcentages

ϳϬϬ € ʹϮϬ й ϱϲϬ €

ϭϬ € ʹϰϬ й 6€

ϯϬ € ʹϲ й Ϯϰ €

ϭϲ € ʹϮϱ й ϭϮ €

hŶ ĞŵƉůŽǇĠ ĚƵ ŵĂŐĂƐŝŶ ͨ DĞĚŝĂƉůĂǇ ͕ͩ ƐƉĠĐŝĂůŝƐƚĞ ĚĞ ůĂ ǀĞŶƚĞ Ě͛ĂƉƉĂƌĞŝůƐ ǀŝĚĠŽ ĞƐƚ ĐŚĂƌŐĠ Ě͛ĠƚĂďůŝƌ ůĂ ĨĂĐƚƵƌĞ ƌĞůĂƟ ǀĞ ă ůĂ ĐŽŵŵĂŶĚĞ ƐƵŝǀĂŶƚĞ ͗ ϰ ƚĠůĠǀŝƐĞƵƌƐ ă ϳϰϵ € ů͛ƵŶŝƚĠ ĠƐŝŐŶĂƟ ŽŶ YƵĂŶƟ ƚĠ Wƌŝǆ ƵŶŝƚĂŝƌĞ ;€Ϳ Wƌŝǆ ƚŽƚĂů ;€Ϳ ϱ ůĞĐƚĞƵƌƐ ǀŝĚĠŽ ă Ϯϱϱ € ů͛ƵŶŝƚĠ ĞƐ ůĞĐƚĞƵƌƐ DWϰ ă ϭϮϰ € ů͛ƵŶŝƚĠ ŽŵƉůğƚĞ ůĂ ĨĂĐƚƵƌĞ ĐŝͲĐŽŶƚƌĞ͘ dŽƚĂů ,d

ϱϮϲϯ

ds Ϯϭ й Total TTC

Les diagrammes 6

sŽŝĐŝ ůĞƐ ƌĠƐƵůƚĂƚƐ ĚΖƵŶ ƐŽŶĚĂŐĞ Ğī ĞĐƚƵĠ ƐƵƌ ůĞƐ ϱϬϬ ĠƚƵĚŝĂŶƚƐ ĚΖƵŶĞ ĠĐŽůĞ ĞƵƌŽƉĠĞŶŶĞ͕ ƉŽƌƚĂŶƚ ƐƵƌ ůĞ ĐŚŽŝǆ ĚĞ ůĂ ĚĞƵǆŝğŵĞ ůĂŶŐƵĞ͘ ƐƉĂŐŶŽů ͗ ϭϱϬ ŶŐůĂŝƐ ͗ ϮϮϱ ůůĞŵĂŶĚ ͗ ϳϱ /ƚĂůŝĞŶ ͗ ϰϬ ZĞƉƌĠƐĞŶƚĞ ĐĞƩ Ğ ƐŝƚƵĂƟ ŽŶ ă ůΖĂŝĚĞ ĚΖƵŶ ĚŝĂŐƌĂŵŵĞ ĐŝƌĐƵůĂŝƌĞ͘

sŽŝĐŝ ůĂ ƌĠƉĂƌƟ Ɵ ŽŶ ĚĞƐ ĚĠƉĞŶƐĞƐ ŵĞŶƐƵĞůůĞƐ Ě͛ƵŶ ŵĠŶĂŐĞ͘ >ŽŐĞŵĞŶƚ ͗ ϲϴϲ € >ŽŝƐŝƌƐ ͗ Ϯϰϱ €

ZƵƐƐĞ ͗ ϭϬ

ůŝŵĞŶƚĂƟ ŽŶ ͗ ϱϯϵ € dƌĂŶƐƉŽƌƚƐ ͗ ϯϰϯ €

,ĂďŝůůĞŵĞŶƚ ͗ ϰϰϭ € ^ĂŶƚĠ ͗ ϭϵϲ €

ZĞƉƌĠƐĞŶƚĞ ĐĞƩ Ğ ƌĠƉĂƌƟ Ɵ ŽŶ ă ů͛ĂŝĚĞ Ě͛ƵŶ ĚŝĂŐƌĂŵŵĞ ĐŝƌĐƵůĂŝƌĞ͘ 8

hŶĞ ĞŶƋƵġƚĞ Ă ĠƚĠ ƌĠĂůŝƐĠĞ ĂƵ ƐĞŝŶ Ě͛ƵŶĞ ĠĐŽůĞ ƉŽƵƌ ĐŽŶŶĂŠƚƌĞ ůĞ ƚĞŵƉƐ ŚĞďĚŽŵĂĚĂŝƌĞ ŵŽǇĞŶ ĐŽŶƐĂĐƌĠ ĂƵ ƐƉŽƌƚ͘ sŽŝĐŝ ůĞƐ ƌĠƐƵůƚĂƚƐ ŽďƚĞŶƵƐ ;ĞŶ ŵŝŶƵƚĞƐͿ ƉŽƵƌ ůĞƐ Ɛŝǆ ĂŶŶĠĞƐ͘ ϭre ĂŶŶĠĞ ͗ ϭϲϬ

Ϯe ĂŶŶĠĞ ͗ ϯϭϬ

ϯe ĂŶŶĠĞ ͗ ϯϯϬ

ϰe ĂŶŶĠĞ ͗ ϭϮϬ

ϱe ĂŶŶĠĞ ͗ ϭϱϬ

6e ĂŶŶĠĞ ͗ ϳϬ

ZĞƉƌĠƐĞŶƚĞ ĐĞƩ Ğ ƐŝƚƵĂƟ ŽŶ ă ů͛ĂŝĚĞ Ě͛ƵŶ ĚŝĂŐƌĂŵŵĞ ĞŶ ďąƚŽŶƐ͘ 9

Ğ ƚĂďůĞĂƵ ĚŽŶŶĞ ůĂ ŵĂƐƐĞ Ě͛ƵŶ ďĠďĠ ĚĞƉƵŝƐ ƐĂ ŶĂŝƐƐĂŶĐĞ ũƵƐƋƵ͛ă ů͛ąŐĞ Ě͛ƵŶ ĂŶ͘ ŐĞ ĞŶ ŵŽŝƐ

ϭϮ

DĂƐƐĞ ĞŶ ŬŐ

ϰ͕ϰϬϬ

ϲ͕ϰϬϬ

ϭϬ

ϭϭ͕ϲϬϬ

ϭϮ͕ϰϬϬ

ŽŶƐƚƌƵŝƐ ƵŶ ŐƌĂƉŚŝƋƵĞ ŵŽŶƚƌĂŶƚ ů͛ĠǀŽůƵƟ ŽŶ ĚĞ ůĂ ŵĂƐƐĞ ĚĞ ĐĞ ďĠďĠ͘

Chapitre 3 Traitement de données et pourcentages

10 >Ğ ĚŝĂŐƌĂŵŵĞ ĐŝƌĐƵůĂŝƌĞ ĐŝͲĐŽŶƚƌĞ ƌĞƉƌĠƐĞŶƚĞ

EXERCICES COMPLÉMENTAIRES Nombre d’enfants par famille

ůĞ ŶŽŵďƌĞ Ě͛ĞŶĨĂŶƚƐ ƉĂƌ ĨĂŵŝůůĞ ƐƵŝƚĞ ă ƵŶĞ ĞŶƋƵġƚĞ ŵĞŶĠĞ ĂƵƉƌğƐ ĚĞ ϳϬ ĨĂŵŝůůĞƐ͘ ĠƚĞƌŵŝŶĞ ůĞ ŶŽŵďƌĞ ĚĞ ĨĂŵŝůůĞƐ Ŷ͛ĂǇĂŶƚ ƉĂƐ Ě͛ĞŶĨĂŶƚ͕ ĂǇĂŶƚ ƵŶ͕ ĚĞƵǆ͕ ƚƌŽŝƐ ĞŶĨĂŶƚƐ ŽƵ ƉůƵƐ ĚĞ ƚƌŽŝƐ ĞŶĨĂŶƚƐ͘

0 enfant 1 enfant 2 enfants 3 enfants plus de 3 enfants

11 WŽƵƌ ůĂ ũŽƵƌŶĠĞ ĚĞ ƉůĞŝŶ Ăŝƌ ĂƵƚŽŵŶĂůĞ͕ ƋƵĂƚƌĞ

Inscrip ons aux quatre ac vités

ĂĐƟ ǀŝƚĠƐ ŽŶƚ ĠƚĠ ƉƌŽƉŽƐĠĞƐ ĂƵǆ ϮϱϬ ĠůğǀĞƐ ĚƵ ƉƌĞŵŝĞƌ ĚĞŐƌĠ Ě͛ƵŶĞ ĠĐŽůĞ ƐĞĐŽŶĚĂŝƌĞ͘ 14% Mini-golf ŝͲĐŽŶƚƌĞ͕ ǀŽŝĐŝ ůĞƐ ƌĠƐƵůƚĂƚƐ ĚĞƐ ŝŶƐĐƌŝƉƟ ŽŶƐ 38% Randonnée pédestre ĂƵǆ Ěŝī ĠƌĞŶƚĞƐ ĂĐƟ ǀŝƚĠƐ͘ 26% ZĠƉŽŶĚƐ ĂƵǆ ƋƵĞƐƟ ŽŶƐ ĐŝͲĚĞƐƐŽƵƐ͘ Randonnée vélo ĂͿ YƵĞůůĞ ĂĐƟ ǀŝƚĠ Ă ĠƚĠ ĐŚŽŝƐŝĞ ƉĂƌ ĂƵ ŵŽŝŶƐ Descente en kayak 22% ƵŶ ĠůğǀĞ ƐƵƌ ƚƌŽŝƐ ͍ ďͿ ŽŵďŝĞŶ Ě͛ĠůğǀĞƐ ƐĞ ƐŽŶƚ ŝŶƐĐƌŝƚƐ ă ůĂ ƌĂŶĚŽŶŶĠĞ ƉĠĚĞƐƚƌĞ ͍ ĐͿ ŽŵďŝĞŶ Ě͛ĠůğǀĞƐ ŶĞ ƉĂƌƟ ĐŝƉĞƌŽŶƚ ƉĂƐ ĂƵ ŵŝŶŝͲŐŽůĨ ͍ ĚͿ >Ă ĚĞƐĐĞŶƚĞ ĞŶ ŬĂǇĂŬ Ă ĠƚĠ ĐŚŽŝƐŝĞ ƉĂƌ ĐŽŵďŝĞŶ Ě͛ĠůğǀĞƐ ĚĞ ƉůƵƐ ƋƵĞ ůĂ ƌĂŶĚŽŶŶĠĞ ƉĠĚĞƐƚƌĞ ͍ 12 sŽŝĐŝ ůĞ ŐƌĂƉŚŝƋƵĞ ƌĞƉƌĠƐĞŶƚĂŶƚ ůĞ ŶŽŵďƌĞ ĚĞ

ŬŝůŽŵğƚƌĞƐ ƉĂƌĐŽƵƌƵƐ ƉĂƌ ƵŶ ĐǇĐůŝƐƚĞ ŚĞƵƌĞ ƉĂƌ ŚĞƵƌĞ ƉĞŶĚĂŶƚ ƐĂ ƌĂŶĚŽŶŶĠĞ ĚĞ ϭϭϬ Ŭŵ͘ ĂͿ 'ƌĂĚƵĞ ů͛ĂǆĞ ǀĞƌƟ ĐĂů͘ ďͿ ŽŵďŝĞŶ ĚĞ ŬŝůŽŵğƚƌĞƐ ĂͲƚͲŝů ƉĂƌĐŽƵƌƵƐ ƉĞŶĚĂŶƚ ůĂ Ϯe ŚĞƵƌĞ ͍ ĐͿ YƵ͛Ă ĨĂŝƚ ůĞ ĐǇĐůŝƐƚĞ ĞŶƚƌĞ ϭϯ Ś Ğƚ ϭϳ Ś ͍ ǆƉůŝƋƵĞ͘ ĚͿ ĂŶƐ ƋƵĞů ŝŶƚĞƌǀĂůůĞ ĚĞ ƚĞŵƉƐ ƐĂ ǀŝƚĞƐƐĞ ĂͲƚͲĞůůĞ ĠƚĠ ůĂ ƉůƵƐ ĠůĞǀĠĞ ͍ ǆƉůŝƋƵĞ͘ ĞͿ WĞŶĚĂŶƚ ĐŽŵďŝĞŶ ĚĞ ƚĞŵƉƐ ĂͲƚͲŝů Ğī ĞĐƟ ǀĞŵĞŶƚ ƌŽƵůĠ ͍

Nombre de kilomètres parcourus par un cycliste

Heures 7 8 9 10 11 12 13 14 15 16 17 18

13 >ĞƐ ĚŝĂŐƌĂŵŵĞƐ ĐŝͲĚĞƐƐŽƵƐ ƉƌĠƐĞŶƚĞŶƚ ůĞƐ ƌĠƐƵůƚĂƚƐ ŽďƚĞŶƵƐ ă EŽģů ĂƵ ĐŽƵƌƐ ĚĞ ŵĂƚŚĠŵĂƟ ƋƵĞ ƉĂƌ

ůĞƐ ĠůğǀĞƐ ĚĞ ĚĞƵǆ ĐůĂƐƐĞƐ͘ ĞƐ ĠůğǀĞƐ ƐŽŶƚ ƌĠƉĂƌƟ Ɛ ĞŶ ϭϬ ŐƌŽƵƉĞƐ ƐĞůŽŶ ůĞƵƌ ƉŽƵƌĐĞŶƚĂŐĞ͘ 'ϭ ͗ ĚĞ Ϭ ă ŵŽŝŶƐ ĚĞ ϭϬ й 'Ϯ ͗ ĚĞ ϭϬ ă ŵŽŝŶƐ ĚĞ ϮϬ й Nbre d’élèves Classe 1A 'ϯ ͗ ĚĞ ϮϬ ă ŵŽŝŶƐ ĚĞ ϯϬ й 'ϰ ͗ ĚĞ ϯϬ ă ŵŽŝŶƐ ĚĞ ϰϬ й 7 'ϱ ͗ ĚĞ ϰϬ ă ŵŽŝŶƐ ĚĞ ϱϬ й 'ϲ ͗ ĚĞ ϱϬ ă ŵŽŝŶƐ ĚĞ ϲϬ й 65 'ϳ ͗ ĚĞ ϲϬ ă ŵŽŝŶƐ ĚĞ ϳϬ й 'ϴ ͗ ĚĞ ϳϬ ă ŵŽŝŶƐ ĚĞ ϴϬ й 4 3 'ϵ ͗ ĚĞ ϴϬ ă ŵŽŝŶƐ ĚĞ ϵϬ й 'ϭϬ ͗ ĚĞ ϵϬ ă ϭϬϬ й 2 1 ĂͿ ĠƚĞƌŵŝŶĞ͕ ƉŽƵƌ ĐŚĂƋƵĞ ĐůĂƐƐĞ͕ ůĞ ŶŽŵďƌĞ Ě͛ĠůğǀĞƐ ĚĞ 0 ĐŚĂƋƵĞ ŐƌŽƵƉĞ͘ G1 G2 G3 G4 G5 G6 G7 G8 ďͿ ĠƚĞƌŵŝŶĞ ůĞ ƉŽƵƌĐĞŶƚĂŐĞ ĚĞƐ ĠůğǀĞƐ ĚĞ ĐŚĂƋƵĞ ĐůĂƐƐĞ ƋƵŝ Nbre d’élèves Classe 1B ŽŶƚ ƵŶ ĠĐŚĞĐ͘ 7 ĐͿ ĠƚĞƌŵŝŶĞ ůĞ ƉŽƵƌĐĞŶƚĂŐĞ ĚĞƐ ĠůğǀĞƐ ĚĞ ĐŚĂƋƵĞ ĐůĂƐƐĞ ƋƵŝ 6 5 ŽŶƚ ĂƵ ŵŽŝŶƐ ϱϬ й͘ 4 ĚͿ ĠƚĞƌŵŝŶĞ ůĞ ƉŽƵƌĐĞŶƚĂŐĞ ĚĞƐ ĠůğǀĞƐ ĚĞ ĐŚĂƋƵĞ ĐůĂƐƐĞ ƋƵŝ 3 2 ŽŶƚ ƉůƵƐ ĚĞ ϴϬ й͘ 1 ĞͿ ǀĞĐ ƵŶ ƚĞů ŐƌĂƉŚŝƋƵĞ͕ ƉĞƵǆͲƚƵ ĚŝƌĞ ƋƵĞůůĞ ĞƐƚ ůĂ ĐůĂƐƐĞ ƋƵŝ 0 G1 G2 G3 G4 G5 G6 G7 G8 Ă ŽďƚĞŶƵ ůĞ ŵĞŝůůĞƵƌ ƌĠƐƵůƚĂƚ ͍

G9 G10

EXERCICES COMPLÉMENTAIRES

Chapitre 3 Traitement de données et pourcentages

1D 14 >Ă ŵĂŵĂŶ ĚƵ ƉĞƟ ƚ EŝĐŽůĂƐ ůƵŝ ƉĞƌŵĞƚ ĚĞ ƉƌĞŶĚƌĞ ƵŶ ďŽŶďŽŶ 1 0 ĚĂŶƐ ƵŶ ƐĂĐŚĞƚ ŽƉĂƋƵĞ͘ >Ğ ŶŽŵďƌĞ ĚĞ ďŽŶďŽŶƐ ĚĞ ĐŚĂƋƵĞ

ĐŽƵůĞƵƌ ĐŽŶƚĞŶƵƐ ĚĂŶƐ ůĞ ƐĂĐŚĞƚ ĞƐƚ ŝůůƵƐƚƌĠ ƉĂƌ ůĞ ŐƌĂƉŚŝƋƵĞ ĞŶ ďąƚŽŶƐ ĐŝͲĐŽŶƚƌĞ͘ ĂͿ >ĞƐ Ăĸ ƌŵĂƟ ŽŶƐ ƐƵŝǀĂŶƚĞƐ ƐŽŶƚͲĞůůĞƐ ǀƌĂŝĞƐ ŽƵ ĨĂƵƐƐĞƐ ͍ EXPLIQUE ƚĂ ƌĠƉŽŶƐĞ͘ ϭͿ >Ğ ƉŽƵƌĐĞŶƚĂŐĞ ĚĞ ďŽŶďŽŶƐ ũĂƵŶĞƐ ĚĂŶƐ ůĞ ƐĂĐŚĞƚ ĞƐƚ ĚĞ ϭϱ й͘ ϮͿ >Ă ƉƌŽƉŽƌƟ ŽŶ ĚĞ ďŽŶďŽŶƐ ǀĞƌƚƐ ĚĂŶƐ ůĞ ƐĂĐŚĞƚ ĞƐƚ ϲͬϴ͘ ďͿ IDENTIFIE ůĞ ĚŝĂŐƌĂŵŵĞ ĐŝƌĐƵůĂŝƌĞ ƋƵŝ ĐŽƌƌĞƐƉŽŶĚ ĂƵ ĐŽŶƚĞŶƵ ĚƵ ƐĂĐŚĞƚ͘

Rouge 25 %

Rose 15 %

Rouge 27 % Jaune 20 %

Orange 10 %

6 5 4 3 2 1 0

Jaune

Rose 18 %

Vert Orange Rouge Rose Couleurs des bonbons Rose 20 %

Rouge 25 % Jaune 15 %

Orange 10 %

Vert 30 %

Nombre de bonbons

Jaune 15 %

Orange 10 % Vert 30 %

Vert 30 %

Le repérage 15 ŽŵƉůğƚĞ ůĞƐ ĐŽƵƉůĞƐ ƉŽƵƌ ƋƵ͛ŝůƐ ƌĠƉŽŶĚĞŶƚ ă ůĂ ĐŽŶĚŝƟ ŽŶ ĠŶŽŶĐĠĞ͘

ĂͿ >͛ĂďƐĐŝƐƐĞ Ğƚ ů͛ŽƌĚŽŶŶĠĞ ƐŽŶƚ ĚĞƵǆ ŶŽŵďƌĞƐ ĐŽŶƐĠĐƵƟ ĨƐ͘ ;ϰ ͖ ͙Ϳ ;͘͘͘ ͖ ϭͿ ;Ϭ ͖ ͘͘͘Ϳ ďͿ >͛ŽƌĚŽŶŶĠĞ ǀĂƵƚ ϯ ĚĞ ƉůƵƐ ƋƵĞ ů͛ĂďƐĐŝƐƐĞ͘

;͘͘͘ ͖ ϳͿ

;ϭ ͖ ͘͘͘Ϳ

;͘͘͘ ͖ ϴͿ

;ϭ ͖ ͘͘͘Ϳ ;ϵ ͖ ͘͘͘Ϳ ;͘͘͘ ͖ ϳͿ ĐͿ >͛ŽƌĚŽŶŶĠĞ ǀĂƵƚ ůĂ ŵŽŝƟ Ġ ĚĞ ů͛ĂďƐĐŝƐƐĞ͘

;Ϭ ͖ ͘͘͘Ϳ

;͘͘͘ ͖ ϭϭͿ

;ϭϯ ͖ ͘͘͘Ϳ

;Ϯ ͖ ͘͘͘Ϳ ;͘͘͘ ͖ ϱͿ ;ϴ ͖ ͘͘͘Ϳ ĚͿ >͛ĂďƐĐŝƐƐĞ ǀĂƵƚ Ϯ ĚĞ ŵŽŝŶƐ ƋƵĞ ů͛ŽƌĚŽŶŶĠĞ͘

;͘͘͘ ͖ ϳͿ

;͘͘͘ ͖ ϬͿ

;ϭϰ ͖ ͘͘͘Ϳ

;ϰ ͖ ͘͘͘Ϳ ;͘͘͘ ͖ ϵͿ ;ϲ ͖ ͘͘͘Ϳ ĞͿ >Ă ƐŽŵŵĞ ĚĞƐ ĐŽŽƌĚŽŶŶĠĞƐ ǀĂƵƚ ϭϱ͘

;͘͘͘ ͖ ϮͿ

;Ϯ ͖ ͘͘͘Ϳ

;ϭϭ ͖ ͘͘͘Ϳ

;Ϭ ͖ ͘͘͘Ϳ

;͘͘͘ ͖ ϵͿ

;͘͘͘ ͖ ϭϮͿ

;ϯ ͖ ͙Ϳ

;͘͘͘ ͖ ϳͿ

;ϱ ͖ ͘͘͘Ϳ

16 ^Ƶƌ ƵŶ ĚŝĂŐƌĂŵŵĞ ĐĂƌƚĠƐŝĞŶ͕ ƉůĂĐĞ ůĞƐ ƉŽŝŶƚƐ ĚŽŶƚ ƚƵ ĐŽŶŶĂŝƐ ůĞƐ ĐŽŽƌĚŽŶŶĠĞƐ͘

;ϯ͕ϱ ͖ ϯͿ

E ;ϳ ͖ ϬͿ

^ ;ϯ͕ϱ ͖ ϭ͕ϱͿ

;Ϭ ͖ Ϯ͕ϱͿ

/ ;ϯ͕ϱ ͖ ϱ͕ϱͿ

d ;ϳ ͖ Ϯ͕ϱͿ

Z ;ϯ͕ϱ ͖ ϰͿ

K ;Ϭ ͖ ϬͿ

ZĞůŝĞ ůĞƐ ƉŽŝŶƚƐ ũƵĚŝĐŝĞƵƐĞŵĞŶƚ ĚĞ ĨĂĕŽŶ ă ĨĂŝƌĞ ĂƉƉĂƌĂŠƚƌĞ ůĞ ůŽŐŽ ĚΖƵŶĞ ǀŽŝƚƵƌĞ ĨƌĂŶĕĂŝƐĞ͘ Ğ ƋƵĞů ůŽŐŽ ƐΖĂŐŝƚͲŝů ͍

Transférer 1

:ƵƐƋƵ͛ă ƉƌĠƐĞŶƚ͕ WĂƵů Ă ŽďƚĞŶƵ ϰϬͬϲϬ ůŽƌƐ ĚĞƐ Ěŝī ĠƌĞŶƚƐ ƚƌĂǀĂƵǆ ĚĞ ĨƌĂŶĕĂŝƐ͘ ƵũŽƵƌĚ͛ŚƵŝ͕ ůĞ ƉƌŽĨĞƐƐĞƵƌ ĚĠĐŝĚĞ ĚĞ ĨĂŝƌĞ ƵŶ ĐŽŶƚƌƀůĞ͘ WĂƵů ǀŽƵĚƌĂŝƚ͕ ĂƵ ƚĞƌŵĞ ĚĞ ĐĞƩ Ğ ŝŶƚĞƌƌŽŐĂƟ ŽŶ͕ ĂǀŽŝƌ ƵŶĞ ŵŽǇĞŶŶĞ ĚĞ ϳϬ й ƉŽƵƌ ů͛ĞŶƐĞŵďůĞ ĚĞ ƐĞƐ ƚƌĂǀĂƵǆ͘ YƵĞůůĞ ĚŽŝƚ ġƚƌĞ ƐĂ ĐŽƚĞ ƐƵƌ ϮϬ ă ĐĞ ĚĞƌŶŝĞƌ ĐŽŶƚƌƀůĞ ͍ hŶĞ ĞŶƚƌĞƉƌŝƐĞ ƋƵŝ ĞŵƉůŽŝĞ ϮϱϬϬ ƉĞƌƐŽŶŶĞƐ ƌĠĂůŝƐĞ ƵŶĞ ĞŶƋƵġƚĞ ƉŽƵƌ ƐĂǀŽŝƌ ƋƵĂŶĚ ƉůĂĐĞƌ ůĂ ĐŚĞ ůĞƐ ƌĠƐƵůƚĂƚƐ ͗ ϱe ƐĞŵĂŝŶĞ ĚĞ ĐŽŶŐĠƐ ƉĂǇĠƐ͘ ƉƌğƐ ůĞ ǀŽƚĞ͕ ůĞ ƉĂƚƌŽŶ Ăĸ EŽģů ͗ ϳϰϵ ƉĞƌƐŽŶŶĞƐപപപപപWƌŝŶƚĞŵƉƐ ͗ ϲϳϭ ƉĞƌƐŽŶŶĞƐപപപപപ ƚĠ ͗ ϭϬϱϮ ƉĞƌƐŽŶŶĞƐ ĂͿ ĂůĐƵůĞ ůĞ ƉŽƵƌĐĞŶƚĂŐĞ ĚĞ ƉĞƌƐŽŶŶĞƐ ĚĞ ů͛ĞŶƚƌĞƉƌŝƐĞ ƋƵŝ ƐŽƵŚĂŝƚĞŶƚ ůĂ ƉůĂĐĞƌ ă EŽģů͕ ĂƵ ƉƌŝŶƚĞŵƉƐ Ğƚ ĞŶ ĠƚĠ͘ ďͿ ĂůĐƵůĞ ůĞ ŶŽŵďƌĞ ĚĞ ƉĞƌƐŽŶŶĞƐ Ŷ͛ĂǇĂŶƚ ƉĂƐ ƌĠƉŽŶĚƵ Ğƚ ůĞ ƉŽƵƌĐĞŶƚĂŐĞ ƋƵ͛ĞůůĞƐ ƌĞƉƌĠƐĞŶƚĞŶƚ ĚĂŶƐ ů͛ĞŶƚƌĞƉƌŝƐĞ͘

Chapitre 3 Traitement de données et pourcentages

EXERCICES COMPLÉMENTAIRES

hŶ ŐĂƌĂŐŝƐƚĞ ǀĞŶĚ ƵŶĞ ǀŽŝƚƵƌĞ ĚĞ Ϯϴ ϰϯϱ € ds ĐŽŵƉƌŝƐĞ͘ /ů ƉƌŽƉŽƐĞ ĂƵ ĐůŝĞŶƚ ĚĞ ůƵŝ ŽĨĨƌŝƌ ƵŶĞ ƌŝƐƚŽƵƌŶĞ ĚĞ Ϯϭ й ƋƵŝ͕ ƐĞůŽŶ ůƵŝ͕ ĠƋƵŝǀĂƵƚ ă ůĂ ds ͘ ĂůĐƵůĞ ůĞ Ɖƌŝǆ ă ƉĂǇĞƌ ƉĂƌ ůĞ ĐůŝĞŶƚ Ğƚ ůĞ ƉŽƵƌĐĞŶƚĂŐĞ ƌĠĞů ĚĞ ůĂ ƌŝƐƚŽƵƌŶĞ ĂĐĐŽƌĚĠĞ ƉĂƌ ůĞ ŐĂƌĂŐŝƐƚĞ͘ ĞƚƚĞ ƌŝƐƚŽƵƌŶĞ ĞƐƚͲĞůůĞ ŝŶĨĠƌŝĞƵƌĞ͕ ƐƵƉĠƌŝĞƵƌĞ ŽƵ ĠŐĂůĞ ĂƵ ŵŽŶƚĂŶƚ ĚĞ ůĂ ds ͍

>ŽƌƐƋƵ͛ŝů ǀĂ ĐŚĞǌ ƐŽŶ ŽĐƵůŝƐƚĞ͕ DŽŶƐŝĞƵƌ >ĞďŽƌŐŶĞ ƉĂŝĞ ϳϱ € ƉŽƵƌ ůĂ ĐŽŶƐƵůƚĂƚŝŽŶ͘ ^Ă ŵƵƚƵĞůůĞ ůƵŝ ƌĞŵďŽƵƌƐĞ ϳϬ й ĚĞ ĐĞ ŵŽŶƚĂŶƚ͘ ^Ƶƌ ůĞ ŵŽŶƚĂŶƚ ƌĞƐƚĂŶƚ ă ƐĂ ĐŚĂƌŐĞ ĂƉƌğƐ ƌĞŵďŽƵƌƐĞŵĞŶƚ ĚĞ ůĂ ŵƵƚƵĞůůĞ͕ ƐŽŶ ĂƐƐƵƌĂŶĐĞ ͨ ƐŽŝŶƐ ĚĞ ƐĂŶƚĠ ͩ ůƵŝ ƌĞŵďŽƵƌƐĞ ϴϬ й͘ YƵĞů ƉŽƵƌĐĞŶƚĂŐĞ ĚƵ Ɖƌŝǆ ĚĞ ůĂ ĐŽŶƐƵůƚĂƚŝŽŶ ĂͲƚͲŝů ĨŝŶĂůĞŵĞŶƚ ƉĂǇĠ ͍

WĂƉĂ Ă ĚĠĐŝĚĠ Ě͛ĂĐŚĞƚĞƌ ƵŶĞ ŶŽƵǀĞůůĞ ǀŽŝƚƵƌĞ Ğƚ ƐĞ ƌĞŶĚ ĂƵ ŐĂƌĂŐĞ ĞůĂƵƚŽ͘ WůƵƐŝĞƵƌƐ ŵŽĚğůĞƐ Ğƚ ŽƉƟ ŽŶƐ ůƵŝ ƐŽŶƚ ƉƌŽƉŽƐĠƐ͘ /ů ĐŽŶƐƵůƚĞ ůĞ ƚĂƌŝĨ ĨŽƵƌŶŝ͘ DŽĚğůĞ

Wƌŝǆ ,ds ;€Ϳ

KƉƟ ŽŶƐ

Wƌŝǆ ,ds ;€Ϳ

ƐƐĞŶĐĞ ϭ͕ϲ ůŝƚƌĞ

ϭϲ ϵϯϬ

ŝƌ ĐŽŶĚŝƟ ŽŶŶĠ

ϭϬϵϬ

ƐƐĞŶĐĞ ϭ͕ϴ ůŝƚƌĞ

ϭϳ ϴϱϬ

WĞŝŶƚƵƌĞ ŵĠƚĂůůŝƐĠĞ

ϰϮϬ

ŝĞƐĞů Ϯ ůŝƚƌĞƐ

ϭϴ ϵϱϬ

WƌŽũĞĐƚĞƵƌƐ ĂŶƟ ďƌŽƵŝůůĂƌĚ

ϭϲϬ

ŝĞƐĞů Ϯ͕Ϯ ůŝƚƌĞƐ

ϭϵ ϰϮϬ

sŝƚƌĂŐĞ ĂƌƌŝğƌĞ ƐƵƌ ƚĞŝŶƚĠ

ϵϬ

ĂͿ WĂƉĂ ĐŚŽŝƐŝƚ ůĞ ŵŽĚğůĞ ĚŝĞƐĞů Ϯ ůŝƚƌĞƐ ĂǀĞĐ ůĞƐ ŽƉƟ ŽŶƐ ͨ Ăŝƌ ĐŽŶĚŝƟ ŽŶŶĠ ͩ Ğƚ ͨ ƉƌŽũĞĐƚĞƵƌƐ ĂŶƟ ďƌŽƵŝůůĂƌĚ ͩ͘ ĂůĐƵůĞ ůĞ Ɖƌŝǆ ,ds ĚƵ ǀĠŚŝĐƵůĞ ĐŚŽŝƐŝ͘ ďͿ /ů ĐŽŵŵĂŶĚĞ ƐŽŶ ǀĠŚŝĐƵůĞ ůŽƌƐ Ě͛ƵŶĞ ũŽƵƌŶĠĞ ͨ WŽƌƚĞƐ ŽƵǀĞƌƚĞƐ ͩ Ğƚ ďĠŶĠĮ ĐŝĞ Ě͛ƵŶĞ ƌĞŵŝƐĞ͘ >Ğ Ɖƌŝǆ ,ds ĚƵ ǀĠŚŝĐƵůĞ ƉĂƐƐĞ ĂůŽƌƐ ă ϭϵ ϯϵϮ €͘ ĂůĐƵůĞ ůĞ ƉŽƵƌĐĞŶƚĂŐĞ ĚĞ ůĂ ƌĞŵŝƐĞ ĚŽŶƚ ŝů Ă ďĠŶĠĮ ĐŝĠ͘ ĐͿ ^ĂĐŚĂŶƚ ƋƵĞ ůĞ ƚĂƵǆ ĚĞ ds ĂƉƉůŝƋƵĠ ĞƐƚ ĚĞ Ϯϭ й͕ ĐĂůĐƵůĞ ůĞ Ɖƌŝǆ ds ƋƵĞ ƉĂŝĞƌĂ ƉĂƉĂ͘ ĚͿ WĂƉĂ ƉĂŝĞ ƵŶ ĂĐŽŵƉƚĞ ůĞ ũŽƵƌ ĚĞ ů͛ĂĐŚĂƚ͘ >Ğ ƌĞƐƚĞ͕ ƐŽŝƚ ϭϴ ϬϬϬ € ĂƵƋƵĞů Ɛ͛ĂũŽƵƚĞŶƚ ĚĞƐ ĨƌĂŝƐ͕ ĞƐƚ ƉĂǇĠ ĞŶ Ϯϰ ŵĞŶƐƵĂůŝƚĠƐ ĚĞ ϳϳϮ͕ϱϬ € ĐŚĂĐƵŶĞ͘ ĂůĐƵůĞ ůĞ ƉŽƵƌĐĞŶƚĂŐĞ ĚĞƐ ĨƌĂŝƐ ƉĂƌ ƌĂƉƉŽƌƚ ă ůĂ ƐŽŵŵĞ ƌĞƐƚĂŶƚĞ ă ƉĂǇĞƌ͘ 6

ĂŶƐ ƵŶĞ ĠĐŽůĞ͕ ŽŶ Ă ĨĂŝƚ ƵŶ ƐŽŶĚĂŐĞ ƉŽƵƌ ĐŽŶŶĂŠƚƌĞ ůĞ ŵŽŶƚĂŶƚ ŚĞďĚŽŵĂĚĂŝƌĞ Ě͛ĂƌŐĞŶƚ ĚĞ ƉŽĐŚĞ ƌĞĕƵ ƉĂƌ ůĞƐ ĠůğǀĞƐ Ğƚ ů͛ƵƟ ůŝƐĂƟ ŽŶ ƋƵ͛ŝůƐ ĞŶ ĨŽŶƚ͘ sŽŝĐŝ ůĞƐ ƌĠƐƵůƚĂƚƐ ĚĞ ĐĞ ƐŽŶĚĂŐĞ͘ ^ŽŵŵĞ ƌĞĕƵĞ Ğ ϭϬ € ă ϭϰ͕ϵϵ € ͗ Ϯϰ й Ğ ϭϱ € ă ϭϵ͕ϵϵ € ͗ Ϯϴ й DŽŝŶƐ ĚĞ ϭϬ € ͗ ϯϮ й Ğ ϮϬ € ă Ϯϰ͕ϵϵ € ͗ ϲ й Ğ Ϯϱ € ă ϯϬ € ͗ ϳ й WůƵƐ ĚĞ ϯϬ € ͗ ϯ й hƟ ůŝƐĂƟ ŽŶ DĂŐĂǌŝŶĞƐ ͗ ϯϬ й Ğƚ s ͗ ϰϬ й

sġƚĞŵĞŶƚƐ ͗ ϰϮ й ĂƌƚĞƐ '^D ͗ Ϯϱ й

:ĞƵǆ ǀŝĚĠŽ ͗ ϱϱ й

ŚŽŝƐŝƐ ůĞ ĚŝĂŐƌĂŵŵĞ ůĞ ŵŝĞƵǆ ĂĚĂƉƚĠ ƉŽƵƌ ƌĞƉƌĠƐĞŶƚĞƌ ͗ ĂͿ ůĂ ƌĠƉĂƌƟ Ɵ ŽŶ ĚƵ ŵŽŶƚĂŶƚ ĚĞ ů͛ĂƌŐĞŶƚ ĚĞ ƉŽĐŚĞ ƌĞĕƵ ƉĂƌ ůĞƐ ũĞƵŶĞƐ ĚĞ ů͛ĠĐŽůĞര͖ ďͿ ů͛ƵƟ ůŝƐĂƟ ŽŶ ĚĞ ĐĞƚ ĂƌŐĞŶƚ ĚĞ ƉŽĐŚĞ͘ CE

1D 7 18

Ğ ĚŝĂŐƌĂŵŵĞ ƌĞƉƌĠƐĞŶƚĞ ůĂ ƌĠƉĂƌƟ Ɵ ŽŶ ĚĞƐ ƉĞƌƐŽŶŶĞƐ ŐƌĂǀĞŵĞŶƚ ďůĞƐƐĠĞƐ ƐƵƌ ůĞƐ ƌŽƵƚĞƐ ĚĂŶƐ ƵŶĞ ǀŝůůĞ ĞŶ ϮϬϭϲ͘ 1/4

1/6 Cyclistes Automobiliste Passagers Piétons Motocyclistes

1/12 1/18

DÉTERMINE ůĂ ĨƌĂĐƟ ŽŶ ĚĞ ƉĞƌƐŽŶŶĞƐ ǀƵůŶĠƌĂďůĞƐ ;ƉŝĠƚŽŶƐ͕ ĐǇĐůŝƐƚĞƐ Ğƚ ŵŽƚŽĐǇĐůŝƐƚĞƐͿ͘ DÉTERMINE ůĞ ŶŽŵďƌĞ ĚΖĂƵƚŽŵŽďŝůŝƐƚĞƐ ƐĂĐŚĂŶƚ ƋƵΖĂƵ ƚŽƚĂů͕ ŝů Ǉ Ă ϭϮϵϲ ƉĞƌƐŽŶŶĞƐ ŐƌĂǀĞŵĞŶƚ ďůĞƐƐĠĞƐ ĞŶ ϮϬϭϲ͘ JUSTIFIE ƋƵĞ ůĞƐ ĂƵƚŽŵŽďŝůŝƐƚĞƐ Ğƚ ůĞƐ ƉĂƐƐĂŐĞƌƐ ƌĞƉƌĠƐĞŶƚĞŶƚ ϱϬ й ĚĞƐ ƉĞƌƐŽŶŶĞƐ ŐƌĂǀĞŵĞŶƚ ďůĞƐƐĠĞƐ͘

EXERCICES COMPLÉMENTAIRES CE

1D 8 18

Chapitre 3 Traitement de données et pourcentages

hŶĞ ĞŶƋƵġƚĞ ĐŽŶĐĞƌŶĂŶƚ ůĞƐ ĐŚŽŝǆ ĐŝŶĠŵĂƚŽŐƌĂƉŚŝƋƵĞƐ ĚΖƵŶ ŐƌŽƵƉĞ ĚĞ ũĞƵŶĞƐ ĠůğǀĞƐ Ă ĠƚĠ ƌĠĂůŝƐĠĞ͘ ŚĂƋƵĞ ũĞƵŶĞ ŶΖĂ ƉƵ ĐŚŽŝƐŝƌ ƋƵΖƵŶ ƐĞƵů ŐĞŶƌĞ Ğƚ ƋƵΖƵŶĞ ƐĞƵůĞ ĚĞƐ ƚƌŽŝƐ ƉƌŽƉŽƐŝƟ ŽŶƐ ĚĞ ŵĠĚŝĂ ͗ ͨ /ŶƚĞƌŶĞƚ ͕ͩ ͨ ŝŶĠŵĂ ͩ Ğƚ ͨ /ŶƚĞƌŶĞƚ Ğƚ ĐŝŶĠŵĂ ͩ͘ >ĞƐ ƌĠƐƵůƚĂƚƐ ĐŽƌƌĞƐƉŽŶĚĂŶƚ ĂƵǆ ĐŚŽŝǆ ĚĞƐ ŐĂƌĕŽŶƐ ŽŶƚ ĠƚĠ ƌĞƉƌĠƐĞŶƚĠƐ ă ůΖĂŝĚĞ ĚĞƐ ĚĞƵǆ ŐƌĂƉŚŝƋƵĞƐ ĐŝͲĚĞƐƐŽƵƐ͘ Choix des garçons

Nombre d’élèves 10 9 8 7 6 5 4 3 2 1 0

Policier

Comédie

Fantas que

Choix des garçons

Nombre d’élèves 12 11 10 9 8 7 6 5 4 3 2 1 0

Ac on Genre

Internet

Cinéma

Internet et cinéma

Média

>ĞƐ ƌĠƐƵůƚĂƚƐ ĐŽƌƌĞƐƉŽŶĚĂŶƚ ĂƵǆ ĐŚŽŝǆ ĚĞƐ Į ůůĞƐ ŽŶƚ ĠƚĠ ƌĞƉƌĠƐĞŶƚĠƐ ă ůΖĂŝĚĞ ĚƵ ŐƌĂƉŚŝƋƵĞ ĐŝͲĚĞƐƐŽƵƐ͘ Choix des ﬁlles

Genre

Internet Cinéma

Ac on

Internet et cinéma Fantas que Comédie Policier 0

Nombre d’élèves

DÉTERMINE ůĞ ŶŽŵďƌĞ ƚŽƚĂů ĚĞ Į ůůĞƐ͘ DÉTERMINE ůĞ ŶŽŵďƌĞ ƚŽƚĂů ĚĞ ŐĂƌĕŽŶƐ͘ DÉTERMINE ůĞ ŶŽŵďƌĞ ĚĞ Į ůůĞƐ ƋƵŝ ŽŶƚ ƌĠƉŽŶĚƵ ͨ ŝŶĠŵĂ ͩ͘ DÉTERMINE Ɛŝ ůĞ ƉŽƵƌĐĞŶƚĂŐĞ ĚĞƐ ũĞƵŶĞƐ ƋƵŝ ŽŶƚ ƌĠƉŽŶĚƵ ͨ /ŶƚĞƌŶĞƚ Ğƚ ĐŝŶĠŵĂ ͩ ĞƐƚ ŵŽŝŶƐ ĠůĞǀĠ ĐŚĞǌ ůĞƐ Į ůůĞƐ ŽƵ ĐŚĞǌ ůĞƐ ŐĂƌĕŽŶƐ͘ ÉCRIS ƚŽƵƐ ƚĞƐ ĐĂůĐƵůƐ͘ CE

1D 9 18

>Ğ ƚĂďůĞĂƵ ĐŝͲĚĞƐƐŽƵƐ ƌĞƉƌĠƐĞŶƚĞ ůĂ ƌĠƉĂƌƟ Ɵ ŽŶ ĚĞƐ ϲϲ ϲϭϮ ŚĂďŝƚĂŶƚƐ ĚΖƵŶĞ ǀŝůůĞ ƉĂƌ ƚƌĂŶĐŚĞ ĚΖąŐĞ ĂƵ ϭer ũĂŶǀŝĞƌ ϮϬϭϳ͘ Âge

&ĞŵŵĞƐ

,ŽŵŵĞƐ

DŽŝŶƐ ĚĞ ϭϱ ĂŶƐ

ϲϯϯϱ

ϲϯϬϴ

Ğ ϭϱ ă Ϯϵ ĂŶƐ

ϱϴϱϴ

ϱϵϯϲ

Ğ ϯϬ ă ϰϰ ĂŶƐ

ϲϰϰϳ

ϲϮϵϵ

Ğ ϰϱ ă ϱϵ ĂŶƐ

ϲϳϮϵ

ϲϰϱϯ

Ğ ϲϬ ă ϳϰ ĂŶƐ

ϱϯϲϳ

ϰϴϮϱ

ϳϱ ĂŶƐ ŽƵ ƉůƵƐ

ϯϳϱϮ

ϮϯϬϯ

>ŽƵŝƐ Ăĸ ƌŵĞ ͗ ͨ Pour chaque tranche d'âge, les femmes sont plus nombreuses que les hommes. ͩ JUSTIFIE ƋƵĞ ůΖĂĸ ƌŵĂƟ ŽŶ ĚĞ >ŽƵŝƐ ĞƐƚ ĨĂƵƐƐĞ͘ DÉTERMINE ůĞ ƉŽƵƌĐĞŶƚĂŐĞ ĚĞ ũĞƵŶĞƐ ĚĞ ŵŽŝŶƐ ĚĞ ϭϱ ĂŶƐ ĚĂŶƐ ĐĞƩ Ğ ǀŝůůĞ͘ DÉTERMINE ƐΖŝů Ǉ Ă ƉůƵƐ ŽƵ ƐΖŝů Ǉ Ă ŵŽŝŶƐ ĚĞ ƉĞƌƐŽŶŶĞƐ ąŐĠĞƐ ĚĞ ϯϬ ă ϰϰ ĂŶƐ ƋƵĞ ĚĞ ũĞƵŶĞƐ ĚĞ ŵŽŝŶƐ ĚĞ ϭϱ ĂŶƐ͘

Chapitre 4 Addition et soustraction avec les nombres entiers Tableaux de compétences Libre EŽŵďƌĞƐ ĞŶƟ ĞƌƐ 7

DĂŠƚƌŝƐĞƌ ůĞƐ ĐŽŶǀĞŶƟ ŽŶƐ Ě͛ĠĐƌŝƚƵƌĞ ŵĂƚŚĠŵĂƟ ƋƵĞ ĚĞƐ ŽƉĠƌĂƟ ŽŶƐ ĂǀĞĐ ĚĞƐ ĞŶƟ ĞƌƐ͘

/ĚĞŶƟ Į Ğƌ Ğƚ Ğī ĞĐƚƵĞƌ ĚĞƐ ŽƉĠƌĂƟ ŽŶƐ ĚĂŶƐ ĚĞƐ ƐŝƚƵĂƟ ŽŶƐ ǀĂƌŝĠĞƐ ĂǀĞĐ ĚĞƐ ĞŶƟ ĞƌƐ͘

KƌĚŽŶŶĞƌ Ğƚ ĐŽŵƉĂƌĞƌ ĚĞƐ ŶŽŵďƌĞƐ ĞŶƟ ĞƌƐ͘

EŽŵďƌĞƐ ƌĂƟ ŽŶŶĞůƐ 10

ƐƐŽĐŝĞƌ ů͛ŝĚĠĞ ĚĞ ͨ ĞƐƚ ĂǀĂŶƚ ͕ͩ ͨ ĞƐƚ ƐƵƌ ͩ Ğƚ ͨ ĞƐƚ ĂƉƌğƐ ͩ ƐƵƌ ůĂ ĚƌŽŝƚĞ ŐƌĂĚƵĠĞ ă ůĂ ŶŽƟ ŽŶ ͨ ĞƐƚ ƉůƵƐ ƉĞƟ ƚ ƋƵĞ ͕ͩ ͨ ĞƐƚ ĠŐĂů ă ͩ ŽƵ ͨ ĞƐƚ ƉůƵƐ ŐƌĂŶĚ ƋƵĞ ͩ ĚĂŶƐ ƵŶ ĞŶƐĞŵďůĞ ĚĞ ŶŽŵďƌĞƐ͘

Nombres 15

:ƵƐƟ Į Ğƌ ƵŶĞ ŵĠƚŚŽĚĞ ĚĞ ĐĂůĐƵů ĞŶ ƵƟ ůŝƐĂŶƚ ůĞƐ ƉƌŽƉƌŝĠƚĠƐ ĚĞƐ ŽƉĠƌĂƟ ŽŶƐ͘

ĂůĐƵů ůŝƩ ĠƌĂů Ğƚ ĠƋƵĂƟ ŽŶƐ 28

ĂůĐƵůĞƌ ĚĞƐ ǀĂůĞƵƌƐ ŶƵŵĠƌŝƋƵĞƐ Ě͛ĞǆƉƌĞƐƐŝŽŶƐ ůŝƩ ĠƌĂůĞƐ͘

Les mouvements dans le plan 42

ƐƐŽĐŝĞƌ ƵŶ ƉŽŝŶƚ Ğƚ ƐŽŶ ĂďƐĐŝƐƐĞ ƐƵƌ ƵŶ ĂǆĞ͘

ƐƐŽĐŝĞƌ ƵŶ ƉŽŝŶƚ Ğƚ ƐĞƐ ĐŽŽƌĚŽŶŶĠĞƐ ƐƵƌ ƵŶ ƋƵĂĚƌŝůůĂŐĞ͘

ACTIVITÉS

Chapitre 4 Addition et soustraction avec les nombres entiers

Kĸ ĐŝĞů Repérer et classer

>ŝƌĞ ů͛ĂďƐĐŝƐƐĞ Ě͛ƵŶ ƉŽŝŶƚ ŽƵ ĞŶ ĚŽŶŶĞƌ ƵŶ ĞŶĐĂĚƌĞŵĞŶƚ͘

ůĂƐƐĞƌ ĚĞƐ ŶŽŵďƌĞƐ ƐƵŝǀĂŶƚ Ěŝī ĠƌĞŶƚƐ ĐƌŝƚğƌĞƐ͘

WůĂĐĞƌ ĚĞƐ ŶŽŵďƌĞƐ ĞŶƟ ĞƌƐ ƐƵƌ ƵŶĞ ĚƌŽŝƚĞ ŐƌĂĚƵĠĞ ;ĂǆĞͿ͘

ĠƚĞƌŵŝŶĞƌ ůĂ ǀĂůĞƵƌ ĂďƐŽůƵĞ Ě͛ƵŶ ŶŽŵďƌĞ ĞŶƟ Ğƌ͘

ZĞĐŽŶŶĂŠƚƌĞ Ğƚ ĠĐƌŝƌĞ ĚĞƵǆ ŶŽŵďƌĞƐ ŽƉƉŽƐĠƐ͘

ZĂŶŐĞƌ ĞŶ ŽƌĚƌĞ ĐƌŽŝƐƐĂŶƚ Ğƚ ĚĠĐƌŽŝƐƐĂŶƚ ĚĞƐ ŶŽŵďƌĞƐ ĞŶƟ ĞƌƐ͘

ŽŵƉĂƌĞƌ ĚĞƵǆ ŶŽŵďƌĞƐ ĞŶƟ ĞƌƐ͘

WůĂĐĞƌ ƵŶ ĐŽƵƉůĞ ĚĞ ŶŽŵďƌĞƐ ĚĂŶƐ ƵŶ ƌĞƉğƌĞ ĐĂƌƚĠƐŝĞŶ͘

ī ĞĐƚƵĞƌ ĚĞƐ ŽƉĠƌĂƟ ŽŶƐ 29

ĂůĐƵůĞƌ ůĂ ƐŽŵŵĞ͕ ůĂ Ěŝī ĠƌĞŶĐĞ Ğƚ ůĞ ƉƌŽĚƵŝƚ ĚĞ ĚĞƵǆ ŶŽŵďƌĞƐ ĞŶƟ ĞƌƐ͘

hƟ ůŝƐĞƌ ůĂ ĐŽŵŵƵƚĂƟ ǀŝƚĠ Ğƚ ů͛ĂƐƐŽĐŝĂƟ ǀŝƚĠ ĚĞ ů͛ĂĚĚŝƟ ŽŶ͘

ǆƉƌĞƐƐŝŽŶƐ ůŝƩ ĠƌĂůĞƐ 48

ĂůĐƵůĞƌ ůĂ ǀĂůĞƵƌ ŶƵŵĠƌŝƋƵĞ Ě͛ƵŶĞ ĞǆƉƌĞƐƐŝŽŶ ůŝƩ ĠƌĂůĞ ĞŶ ĚŽŶŶĂŶƚ ĂƵǆ ǀĂƌŝĂďůĞƐ ĚĞƐ ǀĂůĞƵƌƐ ĞŶƟ ğƌĞƐ͘

ACTIVITÉS

Chapitre 4 Addition et soustraction avec les nombres entiers

ĐƚŝǀŝƚĠ ϭ De nouveaux nombres 1 WŽƵƌ ĐŚĂƋƵĞ ƐŝƚƵĂƚŝŽŶ͕ ƚƌĂĚƵŝƐ ƉĂƌ ƵŶĞ ƉŚƌĂƐĞ ůĂ ƐŝŐŶŝĨŝĐĂƚŝŽŶ ĚĞ ĐŚĂƋƵĞ ŶŽŵďƌĞ͘ ĂͿ WĂƉĂ Ă ĚƸ ĚĞƐĐĞŶĚƌĞ ĂƵ ŶŝǀĞĂƵ ʹϯ ƉŽƵƌ ŐĂƌĞƌ ƐĂ ǀŽŝƚƵƌĞ Ğƚ ŵĂŵĂŶ ŵŽŶƚĞƌ ĂƵ ŶŝǀĞĂƵ нϮ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ďͿ >͛ĠƉĂǀĞ ĚƵ ƉĂƋƵĞďŽƚ dŝƚĂŶŝĐ ƌĞƉŽƐĞ ă ʹϯϴϬϬ ŵ ĚĂŶƐ ů͛ ƚůĂŶƚŝƋƵĞ EŽƌĚ Ğƚ ůĞ DŽŶƚ ůĂŶĐ ĐƵůŵŝŶĞ ă нϰϴϬϳ ŵ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ĐͿ ^Ƶƌ ƵŶ ƚŚĞƌŵŽŵğƚƌĞ͕ ŽŶ Ă ƌĞůĞǀĠ ʹϰΣ ĐŽŵŵĞ ƚĞŵƉĠƌĂƚƵƌĞ ĚĞ ŶƵŝƚ Ğƚ нϴΣ ĐŽŵŵĞ ƚĞŵƉĠƌĂƚƵƌĞ ĚĞ ũŽƵƌ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ĚͿ ĂǀŝĚ ũŽƵĞ ă ƵŶ ũĞƵ ǀŝĚĠŽ ĚŽŶƚ ůĞ ŚĠƌŽƐ ŐĂŐŶĞ ŽƵ ƉĞƌĚ ĚĞƐ ƉŝğĐĞƐ Ě͛Žƌ͖ ůĞ ďŝůĂŶ ĚĞ ƐĂ ƉƌĞŵŝğƌĞ ũŽƵƌŶĠĞ ĞƐƚ ʹϭϱ Ğƚ ĐĞůƵŝ ĚĞ ůĂ ĚĞƵǆŝğŵĞ ũŽƵƌŶĠĞ ĞƐƚ нϭϮ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

dŽƵƐ ůĞƐ ŶŽŵďƌĞƐ ƌĞŶĐŽŶƚƌĠƐ ĚĂŶƐ ůĞƐ ƐŝƚƵĂƚŝŽŶƐ ƉƌĠĐĠĚĞŶƚĞƐ ƐŽŶƚ ĚĞƐ ŶŽŵďƌĞƐ ĞŶƚŝĞƌƐ͘ 2 ^ŝ ů͛ĞŶƐĞŵďůĞ ĚĞ ƚŽƵƐ ůĞƐ ŶŽŵďƌĞƐ ĞŶƚŝĞƌƐ ƐĞ ŶŽƚĞ Z Ğƚ ĐĞůƵŝ ĚĞƐ ŶŽŵďƌĞƐ ĞŶƚŝĞƌƐ ƉŽƐŝƚŝĨƐ ;ŶŽŵďƌĞƐ ŶĂƚƵƌĞůƐͿ ƐĞ ŶŽƚĞ N͕ ĞƐƐĂŝĞ ĚĞ ƉůĂĐĞƌ ůĞƐ ŶŽŵďƌĞƐ ĚĞ ů͛ĞǆĞƌĐŝĐĞ ƉƌĠĐĠĚĞŶƚ ĚĂŶƐ ůĞƐ ĚŝĂŐƌĂŵŵĞƐ ĐŝͲĚĞƐƐŽƵƐ ĞŶ ĂũŽƵƚĂŶƚ ůĞ ŶŽŵďƌĞ Ϭ͘ N Z Z N N

YƵĞ ƌĞŵĂƌƋƵĞƐͲƚƵ ͍ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

3 ^Ƶƌ ůĂ ĚƌŽŝƚĞ Ě͕ ŽŶ ĂƚƚƌŝďƵĞ ů͛ĂďƐĐŝƐƐĞ Ϭ ĂƵ ƉŽŝŶƚ Ğƚ ů͛ĂďƐĐŝƐƐĞ ϭ ĂƵ ƉŽŝŶƚ ͘ ĠƚĞƌŵŝŶĞ ƐƵƌ ĐĞƚƚĞ ĚƌŽŝƚĞ ůĞƐ ƉŽŝŶƚƐ Ě͛ĂďƐĐŝƐƐĞƐ нϯ͕ ʹϮ͕ нϱ͕ ʹϱ͕ ʹϲ Ğƚ нϳ͘ A

^ŝ ŶŽƵƐ ĂƉƉĞůŽŶƐ ůĞ ƉŽŝŶƚ Ě͛ĂďƐĐŝƐƐĞ ϯ͕ ŶŽƵƐ ƵƚŝůŝƐĞƌŽŶƐ ů͛ĂďƌĠǀŝĂƚŝŽŶ ͗ ĂďƐ с ϯ 81

ACTIVITÉS

Chapitre 4 Addition et soustraction avec les nombres entiers

4 ĂͿ WůĂĐĞ ƐƵƌ ůĂ ĚƌŽŝƚĞ ĐŝͲĚĞƐƐŽƵƐ ůĞƐ ƉŽŝŶƚƐ ĚŽŶƚ ƚƵ ĐŽŶŶĂŝƐ ů͛ĂďƐĐŝƐƐĞ͘ ĂďƐ y с ϲ ͖ ĂďƐ z с Ϯ ͖ ĂďƐ с ʹϮ ͖ ĂďƐ s с ʹϲ ͖ ĂďƐ t с ʹϰ ͖ ĂďƐ d с ϰ

p.47 A1

d 0

ďͿ ŽŵƉůğƚĞ ůĞƐ ƉŚƌĂƐĞƐ͘ >ĞƐ ƉŽŝŶƚƐ z Ğƚ ƐŽŶƚ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ƉĂƌ ƌĂƉƉŽƌƚ ĂƵ ƉŽŝŶƚ Ě͛ĂďƐĐŝƐƐĞ Ϭ͘ >ĞƵƌƐ ĂďƐĐŝƐƐĞƐ Ϯ Ğƚ ʹϮ ƐŽŶƚ ĚĞƐ ŶŽŵďƌĞƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͖ ŝůƐ ŽŶƚ ůĂ ŵġŵĞ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Ğƚ ƐŽŶƚ ĚĞ ƐŝŐŶĞƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϲ ĞƐƚ ů͛ŽƉƉŽƐĠ ĚĞ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͖ нϰ ĞƐƚ ů͛ŽƉƉŽƐĠ ĚĞ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ĐͿ ŽŵƉůğƚĞ͘ ^ŝ Ă ĞƐƚ ĠŐĂů ă ϵ͕ ĂůŽƌƐ ů͛ŽƉƉŽƐĠ ĚĞ Ă ĞƐƚ ĠŐĂů ă

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

^ŝ Ă ĞƐƚ ĠŐĂů ă ʹϲ͕ ĂůŽƌƐ ů͛ŽƉƉŽƐĠ ĚĞ Ă ĞƐƚ ĠŐĂů ă ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ^ŝ ů͛ŽƉƉŽƐĠ ĚĞ Ă ĞƐƚ ĠŐĂů ă ʹϴ͕ ĂůŽƌƐ Ă ĞƐƚ ĠŐĂů ă ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ^ŝ ů͛ŽƉƉŽƐĠ ĚĞ Ă ĞƐƚ ĠŐĂů ă ϭϬ͕ ĂůŽƌƐ Ă ĞƐƚ ĠŐĂů ă ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ^ŝ Ă с ϭϱ͕ ĂůŽƌƐ ʹĂ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

^ŝ ʹĂ с ʹϳ͕ ĂůŽƌƐ Ă с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

^ŝ Ă с ʹϰ͕ ĂůŽƌƐ ʹĂ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

^ŝ ʹĂ с ϵ͕ ĂůŽƌƐ Ă с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

p.48 Ϯͳ A3

ĐƚŝǀŝƚĠ Ϯ Comparaison de deux nombres entiers 1 ĂͿ >Ğ ƚŚĞƌŵŽŵğƚƌĞ ĐŝͲĚĞƐƐŽƵƐ͕ ŐƌĂĚƵĠ ĞŶ ĚĞŐƌĠƐ ĞůƐŝƵƐ ;Σ Ϳ͕ ŝŶĚŝƋƵĞ ƵŶĞ ƚĞŵƉĠƌĂƚƵƌĞ ĚĞ ʹϭϬΣ ͘ ^Ƶƌ ůĂ ŐƌĂĚƵĂƚŝŽŶ͕ ƉůĂĐĞ ůĞƐ ƚĞŵƉĠƌĂƚƵƌĞƐ ƐƵŝǀĂŶƚĞƐ ͗ ʹϳΣ ͕ нϴΣ ͕ ʹϭϮΣ ͕ нϯΣ Ğƚ ʹϮΣ ͘ 0

ďͿ ůĂƐƐĞ ůĞƐ ƚĞŵƉĠƌĂƚƵƌĞƐ ƉĂƌ ŽƌĚƌĞ ĐƌŽŝƐƐĂŶƚ ;ĚĞ ůĂ ƉůƵƐ ĨƌŽŝĚĞ ă ůĂ ƉůƵƐ ĐŚĂƵĚĞͿ͘ нϭϮ ʹϰ нϯ ʹϲ нϴ ʹϳ нϳ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ĐͿ ŽŵƉůğƚĞ ƉĂƌ ф ŽƵ х͘

ϭϰ

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Ϯϯ

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϲ

ʹϭϬ

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϱ

ʹϳ

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϯ

ʹϭ

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϮ

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϭ

ʹϯ

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϳ

ʹϯ

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

p.48 A4

ACTIVITÉS

Chapitre 4 Addition et soustraction avec les nombres entiers

2 ĂͿ ŶĂŢƐ Ğƚ ƐĂ ƐƈƵƌ >ŝƐĂ ŽŶƚ ĚĠĐŝĚĠ ĚĞ Ɛ͛ĂĚŽŶŶĞƌ ă ƵŶ ƉĞƚŝƚ ũĞƵ ŵĂƚŚĠŵĂƚŝƋƵĞ͘ ŶĂŢƐ Ă ƉůĂĐĠ ĐŝŶƋ ƉŽŝŶƚƐ ǀĞƌƚƐ ƐƵƌ ƵŶĞ ĚƌŽŝƚĞ ŐƌĂĚƵĠĞ͘ E

A 0

B 1

ůůĞ ǀŽƵĚƌĂŝƚ ƋƵĞ ƐĂ ƐƈƵƌ >ŝƐĂ ĚĠĐŽƵǀƌĞ ůĞ ƉŽŝŶƚ ͨ ŵǇƐƚğƌĞ ͩ ŐƌąĐĞ ĂƵǆ ŝŶĨŽƌŵĂƟ ŽŶƐ ƋƵ͛ĞůůĞ ůƵŝ ĚŽŶŶĞ͘ ĂŶƐ ĐŚĂƋƵĞ ƉŚƌĂƐĞ͕ ƐŽƵůŝŐŶĞ ůĂ ĐŽŶĚŝƟ ŽŶ ƋƵŝ ƚĞ ƉĞƌŵĞƩ ƌĂ ĚĞ ĚĠƚĞƌŵŝŶĞƌ ĐĞ ƉŽŝŶƚ͘ ʹ ^ŽŶ ĂďƐĐŝƐƐĞ ĞƐƚ ƐƵƉĠƌŝĞƵƌĞ ă ʹϰ ŽƵ ƐƵƉĠƌŝĞƵƌĞ ă ʹϮ͘ ʹ ^ŽŶ ĂďƐĐŝƐƐĞ ĞƐƚ ŝŶĨĠƌŝĞƵƌĞ ă ϭ ŽƵ ŝŶĨĠƌŝĞƵƌĞ ă ʹϭ͘ YƵĞů ĞƐƚ ůĞ ƉŽŝŶƚ ŵǇƐƚğƌĞ ͍ ͘ ͘ ͘ ͘ ͘ ͘ ďͿ ĂŶƐ ĐŚĂĐƵŶ ĚĞƐ ĐĂƐ ƐƵŝǀĂŶƚƐ͕ ĞŶĐĂĚƌĞ ů͛ĂďƐĐŝƐƐĞ ĚƵ ƉŽŝŶƚ D ƉĂƌ ĚĞƵǆ ŶŽŵďƌĞƐ ĞŶƚŝĞƌƐ ĐŽŶƐĠĐƵƚŝĨƐ͘ M 0 1 2 3 4 ĂďƐ D х ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ Ğƚ ĂďƐ D ф ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ф ĂďƐ D ф ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

M 0 1 ĂďƐ D х ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ Ğƚ ĂďƐ D ф ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ф ĂďƐ D ф ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

0 1

ĂďƐ D х ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ Ğƚ ĂďƐ D ф ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ф ĂďƐ D ф ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ĂďƐ D х ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ Ğƚ ĂďƐ D ф ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ф ĂďƐ D ф ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ĐƚŝǀŝƚĠ ϯ Somme de deux nombres entiers 1 ĂͿ ĂǀŝĚ ũŽƵĞ ă ƵŶ ũĞƵ ǀŝĚĠŽ ĚŽŶƚ ůĞ ŚĠƌŽƐ ŐĂŐŶĞ ŽƵ ƉĞƌĚ ĚĞƐ ƉŝğĐĞƐ Ě͛Žƌ͘ /ů ĨĂŝƚ ĚĞƵǆ ƉĂƌƚŝĞƐ ƉĂƌ ũŽƵƌ Ğƚ͕ ĐŚĂƋƵĞ ƐŽŝƌ͕ ŝů ƌĞŵƉůŝƚ ƵŶ ƚĂďůĞĂƵ ƌĠĐĂƉŝƚƵůĂŶƚ ƐĞƐ ŐĂŝŶƐ Ğƚ ƐĞƐ ƉĞƌƚĞƐ͘ ϭͿ ŽŵƉůğƚĞ ůĂ ĐŽůŽŶŶĞ ͨ ŝůĂŶ ĚĞ ůĂ ũŽƵƌŶĠĞ ͩ ĚƵ ƚĂďůĞĂƵ͘ ZĠƐƵůƚĂƚ ĚĞ ůĂ 1re ƉĂƌƚŝĞ

ZĠƐƵůƚĂƚ ĚĞ ůĂ 2e ƉĂƌƚŝĞ

>ƵŶĚŝ

'ĂŝŶ ĚĞ ϮϬ ƉŝğĐĞƐ

WĞƌƚĞ ĚĞ ϱ ƉŝğĐĞƐ

DĂƌĚŝ

'ĂŝŶ ĚĞ ϴ ƉŝğĐĞƐ

'ĂŝŶ ĚĞ ϯ ƉŝğĐĞƐ

DĞƌĐƌĞĚŝ

WĞƌƚĞ ĚĞ ϭϭ ƉŝğĐĞƐ

'ĂŝŶ ĚĞ ϲ ƉŝğĐĞƐ

:ĞƵĚŝ

'ĂŝŶ ĚĞ ϭϭ ƉŝğĐĞƐ

WĞƌƚĞ ĚĞ ϭϱ ƉŝğĐĞƐ

sĞŶĚƌĞĚŝ

WĞƌƚĞ ĚĞ ϱ ƉŝğĐĞƐ

WĞƌƚĞ ĚĞ ϰ ƉŝğĐĞƐ

^ĂŵĞĚŝ

'ĂŝŶ ĚĞ ϵ ƉŝğĐĞƐ

WĞƌƚĞ ĚĞ ϯ ƉŝğĐĞƐ

ŝŵĂŶĐŚĞ

WĞƌƚĞ ĚĞ ϰ ƉŝğĐĞƐ

'ĂŝŶ ĚĞ ϭϭ ƉŝğĐĞƐ

ŝůĂŶ ĚĞ ůĂ ũŽƵƌŶĠĞ

ACTIVITÉS

Chapitre 4 Addition et soustraction avec les nombres entiers

ϮͿ WŽƵƌ ĂůůĞƌ ƉůƵƐ ǀŝƚĞ͕ ĂǀŝĚ ĐŚĞƌĐŚĞ ƵŶĞ ĠĐƌŝƚƵƌĞ ŵĂƚŚĠŵĂƚŝƋƵĞ ƋƵŝ ƉĞƌŵĞƚ ĚĞ ƌĞŵƉůĂĐĞƌ ůĞƐ ƌĠƐƵůƚĂƚƐ ĚĞ ůƵŶĚŝ ͗ ͨ 'ĂŝŶ ĚĞ ϮϬ ƉŝğĐĞƐ ͩ Ğƚ ͨ WĞƌƚĞ ĚĞ ϱ ƉŝğĐĞƐ ͩ͘ YƵĞůƐ ŶŽŵďƌĞƐ ƉĞƵƚͲŝů ƵƚŝůŝƐĞƌ ͍ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ Ŷ ƵƚŝůŝƐĂŶƚ ĐĞƚƚĞ ĠĐƌŝƚƵƌĞ ĚĞ ŶŽŵďƌĞƐ͕ ƋƵĞů ĐĂůĐƵů ƚĞ ƉĞƌŵĞƚ ĚĞ ƌĞƚƌŽƵǀĞƌ ůĞ ďŝůĂŶ ĚĞ ůƵŶĚŝ Ğƚ ƋƵĞů ĞƐƚ ůĞ ƌĠƐƵůƚĂƚ ͍ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϯͿ ŽŵƉůğƚĞ ůĂ Ϯe ĐŽůŽŶŶĞ ĚƵ ƚĂďůĞĂƵ ĂǀĞĐ ĐĞƚƚĞ ŶŽƵǀĞůůĞ ŶŽƚĂƚŝŽŶ Ğƚ ŶŽƚĞ ůĞ ƌĠƐƵůƚĂƚ ĚĂŶƐ ůĂ ϯe ĐŽůŽŶŶĞ͘ ŝůĂŶ ĚĞ ůĂ ũŽƵƌŶĠĞ ĂǀĞĐ ůĂ ŶŽƵǀĞůůĞ ĠĐƌŝƚƵƌĞ

ZĠƐƵůƚĂƚ

>ƵŶĚŝ

DĂƌĚŝ DĞƌĐƌĞĚŝ :ĞƵĚŝ sĞŶĚƌĞĚŝ ^ĂŵĞĚŝ ŝŵĂŶĐŚĞ b) sŽŝĐŝ ƵŶ ŽƌŐĂŶŝŐƌĂŵŵĞ ƉĞƌŵĞƚƚĂŶƚ ĚĞ ĐĂůĐƵůĞƌ ůĂ ƐŽŵŵĞ ĚĞ ĚĞƵǆ ŶŽŵďƌĞƐ ĞŶƚŝĞƌƐ͖ ĐŽŵƉůğƚĞͲůĞ͘ KƵŝ

>ĞƐ ĚĞƵǆ ŶŽŵďƌĞƐ ƐŽŶƚͲŝůƐ ĚĞ ŵġŵĞ ƐŝŐŶĞ ͍

On ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Non

KŶ ĚŽŶŶĞ ă ůĂ ƐŽŵŵĞ ůĞ ƐŝŐŶĞ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ůĞ ƐŝŐŶĞ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

On ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ůĞƐ ǀĂůĞƵƌƐ ĂďƐŽůƵĞƐ͘

p.49 B1

ĐͿ hƚŝůŝƐĞ ůĂ ƌğŐůĞ Ě͛ĂĚĚŝƚŝŽŶ ƉŽƵƌ ĐĂůĐƵůĞƌ ůĞƐ ƐŽŵŵĞƐ ƐƵŝǀĂŶƚĞƐ͘

;ʹϰͿ н ;ʹϵͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;нϮϱͿ н ;ʹϭϬͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;нϭϯϱͿ н ;ʹϭϮϱͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;нϵͿ н ;ʹϱͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;ʹϭϬͿ н ;ʹϮϱͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;ʹϮϳϱͿ н ;ʹϳϮϱͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;нϳͿ н ;ʹϭϬͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;нϭϳͿ н ;ʹϮϬͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;нϯϬϰͿ н ;ʹϰϬϯͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;ʹϵͿ н ;ʹϱͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;ʹϭϮͿ н ;ʹϭϮͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;ʹϭϴϱͿ н ;нϲϵϬͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;нϵͿ н ;нϱͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;нϰϬͿ н ;ʹϱϬͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;ʹϭϵϵͿ н ;нϱϬϯͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;нϭϮͿ н ;ʹϴͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;ʹϱϬͿ н ;нϲϬͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;ʹϰϵϵͿ н ;ʹϮϬϵͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ACTIVITÉS

Chapitre 4 Addition et soustraction avec les nombres entiers

ĐƚŝǀŝƚĠ ϰ Différence de deux nombres entiers 1 ĂͿ >Ğ ƚĂďůĞĂƵ ĐŝͲĚĞƐƐŽƵƐ ĐŽŶƚŝĞŶƚ ůĞƐ ƐĐŽƌĞƐ ũŽƵƌŶĂůŝĞƌƐ ŽďƚĞŶƵƐ ƉĂƌ ĂǀŝĚ ĂƵ ƚĞƌŵĞ Ě͛ƵŶĞ ƐĞŵĂŝŶĞ ĚĞ ũĞƵ͘ :ŽƵƌƐ ^ĐŽƌĞƐ

>Ƶ нϭϱ

Ma нϭϭ

Me ʹϱ

Je ʹϰ

sĞ ʹϵ

^Ă нϲ

Di нϳ

ĂůĐƵůĞ ůĂ ƐŽŵŵĞ Ğƚ ůĂ ŵŽǇĞŶŶĞ ũŽƵƌŶĂůŝğƌĞ ĚĞƐ ƐĐŽƌĞƐ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

YƵĞ ĚĞǀŝĞŶŶĞŶƚ ůĂ ƐŽŵŵĞ Ğƚ ůĂ ŵŽǇĞŶŶĞ ũŽƵƌŶĂůŝğƌĞ Ɛŝ ŽŶ ƌĞƚŝƌĞ ůĞ ƐĐŽƌĞ ŵĂǆŝŵĂů ͍ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

YƵĞ ĚĞǀŝĞŶŶĞŶƚ ůĂ ƐŽŵŵĞ Ğƚ ůĂ ŵŽǇĞŶŶĞ ũŽƵƌŶĂůŝğƌĞ Ɛŝ ŽŶ ƌĞƚŝƌĞ ůĞ ƐĐŽƌĞ ŵŝŶŝŵĂů ͍ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

YƵĞ ĚĞǀŝĞŶƚ ůĂ ŵŽǇĞŶŶĞ ũŽƵƌŶĂůŝğƌĞ Ɛŝ ŽŶ ƌĞƚŝƌĞ ůĞƐ ƐĐŽƌĞƐ ĞǆƚƌġŵĞƐ ͍ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ďͿ ĂůĐƵůĞ ůĞƐ ĚŝĨĨĠƌĞŶĐĞƐ ƐƵŝǀĂŶƚĞƐ͘ ;нϮϭͿ ʹ ;нϭϭͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;ʹϮϭͿ ʹ ;ʹϰͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;нϮϭͿ ʹ ;ʹϱͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;ʹϮϭͿ ʹ ;нϳͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ĐͿ ŽŵƉůğƚĞ ůĞƐ ƉŚƌĂƐĞƐ ĂǀĞĐ ůĞƐ ŵŽƚƐ ͨ ĂƵŐŵĞŶƚĞ ͕ͩ ͨ ĚŝŵŝŶƵĞ ͕ͩ ͨ ƉŽƐŝƚŝĨ ͩ ŽƵ ͨ ŶĠŐĂƚŝĨ ͩ͘ ^ŝ ŽŶ ƌĞƚŝƌĞ ƵŶ ƐĐŽƌĞ ƉŽƐŝƚŝĨ͕ ůĂ ƐŽŵŵĞ ĚĞƐ ƐĐŽƌĞƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ZĞƚŝƌĞƌ ƵŶ ŶŽŵďƌĞ ƉŽƐŝƚŝĨ ƌĞǀŝĞŶƚ ă ĂũŽƵƚĞƌ ƵŶ ŶŽŵďƌĞ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ^ŝ ŽŶ ƌĞƚŝƌĞ ƵŶ ƐĐŽƌĞ ŶĠŐĂƚŝĨ͕ ůĂ ƐŽŵŵĞ ĚĞƐ ƐĐŽƌĞƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ZĞƚŝƌĞƌ ƵŶ ŶŽŵďƌĞ ŶĠŐĂƚŝĨ ƌĞǀŝĞŶƚ ă ĂũŽƵƚĞƌ ƵŶ ŶŽŵďƌĞ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

p.49 B2

ĚͿ ŽŵƉůğƚĞ ůĂ ƉŚƌĂƐĞ ͗ ƐŽƵƐƚƌĂŝƌĞ ƵŶ ŶŽŵďƌĞ ĞŶƚŝĞƌ ƌĞǀŝĞŶƚ ă ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ 2 dƌĂŶƐĨŽƌŵĞ ůĞƐ ĚŝĨĨĠƌĞŶĐĞƐ ĞŶ ƐŽŵŵĞƐ͕ ƉƵŝƐ ĐĂůĐƵůĞ͘ ;ʹϰͿ ʹ ;ʹϳͿ с ;͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘Ϳ н ;͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘Ϳ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;ʹϭϱͿ ʹ ;ʹϮϱͿ с ;͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘Ϳ н ;͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘Ϳ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;нϱͿ ʹ ;нϲͿ с ;͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘Ϳ н ;͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘Ϳ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;ʹϳϱͿ ʹ ;нϭϱͿ с ;͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘Ϳ н ;͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘Ϳ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;нϮͿ ʹ ;ʹϱͿ с ;͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘Ϳ н ;͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘Ϳ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;нϰϴͿ ʹ ;ʹϱϳͿ с ;͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘Ϳ н ;͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘Ϳ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;ʹϵͿ ʹ ;нϱͿ с ;͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘Ϳ н ;͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘Ϳ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;нϱϱͿ ʹ ;нϳϭͿ с ;͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘Ϳ н ;͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘Ϳ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;нϳͿ ʹ ;нϴͿ с ;͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘Ϳ н ;͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘Ϳ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;ʹϲϯͿ ʹ ;нϭϳͿ с ;͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘Ϳ н ;͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘Ϳ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;ʹϱͿ ʹ ;ʹϵͿ с ;͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘Ϳ н ;͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘Ϳ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;нϯϴͿ ʹ ;ʹϯϱͿ с ;͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘Ϳ н ;͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘Ϳ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ACTIVITÉS

Chapitre 4 Addition et soustraction avec les nombres entiers

ĐƚŝǀŝƚĠ ϱ Somme et différence de deux nombres entiers sans parenthèses 1 ĂͿ ĂǀŝĚ Ă ŝŶǀŝƚĠ ƐŽŶ ĐŽƉĂŝŶ DŝĐŚĞů ƉŽƵƌ ĐŽŵƉĂƌĞƌ ůĞƵƌ ŚĂďŝůŝƚĠ ĂǀĞĐ ůĞ ŶŽƵǀĞĂƵ ũĞƵ ǀŝĚĠŽ͘ /ů ůƵŝ ŵŽŶƚƌĞ Ě͛ĂďŽƌĚ ƐĂ ŵĂŶŝğƌĞ ĚĞ ĐĂůĐƵůĞƌ ůĞ ƌĠƐƵůƚĂƚ ŐůŽďĂů ĚĞ ĚĞƵǆ ƉĂƌƚŝĞƐ͘ DŝĐŚĞů ĞƐƚ ƐƵƌƉƌŝƐ ĐĂƌ ŝů ŶŽƚĞ ůĞƐ ĐĂůĐƵůƐ Ě͛ƵŶĞ ĂƵƚƌĞ ŵĂŶŝğƌĞ ŵĂŝƐ ƚƌŽƵǀĞ ůĞ ŵġŵĞ ƌĠƐƵůƚĂƚ͘

ĂůĐƵůƐ ĚĞ ĂǀŝĚ

ĂůĐƵůƐ ĚĞ DŝĐŚĞů

;нϭϬͿ н ;нϱͿ

нϭϬ н ϱ

;нϭϰͿ н ;ʹϯͿ

нϭϰ ʹ ϯ

;нϵͿ н ;ʹϯͿ ;ʹϰͿ н ;нϭϭͿ ʹϭϭ н ϲ

ŽŵƉůğƚĞ ůĞ ƚĂďůĞĂƵ ƌĞƉƌĞŶĂŶƚ ůĞƐ ƚĞĐŚŶŝƋƵĞƐ ĚĞ ĂǀŝĚ Ğƚ DŝĐŚĞů͘

нϭϭ ʹϭϱ ʹϱ ʹ ϰ

ďͿ ĐƌŝƐ ůĞƐ ƐŽŵŵĞƐ ƐĂŶƐ ƉĂƌĞŶƚŚğƐĞƐ͕ ƉƵŝƐ ĐĂůĐƵůĞ͘ ;ʹϴͿ н ;нϱͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;нϮϮͿ н ;ʹϭϮͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;нϳͿ н ;ʹϵͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;нϭϴͿ н ;нϭϱͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;ʹϰͿ н ;ʹϲͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;ʹϭϳͿ н ;ʹϮϯͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;нϱͿ н ;нϳͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;ʹϭϱͿ н ;нϭϱͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;ʹϯͿ н ;ʹϯͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;нϭϰͿ н ;ʹϭϵͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

2 ĂͿ ĂǀŝĚ ǀŽƵĚƌĂŝƚ ƐĂǀŽŝƌ ĐŽŵŵĞŶƚ ƐŽŶ ĐŽƉĂŝŶ DŝĐŚĞů ŶŽƚĞƌĂŝƚ Ğƚ ĞĨĨĞĐƚƵĞƌĂŝƚ ůĞƐ ĚŝĨĨĠƌĞŶĐĞƐ͘ ŽŵƉůğƚĞ ůĞ ƚĂďůĞĂƵ ƌĞƉƌĞŶĂŶƚ ůĞƐ ĚĞƵǆ ƚĞĐŚŶŝƋƵĞƐ͘ ŝĨĨĠƌĞŶĐĞƐ

ĂůĐƵůƐ ĚĞ ĂǀŝĚ

ĂůĐƵůƐ ĚĞ DŝĐŚĞů

;нϮϭͿ ʹ ;нϭϰͿ

с ;нϮϭͿ н ;ʹϭϰͿ с нϳ

с нϮϭ ʹ ϭϰ с нϳ

;нϮϭͿ ʹ ;ʹϭϭͿ

с ;нϮϭͿ н ;нϭϭͿ с нϯϮ

с нϮϭ н ϭϭ с нϯϮ

;нϮϭͿ ʹ ;нϭϭͿ ;ʹϮϭͿ ʹ ;ʹϰͿ ;ʹϮϭͿ ʹ ;нϳͿ ;ʹϭϮͿ ʹ ;нϭϱͿ ;нϭϳͿ ʹ ;ʹϭϯͿ ďͿ ĐƌŝƐ ůĞƐ ĚŝĨĨĠƌĞŶĐĞƐ ƐĂŶƐ ƉĂƌĞŶƚŚğƐĞƐ͕ ƉƵŝƐ ĐĂůĐƵůĞ͘

;нϲͿ ʹ ;ʹϱͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϭϰ ʹ ;ʹϴͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;ʹϲͿ ʹ ;нϴͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϮϬ ʹ ;нϭϮͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;нϭϳͿ ʹ ;нϰͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϳ ʹ ;нϲͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;ʹϯͿ ʹ ;ʹϵͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;ʹϭϭͿ ʹ ;ʹϱͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;нϭϴͿ ʹ ;нϳͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϭϳ ʹ ;ʹϮϲͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ACTIVITÉS

Chapitre 4 Addition et soustraction avec les nombres entiers

ĐͿ Ŷ ĨŝŶ ĚĞ ũŽƵƌŶĠĞ͕ ĂǀŝĚ ƌĞƚƌŽƵǀĞ ƵŶ ƉĂƉŝĞƌ ƌĞƉƌĞŶĂŶƚ ĚĞƐ ĐĂůĐƵůƐ ĠĐƌŝƚƐ ƉĂƌ ƐŽŶ ĐŽƉĂŝŶ DŝĐŚĞů͘ Ŷ ƵƚŝůŝƐĂŶƚ ƚŽƵƚ Ě͛ĂďŽƌĚ ƵŶĞ ƐŽŵŵĞ͕ ƉƵŝƐ ƵŶĞ ĚŝĨĨĠƌĞŶĐĞ͕ ĂŝĚĞͲůĞ ă ƌĞƚƌŽƵǀĞƌ ůĞƐ ĐĂůĐƵůƐ ĂǀĞĐ ƉĂƌĞŶƚŚğƐĞƐ ƋƵŝ ƐĞ ĐĂĐŚĞŶƚ ĚĞƌƌŝğƌĞ͕ ƉƵŝƐ ĞĨĨĞĐƚƵĞͲůĞƐ͘ ʹϭϮ н ϳ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ŽƵ

ʹϭϮ н ϳ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϲ ʹ ϰ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ŽƵ

ʹϲ ʹ ϰ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

нϭϬ ʹ Ϯ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ŽƵ

нϭϬ ʹ Ϯ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϴ н ϭϰ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ŽƵ

ʹϴ н ϭϰ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

YƵĞůůĞ ĐŽŶĐůƵƐŝŽŶ ƉĞƵǆͲƚƵ ƚŝƌĞƌ ĚĞ ĐĞƚ ĞǆĞƌĐŝĐĞ ͍ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

3 ĨĨĞĐƚƵĞ ůĞƐ ĐĂůĐƵůƐ ĞŶ ůĞƐ ĐŽŶƐŝĚĠƌĂŶƚ ĐŽŵŵĞ ĚĞƐ ƐŽŵŵĞƐ ĚĞ ĚĞƵǆ ƚĞƌŵĞƐ͘ ʹϴ ʹ ϭϱ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϮϬ н ϭϴ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϭϰ ʹ ϭϱ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

нϴ н ϭϱ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϭϴ н ϮϬ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϮϮ ʹ ϭϮ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

нϴ ʹ ϭϱ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϭϴ ʹ ϮϬ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϰϳ н ϯϱ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϭϱ ʹ ϴ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϮϬ ʹ ϭϴ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϯϵ ʹ Ϯϭ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϭϱ н ϴ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϭϴ ʹ ϮϬ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϭϳ н Ϯϯ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

4 ĂͿ ŽŵƉůğƚĞ ůĞƐ ƉǇƌĂŵŝĚĞƐ ƐĂĐŚĂŶƚ ƋƵĞ

–9

–2

a+b a b

–1

–2

–8

ďͿ ĂŶƐ ĐŚĂĐƵŶĞ ĚĞƐ ƐĠƌŝĞƐ ĐŝͲĚĞƐƐŽƵƐ͕ Ɛŝ ƚƵ ĂĚĚŝƚŝŽŶŶĞƐ ĚĞƵǆ ĚĞƐ ƚƌŽŝƐ ŶŽŵďƌĞƐ ƉƌŽƉŽƐĠƐ͕ ŝů Ǉ Ă ƵŶ ƌĠƐƵůƚĂƚ ƋƵĞ ƚƵ Ŷ͛ŽďƚŝĞŶĚƌĂƐ ƉĂƐ ͗ ůĞƋƵĞů ͍ ŶƚŽƵƌĞͲůĞ͘ ϭͿ EŽŵďƌĞƐ ϮͿ EŽŵďƌĞƐ ϯͿ EŽŵďƌĞƐ

ʹϯ ʹϭ ʹϵ

ʹϱ нϲ ʹϮ

нϳ нϭ ʹϭ

ZĠƐƵůƚĂƚƐ ZĠƐƵůƚĂƚƐ ZĠƐƵůƚĂƚƐ

ʹϴ ʹϱ ʹϭϭ

ʹϮ нϱ ʹϭϬ

нϮ Ϭ ʹϯ

нϰ нϳ ʹϵ

ĐƚŝǀŝƚĠ ϲ Somme et différence de deux nombres entiers (synthèse) 1 >Ă ŵĠƚŚŽĚĞ ĚĠĐŽƵǀĞƌƚĞ ƉĂƌ DŝĐŚĞů ă ů͛ĂĐƚŝǀŝƚĠ ƉƌĠĐĠĚĞŶƚĞ ƉĞƌŵĞƚ Ě͛ĠŶŽŶĐĞƌ ƵŶĞ ƌğŐůĞ ĚĞ ƐŝŵƉůŝĨŝĐĂƚŝŽŶ ĚĞƐ ĠĐƌŝƚƵƌĞƐ ĚĞƐ ĐĂůĐƵůƐ͘ ŶŽŶĐĞ ĐĞƚƚĞ ƌğŐůĞ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

p.49 B3

ŽŵƉůğƚĞ ĐŚĂƋƵĞ ĠŐĂůŝƚĠ ƉĂƌ ƵŶ ŶŽŵďƌĞ ĞŶƚŝĞƌ͘ н;ʹϴͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹ;нϳͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹ;ʹϲͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

н;нϰͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ 87

ACTIVITÉS

Chapitre 4 Addition et soustraction avec les nombres entiers

2 ĂůĐƵůĞ ĞŶ ĂƉƉůŝƋƵĂŶƚ ůĂ ƌğŐůĞ ĚĞƐ ƐŝŐŶĞƐ ƐƵĐĐĞƐƐŝĨƐ͘

;нϭϴͿ н ;ʹϭϭͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϳ н ;нϯͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;ʹϭϰͿ н ;нϴͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϳ ʹ ;нϯͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;нϲͿ ʹ ;ʹϭϬͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϳ н ;ʹϯͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;ʹϯϬͿ н ;ʹϭϱͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϳ ʹ ;ʹϯͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;ʹϮϬͿ ʹ ;ʹϮϱͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϳ ʹ ;ʹϯͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;нϭϲͿ ʹ ;нϭϵͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϵ ʹ ;нϱͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;ʹϯϭͿ ʹ ;ʹϴͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϳ ʹ ;нϭϭͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;ʹϭϳͿ н ;нϮϴͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϭϱ н ;ʹϮϱͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

3 ĂŶƐ ůĞƐ ƚĂďůĞĂƵǆ ĐŝͲĚĞƐƐŽƵƐ͕ ĐŽŵƉůğƚĞ ĐŚĂƋƵĞ ĐĂƐĞ ďůĞƵĞ ƉĂƌ ƵŶ ŶŽŵďƌĞ ĞŶƚŝĞƌ Ğƚ ĐŚĂƋƵĞ ĐĂƐĞ ũĂƵŶĞ ƉĂƌ ƵŶ ƐŝŐŶĞ ŽƉĠƌĂƚŽŝƌĞ͘ ʹϲ

н ʹϮ

ʹϯ н

ϭϴ

ʹϱ

ʹϯ

с с с

с н

ʹϮ

с н

ʹϮ с

ʹϱ

4 Ŷ ƐƵŝǀĂŶƚ ůĞ ŵŽĚğůĞ ƉƌŽƉŽƐĠ͕ ĐĂůĐƵůĞ ůĂ ǀĂůĞƵƌ ŶƵŵĠƌŝƋƵĞ ĚĞƐ ĞǆƉƌĞƐƐŝŽŶƐ ƐƵŝǀĂŶƚĞƐ Ɛŝ Ă с нϱ ͕ ď с ʹϰ ͕ Đ с нϲ et Ě с ʹϭϬ͘ Ă н Ě с ;нϱͿ н ;ʹϭϬͿ с нϱ ʹ ϭϬ с ʹϱ

ʹ Ă н Ě с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ď ʹ Đ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹ ď н Đ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Ě ʹ ď с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹ Đ ʹ Ă с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Đ ʹ ď с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹ ď ʹ Đ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ď ʹ Ě с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Ě ʹ Đ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

5 Ŷ ƐƵŝǀĂŶƚ ůĞ ŵŽĚğůĞ ƉƌŽƉŽƐĠ͕ ĐĂůĐƵůĞ ůĂ ǀĂůĞƵƌ ŶƵŵĠƌŝƋƵĞ ĚĞƐ ĞǆƉƌĞƐƐŝŽŶƐ ƐƵŝǀĂŶƚĞƐ Ɛŝ Ă с Ϯ ͕ ď с ʹϱ ͕ Đ с ϳ et Ě с ʹϯ͘

ď н Đ с ʹϱ н ϳ с Ϯ

ʹ Ă н Đ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Ă ʹ Đ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹ Ě н Đ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ď н Ě с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹ Đ ʹ Ě с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ď ʹ Ă с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ACTIVITÉS

Chapitre 4 Addition et soustraction avec les nombres entiers

ĐƚŝǀŝƚĠ ϳ Propriétés de l’addition 1 ĂͿ >Ğ ƚĂďůĞĂƵ ĐŝͲĚĞƐƐŽƵƐ ĐŽŶƚŝĞŶƚ ůĞƐ ƐĐŽƌĞƐ ũŽƵƌŶĂůŝĞƌƐ ŽďƚĞŶƵƐ ƉĂƌ ĂǀŝĚ ĂƵ ƚĞƌŵĞ Ě͛ƵŶĞ ƐĞŵĂŝŶĞ ĚĞ ũĞƵ ĚĞ ĐŝŶƋ ũŽƵƌƐ͘ :ŽƵƌƐ ^ĐŽƌĞƐ

>Ƶ ʹϵ

Ma нϭϮ

Me ʹϳ

Je нϵ

sĞ Ϭ

ĂǀŝĚ ĂĨĨŝƌŵĞ ƋƵ͛ŝů ĞƐƚ ĐĂƉĂďůĞ ĚĞ ĐĂůĐƵůĞƌ ƚƌğƐ ƌĂƉŝĚĞŵĞŶƚ ƐŽŶ ƐĐŽƌĞ ŵŽǇĞŶ͘ ƐƐĂŝĞ ĚĞ ĚĞǀŝŶĞƌ ƐĂ ŵĠƚŚŽĚĞ ĚĞ ĐĂůĐƵů͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ďͿ >Ă ƐĞŵĂŝŶĞ ƐƵŝǀĂŶƚĞ͕ ŝů ĚĠĐŝĚĞ ĚĞ ũŽƵĞƌ ƉĞŶĚĂŶƚ Ɛŝǆ ũŽƵƌƐ Ğƚ ŶŽƚĞ ƐĞƐ ƐĐŽƌĞƐ ũŽƵƌŶĂůŝĞƌƐ ĚĂŶƐ ůĞ ƚĂďůĞĂƵ ĐŝͲĚĞƐƐŽƵƐ͘ :ŽƵƌƐ ^ĐŽƌĞƐ

>Ƶ нϭϲ

Ma нϭϬ

Me ʹϯ

Je нϵ

sĞ ʹϲ

^Ă ʹϴ

ĂǀŝĚ ĐĂůĐƵůĞ ƐŽŶ ƐĐŽƌĞ ŵŽǇĞŶ Ğƚ ƚƌŽƵǀĞ нϯ͘ sĠƌŝĨŝĞ ƐĂ ƌĠƉŽŶƐĞ ĞŶ ƉƌŽĐĠĚĂŶƚ ĚĞ ƉůƵƐŝĞƵƌƐ ŵĂŶŝğƌĞƐ ĚŝĨĨĠƌĞŶƚĞƐ Ğƚ ĞŶ ĠĐƌŝǀĂŶƚ ƚŽƵƚ ůĞ ĚĠƚĂŝů ĚĞ ƚĞƐ ƌĂŝƐŽŶŶĞŵĞŶƚƐ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

p.50 B4

ĐͿ ZĞůŝĞ ĐŚĂƋƵĞ ĠƚĂƉĞ ĚƵ ĐĂůĐƵů ă ůĂ ƉƌŽƉƌŝĠƚĠ ƋƵ͛ŝů ŝůůƵƐƚƌĞ͘ >͛ĂĚĚŝƚŝŽŶ ĞƐƚ ƵŶĞ ŽƉĠƌĂƚŝŽŶ ;ʹϯͿ н ;нϲͿ н ;нϯͿ с ;ʹϯͿ н ;нϯͿ н ;нϲͿ • • ĂƐƐŽĐŝĂƚŝǀĞ͘ >͛ĂĚĚŝƚŝŽŶ ĂĚŵĞƚ ůĞ ŶŽŵďƌĞ с ;;ʹϯͿ н ;нϯͿͿ н ;нϲͿ • • Ϭ ĐŽŵŵĞ ĠůĠŵĞŶƚ ŶĞƵƚƌĞ͘ >͛ĂĚĚŝƚŝŽŶ ĞƐƚ ƵŶĞ ŽƉĠƌĂƚŝŽŶ с Ϭ н ;нϲͿ • • ĐŽŵŵƵƚĂƚŝǀĞ͘ >͛ĂĚĚŝƚŝŽŶ ĞƐƚ ƵŶĞ ŽƉĠƌĂƚŝŽŶ с нϲ • • ƐǇŵĠƚƌŝƐĂďůĞ͘ 89

ACTIVITÉS

Chapitre 4 Addition et soustraction avec les nombres entiers

2 ĂͿ ĂůĐƵůĞ ĞŶ ĂƉƉůŝƋƵĂŶƚ ůĞƐ ƉƌŽƉƌŝĠƚĠƐ ĚĞ ů͛ĂĚĚŝƚŝŽŶ͘ ;нϱͿ н ;ʹϮͿ н ;ʹϳͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϳ н ;ʹϱͿ н ϭϬ н ;ʹϯͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;ʹϮͿ н ;ʹϵͿ н ;нϲͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϯ н ϱ н ϭϮ н ;ʹϭͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;ʹϱͿ н ;нϲͿ н ;нϰͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϮ н ϱ н ;ʹϯͿ н ϳ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϱ н ;ʹϮͿ н ;ʹϯͿ н ϳ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϳϱ н ϯϳ н ϯϴ н ;ʹϰϳͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϰ н ;ʹϲͿ н ϰ н ;ʹϭͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϱϳ н ;ʹϮϭͿ н ϲϰ н ;ʹϱϳͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ďͿ ĂůĐƵůĞ͘

ʹϳ н Ϯ н ϴ ʹ ϵ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϴ н ϭϲ ʹ Ϯϭ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϴ ʹ ϱ н ϯ н ϭϬ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϭϰ ʹ ϭϳ ʹ ϭϴ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϱ ʹ ϳ ʹ Ϯ н ϯ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϮϲ н ϯϵ ʹ ϭϯ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϵ н ϲ ʹ ϰ н ϵ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϭϳ ʹ Ϯϭ ʹ Ϯϭ ʹ ϭϳ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϭϱ ʹ ϴ ʹ ϳ н ϰ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϮϱ ʹ ϯϰ н ϭϯ н ϭϮ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ĐͿ ĂůĐƵůĞ ĂƉƌğƐ ĂǀŽŝƌ ƐŝŵƉůŝĨŝĠ ů͛ĠĐƌŝƚƵƌĞ͘ Ϯϲ н ;ʹϰͿ ʹ ;ʹϳͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ʹϭϳ ʹ ;нϳͿ н ;ʹϭϬͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ Ϯϭ н ;ʹϱͿ н ;ʹϲͿ ʹ ϳ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϵ ʹ ;ʹϱͿ н ;ʹϰͿ ʹ ;нϲͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ;ʹϰͿ н ;ʹϲͿ ʹ ;ʹϵͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϭϱ н ;ʹϮϱͿ н ;ʹϴͿ н ;ʹϳͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϭϴ ʹ ;ʹϴͿ н ;ʹϯͿ ʹ ;нϲͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ʹϳ ʹ ;ʹϳͿ н ;ʹϱͿ ʹ ;нϵͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ Ϯϲ ʹ Ϯϰ ʹ ;ʹϭϯͿ н ϭϭ ʹ ;нϭϬͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϭϯ н ;ʹϳͿ ʹ ;ʹϱͿ н ϳ ʹ ϭϯ н ;ʹϱͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ 3 ĂŶƐ ĐŚĂƋƵĞ ĐĂƐ Ğƚ ƉŽƵƌ ĐŚĂƋƵĞ ĠƚĂƉĞ ĚƵ ĐĂůĐƵů͕ Ɛŝ ƵŶĞ ƉƌŽƉƌŝĠƚĠ ĚĞ ů͛ĂĚĚŝƚŝŽŶ Ă ĠƚĠ ƵƚŝůŝƐĠĞ͕ ŶŽŵŵĞͲůĂ͘ ϳ н ;ʹϰͿ н ϲ н ;ʹϯͿ

с ϳ н ;ʹϰͿ н ;ʹϯͿ н ϲ

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

с ϳ н ;;ʹϰͿ н ;ʹϯͿͿ н ϲ

с ϳ н ;ʹϳͿ н ϲ

с ;ϳ н ;ʹϳͿͿ н ϲ

с Ϭ н ϲ

с ϲ

p.51 B5

ACTIVITÉS

Chapitre 4 Addition et soustraction avec les nombres entiers

ʹϱ н ;ʹϲͿ н ϲ н ϰ н ;ʹϱͿ с ʹϱ н ;;ʹϲͿ н ϲͿ н ϰ н ;ʹϱͿ

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

с ʹϱ н Ϭ н ϰ н ;ʹϱͿ

с ʹϱ н ϰ н ;ʹϱͿ

с ʹϱ н ;ʹϱͿ н ϰ

с ;ʹϱ н ;ʹϱͿͿ н ϰ

с ʹϭϬ н ϰ

с ʹϲ

ĐƚŝǀŝƚĠ ϴ Repérage d’un point du plan

1 sŽŝĐŝ ƵŶĞ ĐĂƌƚĞ ĚĞ ĞůŐŝƋƵĞ ƉůĂĐĠĞ ĚĂŶƐ ƵŶ ƌĞƉğƌĞ ĐĂƌƚĠƐŝĞŶ ĚĠĨŝŶŝ ĚĞ ůĂ ŵĂŶŝğƌĞ ƐƵŝǀĂŶƚĞ ͗ ůĞƐ ĂǆĞƐ ǆ Ğƚ Ǉ ƐŽŶƚ ƉĞƌƉĞŶĚŝĐƵůĂŝƌĞƐ ĂƵ ƉŽŝŶƚ K ƋƵŝ ƌĞƉƌĠƐĞŶƚĞ ůĂ ǀŝůůĞ ĚĞ ƌƵǆĞůůĞƐ Ğƚ ů͛ƵŶŝƚĠ ĞƐƚ ůĞ ĐƀƚĠ Ě͛ƵŶ ƉĞƚŝƚ ĐĂƌƌĠ͘ y

B A

x O T H D

ĂͿ ^Ƶƌ ĐĞƚƚĞ ĐĂƌƚĞ͕ ŽŶ Ă ƌĞƉĠƌĠ ƋƵĞůƋƵĞƐ ǀŝůůĞƐ ͗ sŝƌƚŽŶ ;sͿ͕ dŽƵƌŶĂŝ ;dͿ͕ ŝŶĂŶƚ ; Ϳ͕ ůŽƐƚ ; Ϳ͕ ,ƵǇ ;,Ϳ͕ ƌƵŐĞƐ ; Ϳ Ğƚ DŽů ;DͿ͘ EŽƚĞ ůĞƐ ĐŽŽƌĚŽŶŶĠĞƐ ĚĞƐ ĚŝĨĨĠƌĞŶƚƐ ƉŽŝŶƚƐ ƌĞƉƌĠƐĞŶƚĂŶƚ ĐĞƐ ǀŝůůĞƐ͘ sര;͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͖ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘Ϳ

ര;͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͖ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘Ϳ

,ര;͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͖ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘Ϳ

dര;͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͖ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘Ϳ

ര;͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͖ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘Ϳ

Dര;͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͖ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘Ϳ

ďͿ ƚŽŝ ĚĞ ƌĞƉĠƌĞƌ ƐƵƌ ĐĞƚƚĞ ĐĂƌƚĞ ůĞƐ ǀŝůůĞƐ ƐƵŝǀĂŶƚĞƐ ĚŽŶƚ ǀŽŝĐŝ ůĞƐ ĐŽŽƌĚŽŶŶĠĞƐ͘ ĂǀĞŶƚĞŵ ͗ ര;ϭ ͖ ϭͿ

'ĂŶĚ ͗ 'ര;ʹϱ ͖ ϯͿ

zƉƌĞƐ ͗ zര;ʹϭϭ ͖ ϭͿ EĂŵƵƌ ͗ Eര;ϯ ͖ ʹϱͿ

p.51 C1

&ůŽƌĞŶǀŝůůĞ ͗ &ര;ϳ ͖ ʹϭϯͿ ^ŽŝŐŶŝĞƐ ͗ ^ര;ʹϮ ͖ ʹϰͿ >ŽƵǀĂŝŶͲůĂͲEĞƵǀĞ ͗ >ര;Ϯ ͖ ʹϮͿ 91

ACTIVITÉS

Chapitre 4 Addition et soustraction avec les nombres entiers

2 ĠƚĞƌŵŝŶĞ ůĞƐ ĐŽŽƌĚŽŶŶĠĞƐ ĚĞƐ ƉŽŝŶƚƐ ƌĞƉƌĠƐĞŶƚĠƐ͘ y H C A G

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

^Ƶƌ ĐĞ ƌĞƉğƌĞ͕ ƉůĂĐĞ ůĞƐ x ƉŽŝŶƚƐ ĚŽŶƚ ǀŽŝĐŝ ůĞƐ ĐŽŽƌĚŽŶŶĠĞƐ ͗

1 F

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

1 0

D E

yര;Ϯ ͖ ϱͿ

dര;ϰ ͖ ϬͿ

zര;ʹϯ ͖ ϮͿ

hര;Ϭ ͖ ʹϯͿ

ര;ϰ ͖ ʹϯͿ

tര;ʹϮ ͖ ʹϭͿ

3 ŽŵƉůğƚĞ ůĞƐ ĐŽƵƉůĞƐ ƉŽƵƌ ƋƵ͛ŝůƐ ƌĠƉŽŶĚĞŶƚ ă ůĂ ĐŽŶĚŝƚŝŽŶ ĠŶŽŶĐĠĞ͘ ĂͿ >͛ŽƌĚŽŶŶĠĞ ǀĂƵƚ ϱ ĚĞ ƉůƵƐ ƋƵĞ ů͛ĂďƐĐŝƐƐĞ͘ ;ϰ ͖ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘Ϳ

;͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͖ ϲͿ

;ʹϯ ͖ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘Ϳ

;ʹϱ ͖ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘Ϳ

;͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͖ ϮͿ

;͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͖ ʹϴͿ

;͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͖ ϬͿ

;͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͖ ϭͿ

;͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͖ ʹϱͿ

;ʹϮ ͖ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘Ϳ

;͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͖ ʹϰͿ

;͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͖ ϭϬͿ

;͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͖ ϬͿ

;͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͖ ϭͿ

;͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͖ ʹϱͿ

;͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͖ ϬͿ

;ʹϱ ͖ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘Ϳ

;͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͖ ʹϳͿ

ďͿ >͛ĂďƐĐŝƐƐĞ ĞƐƚ ů͛ŽƉƉŽƐĠ ĚĞ ů͛ŽƌĚŽŶŶĠĞ͘ ;Ϯ ͖ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘Ϳ

;͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͖ ϳͿ

;ʹϯ ͖ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘Ϳ

ĐͿ >Ă ƐŽŵŵĞ ĚĞƐ ĐŽŽƌĚŽŶŶĠĞƐ ǀĂƵƚ ϱ͘ ;ϯ ͖ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘Ϳ

;ϱ ͖ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘Ϳ

;ϴ ͖ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘Ϳ

ĚͿ >Ă ĚŝĨĨĠƌĞŶĐĞ ĞŶƚƌĞ ů͛ĂďƐĐŝƐƐĞ Ğƚ ů͛ŽƌĚŽŶŶĠĞ ǀĂƵƚ ϱ͘ ;ϳ ͖ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘Ϳ

;͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͖ ϴͿ

;ʹϯ ͖ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘Ϳ

ĞͿ >͛ĂďƐĐŝƐƐĞ ĞƐƚ ƉůƵƐ ŐƌĂŶĚĞ ƋƵĞ ů͛ŽƌĚŽŶŶĠĞ͘ ;ϲ ͖ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘Ϳ

;͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͖ ϯͿ

;Ϭ ͖ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘Ϳ

4 ĂͿ dƌŽƵǀĞ ĚĞƐ ĐŽƵƉůĞƐ ĚŽŶƚ ů͛ĂďƐĐŝƐƐĞ ǀĂƵƚ ϲ͘ ;͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͖ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘Ϳ

;͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͖ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘Ϳ

ZĞƉƌĠƐĞŶƚĞ ƚŽƵƐ ůĞƐ ƉŽŝŶƚƐ ĚŽŶƚ ů͛ĂďƐĐŝƐƐĞ ǀĂƵƚ ϲ͘ y

ZĞƉƌĠƐĞŶƚĞ ƚŽƵƐ ůĞƐ ƉŽŝŶƚƐ ĚŽŶƚ ů͛ŽƌĚŽŶŶĠĞ ǀĂƵƚ ʹϱ͘ y

ďͿ dƌŽƵǀĞ ĚĞƐ ĐŽƵƉůĞƐ ĚŽŶƚ ů͛ŽƌĚŽŶŶĠĞ ǀĂƵƚ ʹϱ͘

1 0

dƌĂĚƵŝƐ ĐĞƚƚĞ ĐĂƌĂĐƚĠƌŝƐƚŝƋƵĞ ƉĂƌ ƵŶĞ

ĠŐĂůŝƚĠ ĂůŐĠďƌŝƋƵĞ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

p.51 C2

ACTIVITÉS

Chapitre 4 Addition et soustraction avec les nombres entiers

ĐͿ ŽŵƉůğƚĞ ůĞƐ ĐŽƵƉůĞƐ Ɛŝ ůĂ ƐŽŵŵĞ ĚĞƐ ĐŽŽƌĚŽŶŶĠĞƐ ǀĂƵƚ ʹϮ͘

ĚͿ ŽŵƉůğƚĞ ůĞƐ ĐŽƵƉůĞƐ Ɛŝ ůĂ ƐŽŵŵĞ ĚĞƐ

ĐŽŽƌĚŽŶŶĠĞƐ ǀĂƵƚ Ϭ͘

;ϯ ͖ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘Ϳ

;͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͖ ϬͿ

;͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͖ ʹϰͿ

;Ϯ ͖ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘Ϳ

;͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͖ ʹϰͿ

;͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͖ ϬͿ

;ʹϱ͖ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘Ϳ

രര;ʹϭ͖ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘Ϳ

;͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͖ ʹϲͿ

;ʹϯ ͖ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘Ϳ

;͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͖ ϭͿ

;ϱ ͖ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘Ϳ

ZĞƉƌĠƐĞŶƚĞ ƚŽƵƐ ůĞƐ ĐŽƵƉůĞƐ ĚŽŶƚ ůĂ ƐŽŵŵĞ ĚĞƐ ĐŽŽƌĚŽŶŶĠĞƐ ǀĂƵƚ ʹϮ͘ y

1 0

ZĞƉƌĠƐĞŶƚĞ ƚŽƵƐ ůĞƐ ĐŽƵƉůĞƐ ĚŽŶƚ ůĂ ƐŽŵŵĞ ĚĞƐ ĐŽŽƌĚŽŶŶĠĞƐ ǀĂƵƚ Ϭ͘ y

1 0

dƌĂĚƵŝƐ ĐĞƚƚĞ ĐĂƌĂĐƚĠƌŝƐƚŝƋƵĞ ƉĂƌ ƵŶĞ ĠŐĂůŝƚĠ ĂůŐĠďƌŝƋƵĞ͘

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ĞͿ ŽŵƉůğƚĞ ůĞƐ ĐŽƵƉůĞƐ Ɛŝ ů͛ŽƌĚŽŶŶĠĞ ǀĂƵƚ ϰ ĚĞ ŵŽŝŶƐ ƋƵĞ ů͛ĂďƐĐŝƐƐĞ͘

dƌĂĚƵŝƐ ĐĞƚƚĞ ĐĂƌĂĐƚĠƌŝƐƚŝƋƵĞ ƉĂƌ ĚĞƐ ĐĂůĐƵůƐ͘

;ϳ ͖ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘Ϳ

;Ϭ ͖ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘Ϳ

;͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͖ ϮͿ

;͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͖ ϬͿ

;ʹϯ ͖ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘Ϳ

;͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͖ ʹϱͿ

ZĞƉƌĠƐĞŶƚĞ ƚŽƵƐ ůĞƐ ƉŽŝŶƚƐ ĚŽŶƚ ů͛ŽƌĚŽŶŶĠĞ ǀĂƵƚ ϰ ĚĞ ŵŽŝŶƐ ƋƵĞ ů͛ĂďƐĐŝƐƐĞ͘

dƌĂĚƵŝƐ ĐĞƚƚĞ ĐĂƌĂĐƚĠƌŝƐƚŝƋƵĞ ƉĂƌ ƵŶĞ ĠŐĂůŝƚĠ ĂůŐĠďƌŝƋƵĞ͘ x

1 0

ACTIVITÉS

Chapitre 4 Addition et soustraction avec les nombres entiers

ĐƚŝǀŝƚĠ ϵ Problèmes 1 ŝŶƋ ĂŵŝƐ ũŽƵĞŶƚ ă ƵŶ ũĞƵ ĚĞ ƐŽĐŝĠƚĠ͘ >Ğ ĐĂůĐƵů ĚĞƐ ƐĐŽƌĞƐ ŽďƚĞŶƵƐ ƉĂƌ ĐŚĂƋƵĞ ũŽƵĞƵƌ ă ů͛ŝƐƐƵĞ ĚĞ ĐŚĂƋƵĞ ƉĂƌƚŝĞ ƐĞ ĨĂŝƚ ĚĞ ůĂ ŵĂŶŝğƌĞ ƐƵŝǀĂŶƚĞ ͗ ůĞ ǀĂŝŶƋƵĞƵƌ ĚĞ ůĂ ƉĂƌƚŝĞ ƌĞĕŽŝƚ ƵŶ ŶŽŵďƌĞ ƉŽƐŝƚŝĨ ĚĞ ƉŽŝŶƚƐ ;н ͙Ϳ ƚĂŶĚŝƐ ƋƵĞ ůĞƐ ƉĞƌĚĂŶƚƐ ƌĞĕŽŝǀĞŶƚ ĐŚĂĐƵŶ ƵŶ ŵġŵĞ ŶŽŵďƌĞ ĚĞ ƉŽŝŶƚƐ ŶĠŐĂƚŝĨƐ ;ʹ ͙Ϳ ĚĞ ƚĞůůĞ ƐŽƌƚĞ ƋƵĞ ůĂ ƐŽŵŵĞ ĚĞƐ ƐĐŽƌĞƐ Ě͛ƵŶĞ ƉĂƌƚŝĞ ƐŽŝƚ ŶƵůůĞ͘ ĂͿ ŽŵƉůğƚĞ ůĞ ƚĂďůĞĂƵ ĐŝͲĚĞƐƐŽƵƐ͘ WĂƐĐĂů 1re ƉĂƌƚŝĞ 2e ƉĂƌƚŝĞ

Mike

DĂƌůğŶĞ DĂƌǇƐĞ &ĂďƌŝĐĞ

нϮϴ нϮϰ

3e ƉĂƌƚŝĞ

4e ƉĂƌƚŝĞ

нϯϲ нϰϬ

5e ƉĂƌƚŝĞ

нϯϮ

^ĐŽƌĞ ĨŝŶĂů ďͿ >Ă ƐĞŵĂŝŶĞ ƐƵŝǀĂŶƚĞ͕ ŝůƐ ĚĠĐŝĚĞŶƚ ĚĞ ƌĞũŽƵĞƌ ƚƌŽŝƐ ƉĂƌƚŝĞƐ ă ĐĞ ũĞƵ͘ Ŷ ƚĞŶĂŶƚ ĐŽŵƉƚĞ ĚĞƐ ŝŶĨŽƌŵĂƚŝŽŶƐ ĐŝͲĚĞƐƐŽƵƐ͕ ŶŽƚĞ ĚĂŶƐ ůĞ ƚĂďůĞĂƵ ůĞ ŶŽŵďƌĞ ƚŽƚĂů ĚĞ ƉŽŝŶƚƐ ĚĞ ĐŚĂƋƵĞ ũŽƵĞƵƌ ă ů͛ŝƐƐƵĞ ĚĞ ĐŚĂƋƵĞ ƉĂƌƚŝĞ͘ ͻ ƉƌğƐ ůĂ ϭre ƉĂƌƚŝĞ͕ DĂƌůğŶĞ ƌĞĕŽŝƚ ϰ ƉŽŝŶƚƐ Ğƚ DĂƌǇƐĞ ĞƐƚ ůĂ ŐĂŐŶĂŶƚĞ͘ • ůĂ ĨŝŶ ĚĞ ůĂ Ϯe ƉĂƌƚŝĞ͕ DĂƌǇƐĞ ƐĞ ƌĞƚƌŽƵǀĞ ĂǀĞĐ ƵŶ ƐĐŽƌĞ ĚĞ нϴ Ğƚ WĂƐĐĂů ĞƐƚ ůĞ ŐĂŐŶĂŶƚ͘ ͻ DĂƌůğŶĞ ŐĂŐŶĞ ůĂ ϯe ƉĂƌƚŝĞ Ğƚ ă ůĂ ĨŝŶ ĚĞ ĐĞƚƚĞ ƉĂƌƚŝĞ͕ ƐŽŶ ƐĐŽƌĞ ĞƐƚ ŶƵů͘ WĂƐĐĂů

Mike

DĂƌůğŶĞ DĂƌǇƐĞ &ĂďƌŝĐĞ

dŽƚĂů ĚĞƐ ƉŽŝŶƚƐ ĂƉƌğƐ ůĂ ϭre ƉĂƌƚŝĞ dŽƚĂů ĚĞƐ ƉŽŝŶƚƐ ĂƉƌğƐ ůĂ Ϯe ƉĂƌƚŝĞ dŽƚĂů ĚĞƐ ƉŽŝŶƚƐ ĂƉƌğƐ ůĂ ϯe ƉĂƌƚŝĞ sĠƌŝĨŝĞ ƋƵĞ ůĂ ĚĞƌŶŝğƌĞ ůŝŐŶĞ ĚĞ ƚŽŶ ƚĂďůĞĂƵ ĞƐƚ ĐŽƌƌĞĐƚĞ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

2 WĂƵů Ğƚ :ƵůŝĞ ũŽƵĞŶƚ ĂǀĞĐ ĚĞƵǆ ĚĠƐ͘ ^Ƶƌ ůĞƐ ĨĂĐĞƐ ĚĞ ů͛ƵŶ ĚĞƵǆ ƐŽŶƚ ŝŶƐĐƌŝƚƐ ĚĞƐ ŶŽŵďƌĞƐ ƉŽƐŝƚŝĨƐ ;ĚĞ ϭ ă ϲͿ Ğƚ ƐƵƌ ů͛ĂƵƚƌĞ ĚĞƐ ŶŽŵďƌĞƐ ŶĠŐĂƚŝĨƐ ;ĚĞ ʹϭ ă ʹϲͿ͘ /ůƐ ũĞƚƚĞŶƚ ĐŚĂĐƵŶ ă ůĞƵƌ ƚŽƵƌ ůĞƐ ĚĞƵǆ ĚĠƐ Ğƚ ĐŽŵƉƚĂďŝůŝƐĞŶƚ ůĞƐ ƉŽŝŶƚƐ ŽďƚĞŶƵƐ͘ Ƶ ĚĠƉĂƌƚ͕ ĐŚĂĐƵŶ ĚŝƐƉŽƐĞ Ě͛ƵŶ ĐĂƉŝƚĂů ĚĞ нϭϱ ƉŽŝŶƚƐ͘ ĂͿ ů͛ŝƐƐƵĞ ĚĞ ƐŽŶ ƉƌĞŵŝĞƌ ůĂŶĐĞƌ͕ :ƵůŝĞ ĐŽŵƉƚĂďŝůŝƐĞ нϭϯ ƉŽŝŶƚƐ͘ /ŶĚŝƋƵĞ ůĞƐ ĚŝĨĨĠƌĞŶƚƐ ũĞƚƐ ƉŽƐƐŝďůĞƐ ƉŽƵƌ ĐĞ ĐĂƉŝƚĂů͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ďͿ ƐƚͲŝů ƉŽƐƐŝďůĞ͕ ĂƉƌğƐ ĂǀŽŝƌ ũŽƵĠ ƚƌŽŝƐ ĨŽŝƐ͕ Ě͛ĂǀŽŝƌ ƵŶ ĐĂƉŝƚĂů ŶƵů ͍ hŶ ĐĂƉŝƚĂů ĚŽƵďůĠ ͍ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ACTIVITÉS

Chapitre 4 Addition et soustraction avec les nombres entiers 3

sŽŝĐŝ ƵŶĞ ƐĠƌŝĞ ĚĞ ŶĞƵĨ ŶŽŵďƌĞƐ Ğƚ ĚĞƐ ŝŶĨŽƌŵĂƚŝŽŶƐ ƌĞůĂƚŝǀĞƐ ă ĐĞƵǆͲĐŝ͘ нϭϮϬϬ Ϭ ʹϭϯϱϱ ʹϴϬϭ ʹϭϯϯϱ ʹϲϬϬ нϭϰϰϴ нϳϴϭ ʹϭϯϰϱ ĞƐƚ ƵŶ ŶŽŵďƌĞ ĐŽŵƉƌŝƐ ĞŶƚƌĞ ʹϳϬϬ Ğƚ Ϭ͘ ĞƐƚ ůĞ ƉůƵƐ ŐƌĂŶĚ ŶŽŵďƌĞ ĚĞ ůĂ ƐĠƌŝĞ͘ ' ĞƐƚ ů͛ĂďƐĐŝƐƐĞ ĚĞ ů͛ŽƌŝŐŝŶĞ Ě͛ƵŶĞ ĚƌŽŝƚĞ ŐƌĂĚƵĠĞ͘ , ĞƐƚ ƵŶ ŶŽŵďƌĞ ƐƚƌŝĐƚĞŵĞŶƚ ŶĠŐĂƚŝĨ ŵƵůƚŝƉůĞ ĚĞ ϵ͘ K ĞƐƚ ƵŶ ŶŽŵďƌĞ ƋƵŝ ĞƐƚ ă ůĂ ŵġŵĞ ĚŝƐƚĂŶĐĞ ĚĞ ǌĠƌŽ ƋƵĞ ʹϳϴϭ͘ W ĞƐƚ ůĞ ƉůƵƐ ƉĞƚŝƚ ŶŽŵďƌĞ ĚĞ ůĂ ƐĠƌŝĞ͘ Z ĞƐƚ ƵŶ ŶŽŵďƌĞ ƐƚƌŝĐƚĞŵĞŶƚ ƉŽƐŝƚŝĨ ŵƵůƚŝƉůĞ ĚĞ ϯ͘ d ĞƐƚ ƵŶ ŶŽŵďƌĞ ŶĠŐĂƚŝĨ ĚŽŶƚ ůĞƐ ĐŚŝĨĨƌĞƐ ĚĞƐ ĐĞŶƚĂŝŶĞƐ Ğƚ ĚĞƐ ĚŝǌĂŝŶĞƐ ƐŽŶƚ ůĞƐ ŵġŵĞƐ͘ z ĞƐƚ ƵŶ ŶŽŵďƌĞ ŶĠŐĂƚŝĨ ƉůƵƐ ƉĞƚŝƚ ƋƵĞ ʹϭϯϰϬ Ğƚ ƉůƵƐ ŐƌĂŶĚ ƋƵĞ ʹϭϯϱϱ͘ ĂͿ ZĂŶŐĞ ůĞƐ ŶŽŵďƌĞƐ ƉƌŽƉŽƐĠƐ ƉĂƌ ŽƌĚƌĞ ĐƌŽŝƐƐĂŶƚ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ďͿ ƐƐŽĐŝĞ ĐŚĂƋƵĞ ŶŽŵďƌĞ ĚĞ ůĂ ƐĠƌŝĞ ă ůĂ ůĞƚƚƌĞ ĐŽƌƌĞƐƉŽŶĚĂŶƚ ă ƐĂ ĚĞƐĐƌŝƉƚŝŽŶ͘ >ĞƚƚƌĞ

EŽŵďƌĞ

>ĞƚƚƌĞ

EŽŵďƌĞ

>ĞƚƚƌĞ

EŽŵďƌĞ

ĐͿ Ŷ ƚ͛ĂŝĚĂŶƚ ĚĞ ůĂ ƐƵŝƚĞ ĚĞ ŶŽŵďƌĞƐ ĠĐƌŝƚĞ ĂƵ ďͿ͕ ƌĞƉůĂĐĞ ůĞƐ ůĞƚƚƌĞƐ ĚĂŶƐ ůĞ ďŽŶ ŽƌĚƌĞ Ğƚ ĚĠĐŽƵǀƌĞ ůĞ ŶŽŵ Ě͛ƵŶ ŵĂƚŚĠŵĂƚŝĐŝĞŶ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ 4 ŝŶƋ ĞŶĨĂŶƚƐ ůĂŶĐĞŶƚ ĐŚĂĐƵŶ ƚƌŽŝƐ ĨůĠĐŚĞƚƚĞƐ ƐƵƌ ůĂ ĐŝďůĞ ƌĞƉƌĠƐĞŶƚĠĞ ĐŝͲĐŽŶƚƌĞ͘ dŽƵƚĞ ĨůĠĐŚĞƚƚĞ ŶŽŶ ƉůĂŶƚĠĞ ŽƵ ƉůĂŶƚĠĞ ă ů͛ĞǆƚĠƌŝĞƵƌ ĚĞƐ ƚƌŽŝƐ ƉƌĞŵŝğƌĞƐ ǌŽŶĞƐ ĚŽŶŶĞ ʹϴ ƉŽŝŶƚƐ͘ ůĂ ĨŝŶ ĚĞ ůĂ ƉĂƌƚŝĞ͕ ůĞƐ ƐĐŽƌĞƐ ƐŽŶƚ ůĞƐ ƐƵŝǀĂŶƚƐ ͗ >ŽƵŝƐ ͗ нϭϰ sŝĐƚŽƌ ͗ Ϭ DĂƌŝĞ ͗ ʹϮϰ EŝĐŽůĂƐ ͗ нϰ :ƵůŝĞ ͗ нϲ

–8 –2 +6 +10

WŽƵƌ ĐŚĂƋƵĞ ĞŶĨĂŶƚ͕ ƉƌĠĐŝƐĞ ůĂ ŵĂŶŝğƌĞ ĚŽŶƚ ůĞ ƐĐŽƌĞ Ă ƉƵ ġƚƌĞ ŽďƚĞŶƵ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

5 >ŝƐĂ͕ WĂƵůŝŶĞ͕ :ƵůŝĞŶ Ğƚ dŽŵ ũŽƵĞŶƚ ă ƵŶ ũĞƵ ĚĞ ƐŽĐŝĠƚĠ ĐŽŶƐŝƐƚĂŶƚ ă ƌĠƉŽŶĚƌĞ ă ƵŶ ƋƵĞƐƚŝŽŶŶĂŝƌĞ ă ĐŚŽŝǆ ŵƵůƚŝƉůĞƐ ;Y͘ ͘D͘Ϳ ĐŽŵƉŽƌƚĂŶƚ ŚƵŝƚ ƋƵĞƐƚŝŽŶƐ͘ ĐŚĂƋƵĞ ƌĠƉŽŶƐĞ ĨĂƵƐƐĞ ;&Ϳ͕ ůĞ ũŽƵĞƵƌ ƌĞĕŽŝƚ ƵŶ ũĞƚŽŶ ĂǀĞĐ ůĂ ŶŽƚĞ ʹϯ͘ >ŽƌƐƋƵ͛ŝů ŶĞ ƌĠƉŽŶĚ ƉĂƐ ă ůĂ ƋƵĞƐƚŝŽŶ ;^Ϳ͕ ŝů ƌĞĕŽŝƚ ƵŶ ũĞƚŽŶ ĂǀĞĐ ůĂ ŶŽƚĞ ʹϭ͘ ĐŚĂƋƵĞ ďŽŶŶĞ ƌĠƉŽŶƐĞ ; Ϳ͕ ŝů ƌĞĕŽŝƚ ƵŶ ũĞƚŽŶ ĂǀĞĐ ůĂ ŶŽƚĞ нϰ͘ ĂͿ ĂůĐƵůĞ ůĂ ŶŽƚĞ ĚĞ >ŝƐĂ ĚŽŶƚ ůĞƐ ƌĠƐƵůƚĂƚƐ ĂƵǆ ƋƵĞƐƚŝŽŶƐ ƐŽŶƚ ͗ &͕ ͕ ^͕ &͕ &͕ ͕ Ğƚ ^͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ďͿ dŽŵ Ă ŽďƚĞŶƵ ĐŽŵŵĞ ŶŽƚĞ ʹϲ͘ ^ĂĐŚĂŶƚ ƋƵ͛ŝů Ă ĚĞƵǆ ĨŽŝƐ ƉůƵƐ ĚĞ ŵĂƵǀĂŝƐĞƐ ƌĠƉŽŶƐĞƐ ƋƵĞ ĚĞ ďŽŶŶĞƐ ƌĠƉŽŶƐĞƐ͕ ĚĠƚĞƌŵŝŶĞ ĐŽŵďŝĞŶ ĚĞ ƋƵĞƐƚŝŽŶƐ ƐŽŶƚ ƌĞƐƚĠĞƐ ƐĂŶƐ ƌĠƉŽŶƐĞ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

EXERCICES COMPLÉMENTAIRES

Chapitre 4 Addition et soustraction avec les nombres entiers

Connaître 1 >ĞƐ ŝŶĠŐĂůŝƚĠƐ ƐƵŝǀĂŶƚĞƐ ƐŽŶƚͲĞůůĞƐ ǀƌĂŝĞƐ ŽƵ ĨĂƵƐƐĞƐ ͍

:ƵƐƟ Į Ğ ĞŶ ƵƟ ůŝƐĂŶƚ ůĞƐ ƌğŐůĞƐ ĚĞ ĐŽŵƉĂƌĂŝƐŽŶ ĚĞ ĚĞƵǆ ŶŽŵďƌĞƐ ĞŶƟ ĞƌƐ͘ ϭϰ ф ϭϱ Ϯϭ х ϭϮ Ϭ ф ʹϭϲ ϯϭ ф ʹϯϭ ʹϮϭ х ʹϭϮ ʹϭϯ ф ʹϭϬ Ϭ х ʹϰ ʹϭϱ х ʹϭϴ Ϭ ф ʹϭ ʹϭϳ х ϯ ƌŵĂƟ ŽŶƐ ƐƵŝǀĂŶƚĞƐ ƐŽŶƚͲĞůůĞƐ ǀƌĂŝĞƐ ŽƵ ĨĂƵƐƐĞƐ ͍ 2 >ĞƐ Ăĸ ĂͿ >͛ŽƉƉŽƐĠ Ě͛ƵŶ ŶŽŵďƌĞ ŶĠŐĂƟ Ĩ ĞƐƚ ƵŶ ŶŽŵďƌĞ ƉŽƐŝƟ Ĩ͘ ďͿ ĞƵǆ ŶŽŵďƌĞƐ ĚĞ ƐŝŐŶĞƐ ĐŽŶƚƌĂŝƌĞƐ ƐŽŶƚ ŽƉƉŽƐĠƐ͘ ĐͿ >Ğ ŶŽŵďƌĞ ʹϮ͕ϭ ĞƐƚ ĐŽŵƉƌŝƐ ĞŶƚƌĞ ʹϮ Ğƚ ʹϭ͘ ĚͿ ĞƵǆ ŶŽŵďƌĞƐ ĚĞ ƐŝŐŶĞƐ ĐŽŶƚƌĂŝƌĞƐ ŽŶƚ ůĞƵƌ ƐŽŵŵĞ ŶĠŐĂƟ ǀĞ͘ ĞͿ >Ă ƐŽŵŵĞ ĚĞ ĚĞƵǆ ŶŽŵďƌĞƐ ŶĠŐĂƟ ĨƐ ĞƐƚ ƚŽƵũŽƵƌƐ ŶĠŐĂƟ ǀĞ͘ ĨͿ ^ŝ ůĂ ƐŽŵŵĞ ĚĞ ĚĞƵǆ ŶŽŵďƌĞƐ ĞƐƚ ŶĠŐĂƟ ǀĞ͕ ĂůŽƌƐ ůĞƐ ĚĞƵǆ ŶŽŵďƌĞƐ ƐŽŶƚ ŶĠŐĂƟ ĨƐ͘ ŐͿ >Ă ƐŽŵŵĞ ĚĞ ĚĞƵǆ ŶŽŵďƌĞƐ Ŷ͛ĞƐƚ ŶƵůůĞ ƋƵĞ Ɛŝ ůĞƐ ĚĞƵǆ ŶŽŵďƌĞƐ ƐŽŶƚ ŶƵůƐ͘ ŚͿ ĞƵǆ ŶŽŵďƌĞƐ ŽƉƉŽƐĠƐ ŽŶƚ ůĂ ŵġŵĞ ǀĂůĞƵƌ ĂďƐŽůƵĞ͘ ŝͿ >Ă ǀĂƌŝĂƟ ŽŶ ĚĞ ƚĞŵƉĠƌĂƚƵƌĞ ĞŶƚƌĞ ʹϭϬ Σ Ğƚ ϯ Σ ĞƐƚ ĚĞ ϳ Σ ͘ ũͿ ZĞƟ ƌĞƌ ʹϰ ă ƵŶ ŶŽŵďƌĞ ƌĞǀŝĞŶƚ ă ůƵŝ ĂũŽƵƚĞƌ ϰ͘

3 ŽŵƉůğƚĞ ĂǀĞĐ K͕ ͕ ͕ ͕ ŽƵ ͘

y C

ĂͿ DŽŶ ĂďƐĐŝƐƐĞ ĠŐĂůĞ ŵŽŶ ŽƌĚŽŶŶĠĞ͕ ũĞ ƐƵŝƐ ůĞ ƉŽŝŶƚ ͘͘͘ ďͿ DŽŶ ĂďƐĐŝƐƐĞ ĞƐƚ ůĞ ĚŽƵďůĞ ĚĞ ŵŽŶ ŽƌĚŽŶŶĠĞ͕ ũĞ ƐƵŝƐ ůĞ ƉŽŝŶƚ ͘͘͘ ĐͿ DŽŶ ĂďƐĐŝƐƐĞ ĞƐƚ ůĂ ŵŽŝƟ Ġ ĚĞ ŵŽŶ ŽƌĚŽŶŶĠĞ͕ ũĞ ƐƵŝƐ ůĞ ƉŽŝŶƚ ͘͘͘ ĚͿ DŽŶ ĂďƐĐŝƐƐĞ ĞƐƚ ů͛ŽƉƉŽƐĠ ĚĞ ŵŽŶ ŽƌĚŽŶŶĠĞ͕ ũĞ ƐƵŝƐ ůĞ ƉŽŝŶƚ ͘͘͘ ĞͿ DŽŶ ŽƌĚŽŶŶĠĞ ĞƐƚ ŶĠŐĂƟ ǀĞ͕ ũĞ ƐƵŝƐ ůĞ ƉŽŝŶƚ ͘͘͘ ĨͿ DŽŶ ŽƌĚŽŶŶĠĞ ĞƐƚ ĠŐĂůĞ Ğƚ ŽƉƉŽƐĠĞ ă ŵŽŶ ĂďƐĐŝƐƐĞ͕ ũĞ ƐƵŝƐ ůĞ ƉŽŝŶƚ ͙

A 1

4 :ƵƐƟ Į Ğ ĐŚĂƋƵĞ ĠŐĂůŝƚĠ ƉĂƌ ƵŶĞ ƉƌŽƉƌŝĠƚĠ ŽƵ ƵŶĞ ƌğŐůĞ ĚĞ ĐĂůĐƵů͘

ϳ н Ϭ с ϳ

ϯ н ;ʹϯͿ с Ϭ

ϲ н ;ʹϮͿ с ;ʹϮͿ н ϲ

;ʹϮͿ н ;ʹϱͿ н ϰ с ;;ʹϮͿ н ;ʹϱͿͿ н ϰ

;ʹϯͿ н ;нϳͿ с ϰ

;ʹϱͿ н ;ʹϴͿ с ʹϭϯ

ϵ ʹ ;ʹϯͿ с ϵ н ;нϯͿ

;ʹϱͿ н ϰ н ;ʹϯͿ с ;ʹϱͿ н ;ʹϯͿ н ϰ

1D 5 >ĞƐ ĂǆĞƐ ǆ Ğƚ Ǉ ĚƵ ŐƌĂƉŚŝƋƵĞ ĐŝͲĐŽŶƚƌĞ ŽŶƚ ĠƚĠ Ğī ĂĐĠƐ͘ 1 6 TRACE ĐĞƐ ĂǆĞƐ ;ĚƌŽŝƚĞƐ͕ ƐĞŶƐ Ğƚ ŶŽŵƐͿ ă ƉĂƌƟ ƌ ĚĞƐ

ŝŶĨŽƌŵĂƟ ŽŶƐ ƐƵŝǀĂŶƚĞƐ ͗ ʹ ůĞƐ ĂǆĞƐ ƐŽŶƚ ƐŝƚƵĠƐ ƐƵƌ ůĞ ƋƵĂĚƌŝůůĂŐĞ ͖ ʹ ĂƵĐƵŶ ĚĞƐ ƉŽŝŶƚƐ ŶŽŵŵĠƐ Ŷ͛ĞƐƚ ƐŝƚƵĠ ƐƵƌ ƵŶ ĚĞ ĐĞƐ ĂǆĞƐ ͖ ʹ ƐĞƵůĞŵĞŶƚ ƚƌŽŝƐ ƉŽŝŶƚƐ ŽŶƚ ĚĞƐ ŽƌĚŽŶŶĠĞƐ ƉŽƐŝƟ ǀĞƐ ͖ ʹ ƐĞƵůĞŵĞŶƚ ĐŝŶƋ ƉŽŝŶƚƐ ŽŶƚ ĚĞƐ ĂďƐĐŝƐƐĞƐ ŶĠŐĂƟ ǀĞƐ͘

D B A C H E F G

ƉƉůŝƋƵĞƌ 1

dƌĂĐĞ ƵŶ ĂǆĞ ŐƌĂĚƵĠ ǀĞƌƟ ĐĂů ƐƵƌ ůĞƋƵĞů ϭ Đŵ ĐŽƌƌĞƐƉŽŶĚ ă ϱϬϬ ŵ͕ ƉƵŝƐ ƉůĂĐĞ͕ ůĞ ƉůƵƐ ƉƌĠĐŝƐĠŵĞŶƚ ƉŽƐƐŝďůĞ͕ ůĞƐ ŚĂƵƚĞƵƌƐ Ğƚ ƉƌŽĨŽŶĚĞƵƌƐ ƐƵŝǀĂŶƚĞƐ ĞŶ ƵƟ ůŝƐĂŶƚ ůĞƐ ůĞƩ ƌĞƐ ƋƵŝ ůĞƐ ĚĠƐŝŐŶĞŶƚ͘ & ͗ >Ğ &Žƌƚ ĚĞƐ ZŽƵƐƐĞƐ ĚƵ ,ĂƵƚ :ƵƌĂ ĐƵůŵŝŶĞ ă ĞŶǀŝƌŽŶ ϭϮϬϬ ŵ Ě͛ĂůƟ ƚƵĚĞ͘ d ͗ >Ğ dŽƵƌŵĂůĞƚ ĐƵůŵŝŶĞ ă ϮϭϬϬ ŵ͘ D ͗ >Ă DĞƌ DŽƌƚĞ ĞŶ ƐŝĞ Ă ƵŶĞ ƉƌŽĨŽŶĚĞƵƌ ŵŽǇĞŶŶĞ ĚĞ ϯϱϬ ŵ͘ ͗ >Ğ ĐĂĐŚĂůŽƚ ƉĞƵƚ ƉůŽŶŐĞƌ ũƵƐƋƵ͛ă ϳϬϬ ŵ ƉŽƵƌ ƐĞ ŶŽƵƌƌŝƌ͘ ͗ >Ă ƉůƵƐ ŚĂƵƚĞ ƚŽƵƌ ĚƵ ŵŽŶĚĞ ƐĞ ƚƌŽƵǀĞ ă ƵďĂŝ Ğƚ ĐƵůŵŝŶĞ ă ϴϯϬ ŵ͘ ^ ͗ >Ă ŵĞƌ ĚƵ :ĂƉŽŶ Ă ƵŶĞ ƉƌŽĨŽŶĚĞƵƌ ŵŽǇĞŶŶĞ ĚĞ ϭϯϱϬ ŵ͘

EXERCICES COMPLÉMENTAIRES

Chapitre 4 Addition et soustraction avec les nombres entiers

2 WŽƵƌ ĐŚĂƋƵĞ ĐĂƐ͕ ŶŽƚĞ ůĞƐ ĂďƐĐŝƐƐĞƐ ĚĞƐ ƉŽŝŶƚƐ ͕ ͕ ͕ Ğƚ ͘

ĂͿ

B 0

ďͿ

E 0

3 WůĂĐĞ ƐƵƌ ůĂ ĚƌŽŝƚĞ ŐƌĂĚƵĠĞ ůĞƐ ƉŽŝŶƚƐ ͕ ͕ ͕ Ğƚ Ɛŝ ƚƵ ƐĂŝƐ ƋƵĞ

ĂďƐ с ʹϮ

ĂďƐ с ϰ͕ϱ

ĂďƐ с ʹϯ͕ϱ

ĂďƐ с ϲ͕ϱ

ĂďƐ с ʹϱ

4 >ĞƐ ƉŽŝŶƚƐ ͕ ͕ ͕ Ğƚ ŽŶƚ ƉŽƵƌ ĂďƐĐŝƐƐĞƐ ƌĞƐƉĞĐƟ ǀĞƐ Ϯ͕ ʹϰ͕ ϰ͕ ʹϱ Ğƚ ϲ͘

ĂͿ ĠƚĞƌŵŝŶĞ ů͛ĂďƐĐŝƐƐĞ ĚƵ ŵŝůŝĞƵ D ĚƵ ƐĞŐŵĞŶƚ ΀ ΁͘ ďͿ ĠƚĞƌŵŝŶĞ ů͛ĂďƐĐŝƐƐĞ ĚƵ ƉŽŝŶƚ W ƚĞů ƋƵĞ ůĞ ƉŽŝŶƚ ƐŽŝƚ ůĞ ŵŝůŝĞƵ ĚƵ ƐĞŐŵĞŶƚ ΀ W΁͘

5 ŽŵƉůğƚĞ ĞŶ ƵƟ ůŝƐĂŶƚ ĚĞƐ ŶŽŵďƌĞƐ ĞŶƟ ĞƌƐ ĐŽŶƐĠĐƵƟ ĨƐ͘

ĂͿ ͙ ф ϱ͕ϰ ф ͙ ͙ ф ʹϯ͕ϰ ф ͙

ďͿ ͙ ф Ϭ͕ϲ ф ͙ ͙ ф ʹϭ͕ϱ ф ͙

ĐͿ ͙ ф ϭ͕Ϯ ф ͙ ͙ ф ʹϰ͕ϴ ф ͙

6 WŽƵƌ ĐŚĂƋƵĞ ĞŶĐĂĚƌĞŵĞŶƚ͕ ĞŶƚŽƵƌĞ ůĞƐ ŶŽŵďƌĞƐ ĚĞ ůĂ ůŝŐŶĞ ƋƵŝ ƉĞƵǀĞŶƚ ƌĞŵƉůĂĐĞƌ ůĂ ǀĂƌŝĂďůĞ ǆ͘

ĂͿ ʹϱ ф ǆ ф ʹϭ ďͿ ϯ͕ϲ ф ǆ ф ϯ͕ϳ ĐͿ ʹϯ ф ǆ ф Ϯ

ʹϰ ϯ͕ϲ ʹϭ

Ϭ Ϭ Ϭ

Ϯ ϯ͕ϲϭ ʹϮ͕ϵ

ʹϮ ϯ Ϯ͕ϭ

ʹϱ ϯ͕Ϭϲϱ ʹϯ͕ϭ

ʹϯ ϯ͕ϲϬϱ ϭ͕ϵ

ƌŵĂƟ ŽŶƐ ƐƵŝǀĂŶƚĞƐ͘ 7 ZĠƉŽŶĚƐ ƉĂƌ ǀƌĂŝ ŽƵ ĨĂƵǆ ă ĐŚĂĐƵŶĞ ĚĞƐ Ăĸ

E –3,4

D 1,4

ĂͿ /ů Ǉ Ă ĞǆĂĐƚĞŵĞŶƚ ƋƵĂƚƌĞ ŶŽŵďƌĞƐ ĞŶƟ ĞƌƐ ĐŽŵƉƌŝƐ ĞŶƚƌĞ ůĞƐ ĂďƐĐŝƐƐĞƐ ĚĞƐ ƉŽŝŶƚƐ Ğƚ ͘ ďͿ >͛ĂďƐĐŝƐƐĞ ĚƵ ƉŽŝŶƚ ĞƐƚ ʹϭ͕Ϯ͘ ĐͿ >͛ĂďƐĐŝƐƐĞ ĚƵ ƉŽŝŶƚ ĞƐƚ ƉŽƐŝƟ ǀĞ͘ ĚͿ >͛ĂďƐĐŝƐƐĞ ĚƵ ƉŽŝŶƚ ĞƐƚ ʹϮ͕ϴ͘ ĞͿ >͛ŽƌŝŐŝŶĞ ĚƵ ƌĞƉğƌĞ ĚĞ ĐĞƚ ĂǆĞ ƐĞ ƐŝƚƵĞ ĞŶƚƌĞ ůĞƐ ƉŽŝŶƚƐ Ğƚ ͘ 8 ZĂŶŐĞ ůĞƐ ŶŽŵďƌĞƐ ĚĂŶƐ ů͛ŽƌĚƌĞ ĐƌŽŝƐƐĂŶƚ͘

ĂͿ ʹϯ ďͿ ʹϮ͕ϯ

ϱ ϰ

ʹϵ ʹϯ͕Ϯ

Ϭ ϰ͕ϭ

ʹϱ ʹϯ͕ϱ

ϴ ϰ͕ϲ

ʹϲ ϳ͕ϯ

ϱ ϳ͕ϭ

9 ZĂŶŐĞ ůĞƐ ŶŽŵďƌĞƐ ĚĂŶƐ ů͛ŽƌĚƌĞ ĚĠĐƌŽŝƐƐĂŶƚ͘

ĂͿ ʹϳ ďͿ ʹϳ͕ϱ

ϲ Ϯ͕ϳ

ʹϰ ʹϳ͕ϯ

Ϭ ϳ͕Ϯ

10 ŽŵƉůğƚĞ ƉĂƌ ф ŽƵ х͘

ĂͿ

ϳപ͙പʹϱ ďͿ ϯപ͙പʹϮ ĐͿ ʹϭϱപ͙പʹϱ ĚͿ Ϯപ͙പϯ ϭϭപ͙പϯϭ ϴപ͙പϳ Ϯപ͙പʹϮ ʹϴപ͙പϬ ʹϳപ͙പʹϱ ϱപ͙പϬ Ϭപ͙പʹϳ ʹϳപ͙പϱ ʹϱപ͙പʹϭ ʹϭϮപ͙പʹϱ ʹϮപ͙പʹϯ ʹϰപ͙പʹϲ 11 ŽŵƉůğƚĞ ůĞƐ ĐŽƵƉůĞƐ ĚĞ ŶŽŵďƌĞƐ ƉŽƵƌ ƋƵĞ ĐĞƵǆͲĐŝ ƐŽŝĞŶƚ ĐŽŶƐĠĐƵƟ ĨƐ Ğƚ ƋƵĞ ůĞ ƉƌĞŵŝĞƌ ƐŽŝƚ ƚŽƵũŽƵƌƐ ŝŶĨĠƌŝĞƵƌ ĂƵ ƐĞĐŽŶĚ͘ ;ϯ ͖ ͘͘͘͘͘Ϳ ;ʹϳ ͖ ͘͘͘͘͘Ϳ ;͘͘͘͘͘ ͖ ϱͿ ;͘͘͘͘͘ ͖ ʹϵͿ ;Ϭ ͖ ͘͘͘͘͘Ϳ ;͘͘͘͘͘ ͖ ϬͿ 12 ĂůĐƵůĞ ůĞƐ ƐŽŵŵĞƐ ƐƵŝǀĂŶƚĞƐ͘

ĂͿ ;ʹϱͿ н ;ʹϴͿ с ;нϰͿ н ;ʹϵͿ с ;нϭϮͿ н ;ʹϭϱͿ с ;ʹϰͿ н ;ʹϲͿ с

ďͿ ;ʹϱͿ н ;нϭϰͿ с ;ʹϮϱͿ н ;ʹϰϱͿ с ;ʹϯϮͿ н ;нϭϱͿ с ;нϭϳͿ н ;нϭϮͿ с

ĐͿ ;нϮϭͿ н ;ʹϭϱͿ с ;нϭϵͿ н ;ʹϰϭͿ с ;ʹϭϮϰͿ н ;ʹϭϵϵͿ с ;нϮϲϱͿ н ;ʹϮϬϱͿ с

ĚͿ ;ʹϮϵϯͿ н ;ʹϭϬϳͿ с ;нϮϵϯͿ н ;ʹϭϬϳͿ с ;ʹϰϱϮͿ н ;нϯϵϳͿ с ;ʹϱϲϴͿ н ;нϲϳϯͿ с

EXERCICES COMPLÉMENTAIRES

Chapitre 4 Addition et soustraction avec les nombres entiers

13 ĂůĐƵůĞ ƌĂƉŝĚĞŵĞŶƚ ůĞƐ ƐŽŵŵĞƐ ƐƵŝǀĂŶƚĞƐ͘

ĂͿ ʹϱ ʹ ϲ с ϱ ʹ ϵ с ʹϱ ʹ ϵ с ϱ ʹ ϲ с

ďͿ ϭϮ ʹ ϮϬ с ʹϭϮ ʹ ϮϬ с ʹϭϯ ʹ ϲϰ с ʹϭϯ н ϲϰ с

ĐͿ ʹϱϲ н ϵ с ʹϵ ʹ ϱϲ с ϵ ʹ ϱϲ с ʹϱϵ н ϲ с

ĚͿ ʹϲ н ϱϵ с ʹϱϵ ʹ ϲ с ϵϵ ʹ ϭϬϯ с ʹϭϬϯ ʹ ϵϵ с

ĞͿ ϭϬϯ ʹ ϵϵ с ʹϭϮϱ ʹ ϭϯϭ с ϭϮϱ ʹ ϭϯϭ с ʹϭϮϱ н ϭϯϭ с

14 dƌĂŶƐĨŽƌŵĞ ůĞƐ Ěŝī ĠƌĞŶĐĞƐ ĞŶ ƐŽŵŵĞƐ͕ ƉƵŝƐ ĐĂůĐƵůĞ͘

ĂͿ ;ʹϵͿ ʹ ;нϴͿ с ;нϳͿ ʹ ;ʹϴͿ с ;ʹϮͿ ʹ ;нϭϱͿ с ;ʹϭϬͿ ʹ ;ʹϰͿ с

ďͿ ;нϭϮͿ ʹ ;ʹϲͿ с ;ʹϴͿ ʹ ;ʹϭϮͿ с ;ʹϯϱͿ ʹ ;ʹϮϱͿ с ;ʹϰϮͿ ʹ ;нϱͿ с

ĐͿ ;нϮϲͿ ʹ ;нϮϲͿ с ;нϭϱͿ ʹ ;ʹϱϱͿ с ;ʹϭϵͿ ʹ ;нϮϭͿ с ;ʹϮϰϯͿ ʹ ;ʹϵϵͿ с

ĚͿ ;ʹϮϳϱͿ ʹ ;нϵϵͿ с ;ʹϯϲϭͿ ʹ ;ʹϭϬϭͿ с ;нϮϵϯͿ ʹ ;нϮϬϳͿ с ;ʹϱϮϭͿ ʹ ;ʹϯϳϴͿ с

15 ĂůĐƵůĞ ĂƉƌğƐ ĂǀŽŝƌ ƵƟ ůŝƐĠ ůĂ ƌğŐůĞ ĚĞƐ ƐŝŐŶĞƐ ƐƵĐĐĞƐƐŝĨƐ͘

ĂͿ ;ʹϱͿ н ;ʹϵͿ с ;ʹϴͿ ʹ ;ʹϭϮͿ с ;ʹϰͿ ʹ ;нϵͿ с ;ʹϴͿ н ;нϭϭͿ с

ďͿ ;нϱͿ ʹ ;ʹϵͿ с ʹ ϳ ʹ ;ʹϳͿ с ʹϲ н ;ʹϭϰͿ с ʹϱ ʹ ;нϵͿ с

ĐͿ ʹϱ ʹ ;ʹϭϮͿ с ʹϭϮ н ;нϱͿ с ʹϲ ʹ ;ʹϲͿ с ʹϮϰ н ;ʹϵͿ с

ĚͿ ;ʹϳϱͿ ʹ ;ʹϱϵͿ с ϲϰ ʹ ;нϳϵͿ с ʹϵϴ н ;нϵϳͿ с ϱϯ н ;ʹϯϵͿ с

16 ĂůĐƵůĞ ĂƉƌğƐ ĂǀŽŝƌ ƵƟ ůŝƐĠ ůĂ ƌğŐůĞ ĚĞƐ ƐŝŐŶĞƐ ƐƵĐĐĞƐƐŝĨƐ͘

ĂͿ Ϯ н ;ʹϱͿ ʹ ;ʹϳͿ с ʹϱ ʹ ;нϯͿ н ;нϳͿ ʹ ;нϲͿ с ;ʹϲͿ ʹ ;нϮͿ н ;ʹϴͿ ʹ ;ʹϰͿ с ʹϱ н ;ʹϲͿ ʹ ;ʹϱͿ н ;ʹϴͿ ʹ ;ʹϲͿ с ʹϮ н ;нϱͿ ʹ ;ʹϲͿ ʹ ;нϮͿ н ;ʹϱͿ с

ďͿ ϱ ʹ ϲ н ;ʹϴͿ ʹ ;ʹϱͿ с ʹϵ н ;ʹϴͿ ʹ ;ʹϵͿ н ;ʹϰͿ н ϴ с ʹϭϮ н ;ʹϴϴͿ н ϭϱ ʹ ;ʹϴϱͿ с ϳϱ ʹ ;ʹϭϮͿ н ;ʹϴͿ ʹ ϰ с ʹϰϱ ʹ ;ʹϭϱͿ н ;ʹϰϱͿ н ϭϬ с

17 ĂůĐƵůĞ ƌĂƉŝĚĞŵĞŶƚ͘

ĂͿ ʹϲ н Ϯ н ϵ ʹ ϴ с ʹϵ ʹ ϰ н ϱ с ϳ ʹ ϵ ʹ Ϯ н ϱ с ʹϴ н ϳ ʹ ϯ н ϴ с

ďͿ ϭϯ ʹ ϴ ʹ ϱ н ϲ с ʹϳ н ϭϰ ʹ Ϯϰ с ϭϮ ʹ ϭϱ ʹ ϭϯ с ʹϮϯ н ϭϱ ʹϭϴ с

ĐͿ ʹϮϯ н ϯϱ н ϭϳ с ϭϲ ʹ Ϯϳ ʹ Ϯϳ ʹ ϭϲ с ʹϵ ʹ ϭϭ н ϲ н ϱ с ϭϮ ʹ ϵ ʹ ϳ н ϭϱ с

ĚͿ ϭϴ н ϲ ʹ ϮϮ н ϭϬ с ʹϮϵ н ϭϭ ʹ ϴ ʹ ϳ с ϯϴ н ϭϰ ʹ Ϯϰ н ϲ с ʹϯϰ н ϴϰ ʹ ϭϱ н ϭϴ с

18 ZĞůŝĞ ůĞƐ ƐŽŵŵĞƐ ĠŐĂůĞƐ͘

ĂͿ ϭϱ н ;ʹϭϴͿ ʹϭϯ н ;ʹϳͿ ϭϭ н ;ʹϵͿ ʹϲ н Ϯϲ ʹϭϮ н ϭϮ

• • • • •

ϰ н ;ʹϮϰͿ ϭϭ н ;ʹϭϭͿ ʹϯϮ н Ϯϵ ʹϭϱ н ϭϳ ϯϯ н ;ʹϭϯͿ

ďͿ ʹϱ͕Ϯ ʹ Ϯ͕ϴ ʹϰ͕ϲ н ϳ͕ϭ ʹϯ͕ϲ н ϭ͕ϱ ʹϮ͕ϳ н Ϯ͕ϳ ϲ͕ϯ ʹ ϳ͕ϵ

• • • • •

ʹϲ͕ϯ н ϴ͕ϴ ʹϱ͕Ϯ н ϱ͕Ϯ ϳ͕ϴ ʹ ϵ͕ϰ ʹϵ͕ϯ н ϭ͕ϯ ϴ͕ϵ ʹ ϭϭ

• • • • •

19 ŽŵƉůğƚĞ ůĞƐ ƉǇƌĂŵŝĚĞƐ ĞŶ ƌĞƐƉĞĐƚĂŶƚ ůĞƐ ĐŽŶƐŝŐŶĞƐ͘

ĂͿ

Ăнď a

ďͿ

Ăнď

ĐͿ ď

Ăʹď a

ĚͿ ď

Ăʹď ď

a ʹϯ

ϱ ϱ

ϯϲ

ʹϮϰ

ʹϭ

ϭϰ

ϴ ϳ

ʹϯ

ʹϭ

ďͿ

ϰϮ

ʹϰϯ

ʹϭ

20 ŽŵƉůğƚĞ ůĞƐ ƚĂďůĞĂƵǆ ĐŝͲĚĞƐƐŽƵƐ͘

ĂͿ

ď Ă н ď

ϭϱ ʹϮ

ʹϯ

ϭϯ

ʹϭϲ ϮϬ

ʹϭϱ

ʹϭϬ ʹϭϰ

ϭϭ

Ă ʹ ď

ϭϬϮ ϮϮ

ϭϳ

ʹϭϮ ʹϭϳ ʹϮϰ

ʹϮϬ ʹϯϱ ϭϱϮ ʹϯϵ

EXERCICES COMPLÉMENTAIRES

Chapitre 4 Addition et soustraction avec les nombres entiers

21 ŽŵƉůğƚĞ ůĞƐ ĠŐĂůŝƚĠƐ ƐƵŝǀĂŶƚĞƐ͘

ĂͿ ;нϱͿ н ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ с нϭϴ ʹϳ ʹ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ с ʹϯ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ н ;ʹϯϲͿ с Ϭ ;нϰϬͿ н ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ с ʹϴ ʹϰ н ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ с ʹϮϬ

ďͿ ;ʹϲͿ ʹ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ с ϭϬ ʹϱ ʹ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ с ϱ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ н ϱ с ʹϭϴ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ н ϴ с ϳ ʹϮϬ ʹ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ с ϴ

ĐͿ ;ʹϭϱͿ н ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ с ϰϱ ;нϭϭͿ ʹ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ с ϲϭ ʹϵ ʹ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ с ʹϰ ʹϭϭ н ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ с ʹϱ ;ʹϮͿ ʹ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ с Ϭ

22 ĂůĐƵůĞ ůĂ ǀĂůĞƵƌ ŶƵŵĠƌŝƋƵĞ ĚĞƐ ĞǆƉƌĞƐƐŝŽŶƐ ĐŝͲĚĞƐƐŽƵƐ͕ Ɛŝ ƚƵ ƐĂŝƐ ƋƵĞ

Ă с ʹϰ ĂͿ Ă н ď с Đ ʹ Ě с ď ʹ Đ с Ě ʹ Ă с Ě н Đ с

ď с нϱ

ďͿ ď н Đ ʹ Ă с Đ н Ă ʹ Ě с Ě ʹ ď ʹ Ă с Ă н Ě ʹ Đ с ď ʹ Ě н Ă с

Đ с ʹϯ

Ě с нϮ

ĐͿ ʹ Ă с ʹ ď с ʹ Đ с ʹ Ě с ʹ ;ʹĂͿ с

ĚͿ ʹď н Ă ʹ Đ с ĞͿ Ă н ;ʹďͿ ʹ ;ʹĐͿ с ʹĐ ʹ Ă н Ě ʹ ď с Đ ʹ ;ʹĚͿ н ;ʹĂͿ с ʹĚ н ď ʹ Đ н Ă с Ě н ;ʹĐͿ ʹ ;ʹďͿ с ʹĂ ʹ Ě н Đ ʹ ď с ʹď ʹ ;ʹĂͿ н ;ʹĚͿ с Ě н Ă ʹ Đ н ď с ʹĐ н ;ʹďͿ н Đ ʹ Ě с

23 ĂŶƐ ĐŚĂƋƵĞ ĐĂƐ Ğƚ ƉŽƵƌ ĐŚĂƋƵĞ ĠƚĂƉĞ ĚƵ ĐĂůĐƵů͕ Ɛŝ ƵŶĞ ƉƌŽƉƌŝĠƚĠ ĚĞ ů͛ĂĚĚŝƟ ŽŶ Ă ĠƚĠ ƵƟ ůŝƐĠĞ͕

ŶŽŵŵĞͲůĂ͘ ĂͿ ϵ н ;ʹϰͿ н ϭϮ н ;ʹϱͿ с ϵ н ;ʹϰͿ н ;ʹϱͿ н ϭϮ с ϵ н ;;ʹϰͿ н ;ʹϱͿͿ н ϭϮ с ϵ н ;ʹϵͿ н ϭϮ с ;ϵ н ;ʹϵͿͿ н ϭϮ с Ϭ н ϭϮ с ϭϮ

ďͿ ʹϳ н ϴ н ϯ н ;ʹϴͿ н ;ʹϳͿ с ʹϳ н ϴ н ;ʹϴͿ н ϯ н ;ʹϳͿ с ʹϳ н ;ϴ н ;ʹϴͿͿ н ϯ н ;ʹϳͿ с ʹϳ н Ϭ н ϯ н ;ʹϳͿ с ʹϳ н ϯ н ;ʹϳͿ с ʹϳ н ;ʹϳͿ н ϯ с ;ʹϳ н ;ʹϳͿͿ н ϯ с ʹϭϰ н ϯ с ʹϭϭ

24 ŽŵƉůğƚĞ ůĞƐ ĐŽƵƉůĞƐ ƉŽƵƌ ƋƵ͛ŝůƐ ƌĠƉŽŶĚĞŶƚ ă ůĂ ĐŽŶĚŝƟ ŽŶ ĠŶŽŶĐĠĞ͘

ĂͿ >͛ĂďƐĐŝƐƐĞ ǀĂƵƚ ϱ ĚĞ ŵŽŝŶƐ ƋƵĞ ů͛ŽƌĚŽŶŶĠĞ ͗ ďͿ >͛ŽƌĚŽŶŶĠĞ ǀĂƵƚ ϯ ĚĞ ƉůƵƐ ƋƵĞ ů͛ĂďƐĐŝƐƐĞ ͗ ĐͿ >͛ĂďƐĐŝƐƐĞ ĞƐƚ ů͛ŽƉƉŽƐĠ ĚĞ ů͛ŽƌĚŽŶŶĠĞ ͗ ĚͿ >Ă ƐŽŵŵĞ ĚĞƐ ĐŽŽƌĚŽŶŶĠĞƐ ǀĂƵƚ ϳ ͗ ĞͿ >͛ŽƌĚŽŶŶĠĞ ǀĂƵƚ ϰ ĚĞ ŵŽŝŶƐ ƋƵĞ ů͛ĂďƐĐŝƐƐĞ ͗

;͘͘͘ ͖ ϮͿപ;͘͘͘ ͖ ʹϲͿപ;ϴ ͖ ͘͘͘Ϳപ;ʹϮ ͖ ͘͘͘Ϳപ;Ϭ ͖ ͘͘͘Ϳ ;ϭ ͖ ͘͘͘Ϳപ;ʹϮ ͖ ͘͘͘Ϳപ;͘͘͘ ͖ ϱͿപ;͘͘͘ ͖ ʹϰͿപ;ʹϯ ͖ ͘͘͘Ϳ ;Ϯ ͖ ͘͘͘Ϳപ;͘͘͘ ͖ ϱͿപഩ;ʹϭ ͖ ͘͘͘Ϳഩ;͘͘͘ ͖ ʹϯͿപ;Ϭ ͖ ͘͘͘Ϳ ;͘͘͘ ͖ ϲͿപ;͘͘͘ ͖ ʹϱͿപ;ϰ ͖ ͘͘͘Ϳപ;ʹϵ ͖ ͘͘͘Ϳപ;ʹϳ ͖ ͘͘͘Ϳ ;ϰ ͖ ͘͘͘Ϳപ;ʹϯ ͖ ͘͘͘Ϳപ;͘͘͘ ͖ ϯͿപ;͘͘͘ ͖ ʹϮͿപ;Ϭ ͖ ͘͘͘Ϳ

25 WŽƵƌ ĐŚĂƋƵĞ ĚƌŽŝƚĞ ͗ ƌĞƚƌŽƵǀĞ ůĞƐ ĐŽŽƌĚŽŶŶĠĞƐ ĚĞ ƋƵĂƚƌĞ ƉŽŝŶƚƐ͕ ĚŽŶŶĞ ůĂ ĐĂƌĂĐƚĠƌŝƐƟ ƋƵĞ

ĐŽŵŵƵŶĞ ĚĞƐ ĐŽƵƉůĞƐ ƚƌŽƵǀĠƐ Ğƚ ƚƌĂĚƵŝƐͲůĂ ƉĂƌ ƵŶĞ ĠŐĂůŝƚĠ ĂůŐĠďƌŝƋƵĞ͘

ĂͿ

ďͿ

b 1 0

a c d

EXERCICES COMPLÉMENTAIRES

Chapitre 4 Addition et soustraction avec les nombres entiers

Transférer 1 ĐƌŝƐ ůĞƐ ƚƌŽŝƐ ƚĞƌŵĞƐ ƐƵŝǀĂŶƚƐ ĚĞ ĐŚĂĐƵŶĞ ĚĞƐ ƐƵŝƚĞƐ ĐŝͲĚĞƐƐŽƵƐ ĞŶ ƌĞƐƉĞĐƚĂŶƚ ůĞƵƌ ƌĠŐƵůĂƌŝƚĠ͘

ĂͿ Ϯϱ͕ ϭϵ͕ Ϯϯ͕ ϭϳ͕ Ϯϭ͕ ͙ ͕ ͙ ͕ ͙

ďͿ ʹϰ͕ ʹϯ͕ ʹϱ͕ ʹϮ͕ ʹϲ͕ ͙ ͕ ͙ ͕ ͙

ĐͿ ϱϬ͕ ϭϴ͕ Ϯ͕ ʹϲ͕ ʹϭϬ͕ ͙ ͕ ͙ ͕ ͙

ĚͿ ʹϭϱ͕ ʹϭϳ͕ ʹϭϬ͕ ʹϭϮ͕ ʹϱ͕ ͙ ͕ ͙͕ ͙

2 >ĞƐ ƉŽŝŶƚƐ ͕ ͕ ͕ ͕ Ğƚ & ĂƉƉĂƌƟ ĞŶŶĞŶƚ ă ƵŶĞ ĚƌŽŝƚĞ ŐƌĂĚƵĠĞ ĚŽŶƚ ů͛ƵŶŝƚĠ ĞƐƚ ůĞ ĐĞŶƟ ŵğƚƌĞ͘

ĂͿ ^ŝ ů͛ĂďƐĐŝƐƐĞ ĚƵ ƉŽŝŶƚ ǀĂƵƚ ϰ͕ ƋƵĞůůĞ ƉĞƵƚ ġƚƌĞ ů͛ĂďƐĐŝƐƐĞ ĚƵ ƉŽŝŶƚ ƐĂĐŚĂŶƚ ƋƵĞ ͮ ͮ с ϴ Đŵ ͍ ďͿ ^ŝ ů͛ĂďƐĐŝƐƐĞ ĚƵ ƉŽŝŶƚ ǀĂƵƚ ʹϯ͕ ƋƵĞůůĞ ƉĞƵƚ ġƚƌĞ ů͛ĂďƐĐŝƐƐĞ ĚƵ ƉŽŝŶƚ ƐĂĐŚĂŶƚ ƋƵĞ ͮ ͮ с Ϯ Đŵ ͍ ĐͿ ^ŝ ů͛ĂďƐĐŝƐƐĞ ĚƵ ƉŽŝŶƚ ǀĂƵƚ ʹϱ͕ ĚĠƚĞƌŵŝŶĞ ů͛ĂďƐĐŝƐƐĞ ĚƵ ƉŽŝŶƚ & ƐĂĐŚĂŶƚ ƋƵĞ ͮ &ͮ с ϵ Đŵ Ğƚ ƋƵĞ ů͛ĂďƐĐŝƐƐĞ ĚĞ & ĞƐƚ ŝŶĨĠƌŝĞƵƌĞ ă ĐĞůůĞ ĚĞ ͘

3 ĂŶƐ ĐŚĂƋƵĞ ĐĂƐ͕ ĚĠƚĞƌŵŝŶĞ ƚŽƵƐ ůĞƐ ĞŶƟ ĞƌƐ Ă Ğƚ ď ƌĠƉŽŶĚĂŶƚ ĂƵǆ ĐŽŶĚŝƟ ŽŶƐ ĚŽŶŶĠĞƐ͘

ĂͿ Ă н ď с ϰ

ʹϱ͕Ϯ ф Ă ф ʹϯ͕ϳ

ďͿ Ă н ď с ʹϮ

ʹϱ͕Ϯ ф Ă ф ʹϯ͕ϳ

ĐͿ Ă ʹ ď с Ϯ

രĞƚ

ʹϭ͕ϯ ф Ă ф ϯ͕ϱ

ĚͿ Ă ʹ ď с ʹϭ

രĞƚ

ʹϭ͕ϯ ф Ă ф ϯ͕ϱ

4 >Ğ ƉƌŽĨĞƐƐĞƵƌ DĂƚŚŽǀŽƌĞ ĚŽŶŶĞ ă ƐĞƐ ĠůğǀĞƐ ƵŶ ƋƵĞƐƟ ŽŶŶĂŝƌĞ ă ĐŚŽŝǆ ŵƵůƟ ƉůĞƐ ĐŽŵƉŽƌƚĂŶƚ

ŚƵŝƚ ƋƵĞƐƟ ŽŶƐ͘ sŽŝĐŝ ƐĂ ŵĂŶŝğƌĞ ĚĞ ĐŽƚĞƌ͘ ZĠƉŽŶƐĞ ĨĂƵƐƐĞ ;&Ϳ ͗ ʹϯ ƉŽŝŶƚƐപഩWĂƐ ĚĞ ƌĠƉŽŶƐĞ ;WͿ ͗ ʹϭ ƉŽŝŶƚപഩ ŽŶŶĞ ƌĠƉŽŶƐĞ ; Ϳ ͗ нϰ ƉŽŝŶƚƐ ĂͿ ĂůĐƵůĞ ůĂ ĐŽƚĞ ĚĞ DĂƌůğŶĞ ĚŽŶƚ ůĞƐ ƌĠƐƵůƚĂƚƐ ĂƵǆ ƋƵĞƐƟ ŽŶƐ ƐŽŶƚ ͗ &͕ ͕ W͕ &͕ &͕ ͕ ͕ W͘ ďͿ DĂƌƟ Ŷ Ă ŽďƚĞŶƵ ůĂ ƉůƵƐ ďĂƐƐĞ ĐŽƚĞ ƋƵ͛ŝů ĞƐƚ ƉŽƐƐŝďůĞ Ě͛ŽďƚĞŶŝƌര͖ ƋƵĞ ǀĂƵƚͲĞůůĞ ͍ ĐͿ WĂƐĐĂů Ă ŽďƚĞŶƵ ůĂ ƉůƵƐ ŚĂƵƚĞ ĐŽƚĞ ƋƵ͛ŝů ĞƐƚ ƉŽƐƐŝďůĞ Ě͛ŽďƚĞŶŝƌര͖ ƋƵĞ ǀĂƵƚͲĞůůĞ ͍ 5 &ůŽƌŝĂŶĞ ƉŽƐƐğĚĞ ϭϭ ƉĞƌůĞƐ͘ ^Ƶƌ ĐŚĂĐƵŶĞ Ě͛ĞůůĞƐ ƐĞ ƚƌŽƵǀĞ ƵŶ ŶŽŵďƌĞ ĞŶƟ Ğƌ ĚĞ ʹϱ ă нϱ͘

ůůĞ ǀĞƵƚ ĨĂŝƌĞ ƵŶ ĐŽůůŝĞƌ ĚĞ ƚĞůůĞ ƐŽƌƚĞ ƋƵĞ͕ ůŽƌƐƋƵ͛ŝů ĞƐƚ ĨĞƌŵĠ͕ ůĂ ƐŽŵŵĞ ĚĞƐ ŶŽŵďƌĞƐ ƉŽƌƚĠƐ ƉĂƌ ĚĞƵǆ ƉĞƌůĞƐ ǀŽŝƐŝŶĞƐ ƐŽŝƚ ƚŽƵũŽƵƌƐ ĠŐĂůĞ ă ʹϭ͕ Ϭ ŽƵ ϭ͘ ŽŵďŝĞŶ Ǉ ĂͲƚͲŝů ĚĞ ƐŽůƵƟ ŽŶƐ ͍ ǆƉůŝƋƵĞ͘ 6 >͛ĞŶƌĞŐŝƐƚƌĞƵƌ ĂƵƚŽŵĂƟ ƋƵĞ ĚƵ ƉĂƌŬŝŶŐ Ě͛ƵŶĞ ƐŽĐŝĠƚĠ Ă ƚƌĂĚƵŝƚ ůĞƐ ĞŶƚƌĠĞƐ ; Ϳ ĚĞƐ ǀŽŝƚƵƌĞƐ ƉĂƌ

ĚĞƐ ŶŽŵďƌĞƐ ƉŽƐŝƟ ĨƐ Ğƚ ůĞƐ ƐŽƌƟ ĞƐ ;^Ϳ ƉĂƌ ĚĞƐ ŶŽŵďƌĞƐ ŶĠŐĂƟ ĨƐ͘ >Ğ ƚĂďůĞĂƵ ĐŝͲĚĞƐƐŽƵƐ ĚŽŶŶĞ ůĞƐ ƌĞůĞǀĠƐ ĚĞƐ ǀĂͲĞƚͲǀŝĞŶƚ ƐƵƌ ƵŶĞ ĚƵƌĠĞ ĚĞ ϴ Ś ă ϭϵ Ś͘ ϴ Ś

ϵ Ś

ϭϬ Ś

ϭϭ Ś

ϭϮ Ś

ϭϯ Ś

ϭϰ Ś

ϭϱ Ś

ϭϲ Ś

ϭϳ Ś

ϭϴ Ś

ϭϵ Ś

нϰ

нϴ

нϵ

нϱ

нϳ

нϮ

нϳ

нϰ

нϱ

нϵ

нϴ

ʹϲ

ʹϳ

ʹϯ

ʹϱ

ʹϲ

ʹϮ

ʹϱ

ʹϮ

ʹϴ

ʹϵ

ʹϭϬ

^ĂĐŚĂŶƚ ƋƵ͛ĞŶ ĚĠďƵƚ ĚĞ ũŽƵƌŶĠĞ ŝů Ǉ ĂǀĂŝƚ ϯϬ ǀŽŝƚƵƌĞƐ ĚĂŶƐ ůĞ ƉĂƌŬŝŶŐ͕ ĐŽŵďŝĞŶ Ǉ ĞŶ ĂǀĂŝƚͲŝů Į Ŷ ĚĞ ũŽƵƌŶĠĞ ͍ 7 DĂƌŝĞ Ğƚ EŽĂŚ ũŽƵĞŶƚ ĂƵ ͨ ũĞƵ ĚĞƐ ŐƌĂĚƵĂƟ ŽŶƐ ͩ͘ DĂƌŝĞ ƉůĂĐĞ ƐƵƌ ƵŶĞ ĚƌŽŝƚĞ ŐƌĂĚƵĠĞ ůĞƐ ƉŽŝŶƚƐ

͕ Ğƚ Ě͛ĂďƐĐŝƐƐĞƐ ƌĞƐƉĞĐƟ ǀĞƐ нϮ͕ нϰ Ğƚ ʹϯ͘ EŽĂŚ ŽďƐĞƌǀĞ ůĂ ĚƌŽŝƚĞ Ğƚ Ěŝƚ ͗ ͨ ǀĞĐ ƵŶĞ ĂƵƚƌĞ ŽƌŝŐŝŶĞ Ğƚ ƵŶĞ ĂƵƚƌĞ ŐƌĂĚƵĂƟ ŽŶ͕ ůĞƐ ĂďƐĐŝƐƐĞƐ ĚĞƐ ƉŽŝŶƚƐ ͕ Ğƚ ƐĞƌĂŝĞŶƚ нϭϮ͕ нϭϲ Ğƚ нϮ ͩ͘ dƌĂĐĞ ůĂ ĚƌŽŝƚĞ ĚĞ DĂƌŝĞ Ğƚ͕ ƐƵƌ ĐĞůůĞͲĐŝ͕ ƉůĂĐĞ ĞŶ ĐŽƵůĞƵƌ ůĞ ƌĞƉğƌĞ ƵƟ ůŝƐĠ ƉĂƌ EŽĂŚ͘

100

Chapitre 5 Transformations du plan Tableaux de compétences Libre Les mouvements dans le plan 36

ŽŵƉƌĞŶĚƌĞ Ğƚ ƵƟ ůŝƐĞƌ͕ ĚĂŶƐ ůĞƵƌ ĐŽŶƚĞǆƚĞ͕ ĚĞƐ ƚĞƌŵĞƐ ƵƐƵĞůƐ ƉƌŽƉƌĞƐ ă ůĂ ŐĠŽŵĠƚƌŝĞ ƉůĂŶĞ͘

ŽŵƉĂƌĞƌ ĚĞƐ Į ŐƵƌĞƐ Ğƚ ƌĞĐŽŶŶĂŠƚƌĞ ůĂ ƚƌĂŶƐĨŽƌŵĂƟ ŽŶ ƋƵŝ ůĞƐ ĂƐƐŽĐŝĞ͘

ĂŶƐ ƵŶ ĐŽŶƚĞǆƚĞ ĚĞ ƉůŝĂŐĞ͕ ĚĞ ĚĠĐŽƵƉĂŐĞ͕ ĚĞ ƉĂǀĂŐĞ Ğƚ ĚĞ ƌĞƉƌŽĚƵĐƟ ŽŶ ĚĞ ĚĞƐƐŝŶƐ͕ ƌĞůĞǀĞƌ ůĂ ƉƌĠƐĞŶĐĞ Ě͛ŝŶǀĂƌŝĂŶƚƐ ĨŽŶĚĂŵĞŶƚĂƵǆ͘

ĠĐƌŝƌĞ ůĞƐ Ěŝī ĠƌĞŶƚĞƐ ĠƚĂƉĞƐ ĚĞ ůĂ ĐŽŶƐƚƌƵĐƟ ŽŶ ĚĞ ů͛ŝŵĂŐĞ Ě͛ƵŶĞ Į ŐƵƌĞ ƉĂƌ ƵŶĞ ƚƌĂŶƐĨŽƌŵĂƟ ŽŶ͘

>ĞƐ Į ŐƵƌĞƐ ƉůĂŶĞƐ 61

dƌĂĐĞƌ ƵŶĞ ĚƌŽŝƚĞ ƉĞƌƉĞŶĚŝĐƵůĂŝƌĞ ;ƉĂƌĂůůğůĞͿ ă ƵŶĞ ĂƵƚƌĞ͘

101

ACTIVITÉS

Chapitre 5 Transformations du plan

Kĸ ĐŝĞů &ŝŐƵƌĞƐ ŐĠŽŵĠƚƌŝƋƵĞƐ ĠůĠŵĞŶƚĂŝƌĞƐ Ğƚ ĚŝƐƚĂŶĐĞƐ 68

dƌĂĐĞƌ ƵŶĞ ĚƌŽŝƚĞ ƉĂƌĂůůğůĞ ă ƵŶĞ ĂƵƚƌĞ ĚƌŽŝƚĞ͘

dƌĂĐĞƌ ƵŶĞ ĚƌŽŝƚĞ ƉĞƌƉĞŶĚŝĐƵůĂŝƌĞ ă ƵŶĞ ĂƵƚƌĞ ĚƌŽŝƚĞ͘

DĞƐƵƌĞƌ ƵŶ ƐĞŐŵĞŶƚ ĚĞ ĚƌŽŝƚĞ͘

ZĞƉŽƌƚĞƌ ƵŶ ƐĞŐŵĞŶƚ ĚĞ ĚƌŽŝƚĞ ĚŽŶŶĠ͘

dƌĂŶƐĨŽƌŵĂƟ ŽŶƐ ĚƵ ƉůĂŶ

ZĞĐŽŶŶĂŠƚƌĞ ů͛ŝƐŽŵĠƚƌŝĞ ƋƵŝ ƉĞƌŵĞƚ ĚĞ ƉĂƐƐĞƌ ĚĞ ů͛ŽďũĞƚ ă ƐŽŶ ŝŵĂŐĞ͘

ĠƚĞƌŵŝŶĞƌ ůĞ ŽƵ ůĞƐ ĠůĠŵĞŶƚƐ ĐĂƌĂĐƚĠƌŝƐƟ ƋƵĞƐ ĚĞ ĐŚĂĐƵŶĞ ĚĞ ĐĞƐ ŝƐŽŵĠƚƌŝĞƐ͘

ZĞĐŽŶŶĂŠƚƌĞ ůĞƐ ŝƐŽŵĠƚƌŝĞƐ ĚƵ ƉůĂŶ ĚĂŶƐ ůĞƐ ĨƌŝƐĞƐ͕ ƉĂǀĂŐĞƐ͕ ƉĂƉŝĞƌƐ ƉĞŝŶƚƐ Ğƚ ƌŽƐĂĐĞƐ͘

ZĞĐŽŶŶĂŠƚƌĞ ůĞƐ ŝŶǀĂƌŝĂŶƚƐ ĐŽŵŵƵŶƐ ĂƵǆ ƋƵĂƚƌĞ ŝƐŽŵĠƚƌŝĞƐ ͗ ĐŽŶƐĞƌǀĂƟ ŽŶ ĚĞ ů͛ĂůŝŐŶĞŵĞŶƚ͕ ĚĞ ůĂ ůŽŶŐƵĞƵƌ Ě͛ƵŶ ƐĞŐŵĞŶƚ͕ ĚĞ ů͛ĂŵƉůŝƚƵĚĞ Ě͛ƵŶ ĂŶŐůĞ͕ ĚƵ ƉĂƌĂůůĠůŝƐŵĞ͘

ŽŶƐƚƌƵŝƌĞ ĂƵǆ ŝŶƐƚƌƵŵĞŶƚƐ ů͛ŝŵĂŐĞ ĚĞ Į ŐƵƌĞƐ ƉĂƌ ƵŶĞ ƚƌĂŶƐůĂƟ ŽŶ͕ ƵŶĞ ƐǇŵĠƚƌŝĞ ŽƌƚŚŽŐŽŶĂůĞ͕ ƵŶĞ ƐǇŵĠƚƌŝĞ ĐĞŶƚƌĂůĞ͘

102

Chapitre 5 Transformations du plan

ACTIVITÉS

ĐƚŝǀŝƚĠ ϭ ĠĐŽƵǀĞƌƚĞ ĚĞƐ ƚƌĂŶƐĨŽƌŵĂƚŝŽŶƐ 1 dŚŽŵĂƐ ĞƐƚ ƵŶ ĨĂŶ ĚĞ ƐĐŝĞŶĐĞͲĨŝĐƚŝŽŶ͘ /ů Ă ƚŽƵƚĞ ůĂ ĐŽůůĞĐƚŝŽŶ ĚĞƐ ĨŝůŵƐ ͨ >Ă ŐƵĞƌƌĞ ĚĞƐ ĠƚŽŝůĞƐ ͩ͘ ^Ă ŵĂŵĂŶ ůƵŝ Ă ĚĞŵĂŶĚĠ ĚĞ ĐŚŽŝƐŝƌ ůĞ ƉĂƉŝĞƌͲƉĞŝŶƚ ƋƵ͛ŝů ƐŽƵŚĂŝƚĂŝƚ ĚĂŶƐ ƐĂ ĐŚĂŵďƌĞ͘ sŽŝĐŝ ůĞ ĐŚŽŝǆ ĚĞ dŚŽŵĂƐ͘

dŚŽŵĂƐ ĐŽŶƐƚĂƚĞ ƋƵĞ ůĞƐ ŵŽƚŝĨƐ ƐĞ ƌĠƉğƚĞŶƚ ƌĠŐƵůŝğƌĞŵĞŶƚ ŵĂŝƐ ƋƵĞ ůĂ ŵĂŶŝğƌĞ ĚŽŶƚ ŝůƐ ŽŶƚ ĠƚĠ ŵĂŶŝƉƵůĠƐ ĞƐƚ ĚŝĨĨĠƌĞŶƚĞ ƐĞůŽŶ ůĞ ŵŽƚŝĨ͘ ĂŶƐ ĐŚĂƋƵĞ ĐĂƐ͕ ĂƐƐŽĐŝĞ ůĞ ƉĂƐƐĂŐĞ Ě͛ƵŶ ŵŽƚŝĨ ă ƵŶ ĂƵƚƌĞ ĂƵ ǀĞƌďĞ Ě͛ĂĐƚŝŽŶ ĐŽƌƌĞƐƉŽŶĚĂŶƚ ƋƵŝ ů͛ŝůůƵƐƚƌĞ͘ WĂƐƐĂŐĞ ĚΖƵŶĞ ƐŽƵĐŽƵƉĞ ŵĂƵǀĞ ă ƵŶĞ • • Tourner ƐŽƵĐŽƵƉĞ ǀĞƌƚĞ WĂƐƐĂŐĞ Ě͛ƵŶĞ ĨƵƐĠĞ ũĂƵŶĞ ă ƵŶĞ ĨƵƐĠĞ ďůĞƵĞ • • 'ůŝƐƐĞƌ WĂƐƐĂŐĞ Ě͛ƵŶ ƌŽďŽƚ ǀĞƌƚ ă ƵŶ ƌŽďŽƚ ƌŽƵŐĞ • • dŽƵƌŶĞƌ Ě͛ƵŶ ĚĞŵŝͲƚŽƵƌ WĂƐƐĂŐĞ Ě͛ƵŶ ͨ > D ͩ ǀĞƌƚ ă ƵŶ ͨ > D ͩ ƌŽƵŐĞ • • Retourner 2 ^ĂŵĞĚŝ ĚĞƌŶŝĞƌ͕ ZŽŵĂŶĞ Ă ƉĂƌƚŝĐŝƉĠ ă ƵŶ ŵĞĞƚŝŶŐ ĂĠƌŽŶĂƵƚŝƋƵĞ͘ sŽŝĐŝ ƋƵĞůƋƵĞƐ ƉĂƐƐĂŐĞƐ ĚĞ ĚĞƵǆ ĂǀŝŽŶƐ ĚĞ ͨ >Ă WĂƚƌŽƵŝůůĞ ĚĞ &ƌĂŶĐĞ ͩ ŝŶǀŝƚĠĞ ĂƵ ŵĞĞƚŝŶŐ͘ WŽƵƌ ĐŚĂƋƵĞ ƉŚŽƚŽ ƌĠĂůŝƐĠĞ͕ ŝŶĚŝƋƵĞ ů͛ĂĐƚŝŽŶ ƋƵŝ ĂƐƐŽĐŝĞ ůĞƐ ĚĞƵǆ ĂǀŝŽŶƐ Ğƚ ŶŽƚĞ ůĞ ŶŽŵ ĚĞ ůĂ ƚƌĂŶƐĨŽƌŵĂƚŝŽŶ ĚƵ ƉůĂŶ ƋƵŝ Ǉ ĞƐƚ ĂƐƐŽĐŝĠĞ͘

sĞƌďĞ Ě͛ĂĐƟ ŽŶ

dƌĂŶƐĨŽƌŵĂƟ ŽŶ

103

ACTIVITÉS

Chapitre 5 Transformations du plan

3 ƐƐŽĐŝĞ ĐŚĂƋƵĞ ƚƌĂŶƐĨŽƌŵĂƚŝŽŶ ă ƵŶ ǀĞƌďĞ Ğƚ ă ƐŽŶ ĠůĠŵĞŶƚ ĐĂƌĂĐƚĠƌŝƐƚŝƋƵĞ͘ Tourner • • ^ǇŵĠƚƌŝĞ ŽƌƚŚŽŐŽŶĂůĞ • • Centre dŽƵƌŶĞƌ Ě͛ƵŶ ĚĞŵŝ ƚŽƵƌ • • dƌĂŶƐůĂƚŝŽŶ • • ǆĞ Retourner • • ZŽƚĂƚŝŽŶ • • sĞĐƚĞƵƌ 'ůŝƐƐĞƌ • • ^ǇŵĠƚƌŝĞ ĐĞŶƚƌĂůĞ • • ĞŶƚƌĞ Ğƚ ĂŶŐůĞ ;ƐĞŶƐͿ 4 sŽŝĐŝ Ě͛ĂƵƚƌĞƐ ƉŚŽƚŽƐ ĚĞ ƉĂƐƐĂŐĞƐ ĚĞƐ ĚĞƵǆ ĂǀŝŽŶƐ͘ WŽƵƌ ĐŚĂƋƵĞ ƉŚŽƚŽ͕ ƌĞƚƌŽƵǀĞ ůĂ ƚƌĂŶƐĨŽƌŵĂƚŝŽŶ ƋƵŝ ĂƉƉůŝƋƵĞ ů͛ĂǀŝŽŶ ďůĂŶĐ ƐƵƌ ů͛ĂǀŝŽŶ ĐŽůŽƌĠ Ğƚ ƚƌĂĐĞ ƐƵƌ ĐŚĂƋƵĞ ĚĞƐƐŝŶ ů͛ĠůĠŵĞŶƚ ĐĂƌĂĐƚĠƌŝƐƚŝƋƵĞ͘

5 ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

5 ƋƵĞůůĞ;ƐͿ ƚƌĂŶƐĨŽƌŵĂƚŝŽŶ;ƐͿ ĚƵ ƉůĂŶ ƚĞ ĨŽŶƚ ƉĞŶƐĞƌ ůĞƐ ůŽŐŽƐ ĐŝͲĚĞƐƐŽƵƐ ͍

104

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

p.52 A

ACTIVITÉS

Chapitre 5 Transformations du plan

ĐƚŝǀŝƚĠ Ϯ ZĞĐŚĞƌĐŚĞ ĚĞ ƚƌĂŶƐĨŽƌŵĂƚŝŽŶƐ 1 ZĞĐŽŶŶĂŝƐ ůĂ ;ůĞƐͿ ƚƌĂŶƐĨŽƌŵĂƚŝŽŶ;ƐͿ ĚƵ ƉůĂŶ ƋƵŝ ĂƉƉůŝƋƵĞ;ŶƚͿ ůĞ ůŽŐŽ ďůĂŶĐ ƐƵƌ ůĞ ůŽŐŽ ĐŽůŽƌĠ Ğƚ ƌĞƉƌĠƐĞŶƚĞ ƐŽŶ ;ůĞƵƌƐͿ ĠůĠŵĞŶƚ;ƐͿ ĐĂƌĂĐƚĠƌŝƐƚŝƋƵĞ;ƐͿ͘ ϭ͘

Ϯ͘

ϯ͘

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϰ͘

ϱ͘

ϲ͘

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϳ͘

ϴ͘

ϵ͘

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

105

ACTIVITÉS

Chapitre 5 Transformations du plan

2 WĂƌŵŝ ůĞƐ ƋƵĂƚƌĞ ĚĞƐƐŝŶƐ Ě͛ƵŶĞ ŵġŵĞ ůŝŐŶĞ͕ ƚƌŽŝƐ ƌĞƉƌĠƐĞŶƚĞŶƚ ƵŶĞ ƚƌĂŶƐĨŽƌŵĂƚŝŽŶ ĚƵ ƉůĂŶ ƋƵŝ ĂƉƉůŝƋƵĞ ůĂ ĨŝŐƵƌĞ ĐŽůŽƌĠĞ ƐƵƌ ůĂ ĨŝŐƵƌĞ ďůĂŶĐŚĞ͘ ZĞĐŽŶŶĂŝƐͲůĂ Ğƚ ĚĠƚĞƌŵŝŶĞ ƐŽŶ ĠůĠŵĞŶƚ ĐĂƌĂĐƚĠƌŝƐƚŝƋƵĞ͘ ĂƌƌĞ ůĞ ĚĞƐƐŝŶ ŶĞ ƌĞƉƌĠƐĞŶƚĂŶƚ ĂƵĐƵŶĞ ĚĞƐ ƚƌĂŶƐĨŽƌŵĂƚŝŽŶƐ͘

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

3 Ƶ ĐŽƵƌƐ ĚĞ ĚĞƐƐŝŶ͕ YƵĞŶƚŝŶ Ă ƌĠĂůŝƐĠ ƵŶĞ ƌŽƐĂĐĞ ĚĠĐŽƌĂƚŝǀĞ͘ ĠƚĞƌŵŝŶĞ ůĞƐ ƚƌĂŶƐĨŽƌŵĂƚŝŽŶƐ ĚƵ ƉůĂŶ ƋƵŝ ĂƉƉůŝƋƵĞŶƚ ͙ ůĞ ŵĂƐƋƵĞ ϭ ƐƵƌ ůĞ ŵĂƐƋƵĞ Ϯ͘ 1

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ůĞ ŵĂƐƋƵĞ Ϯ ƐƵƌ ůĞ ŵĂƐƋƵĞ ϰ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ůĞ ŵĂƐƋƵĞ ϯ ƐƵƌ ůĞ ŵĂƐƋƵĞ ϲ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ůĂ ĨůğĐŚĞ ϭ ƐƵƌ ůĂ ĨůğĐŚĞ Ϯ͘

5 3

ůĂ ĨůğĐŚĞ ϯ ƐƵƌ ůĂ ĨůğĐŚĞ ϱ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ůĂ ĨůğĐŚĞ ϰ ƐƵƌ ůĂ ĨůğĐŚĞ ϭ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

106

ACTIVITÉS

Chapitre 5 Transformations du plan

ĐƚŝǀŝƚĠ ϯ ^ǇŵĠƚƌŝĞ ŽƌƚŚŽŐŽŶĂůĞ 1 ĂŶƐ ĐŚĂƋƵĞ ĐĂƐ͕ ĐŽŶƐƚƌƵŝƐ ůĞ ƐǇŵĠƚƌŝƋƵĞ ĚĞ ůĂ ĨŝŐƵƌĞ ƉĂƌ ƌĂƉƉŽƌƚ ă ůĂ ĚƌŽŝƚĞ Ě͘

2 ĂŶƐ ĐŚĂƋƵĞ ĐĂƐ͕ ĐŽůŽƌŝĞ ůĞ ƐǇŵĠƚƌŝƋƵĞ ĚĞƐ ƉŽŝŶƚƐ Ğƚ ƉĂƌ ƌĂƉƉŽƌƚ ă ů͛ĂǆĞ Ě͘ d B1 A2 A3 B2 B A1 A B B3 B1 B2 A1 A2 d

B1 B2 B3

A1 A2 A3

3 ŽŵƉůğƚĞ ůĂ ƉŚƌĂƐĞ ƐƵŝǀĂŶƚĞ͘ hŶĞ ƐǇŵĠƚƌŝĞ ŽƌƚŚŽŐŽŶĂůĞ ĞƐƚ ƵŶĞ ƚƌĂŶƐĨŽƌŵĂƚŝŽŶ ĚƵ ƉůĂŶ ƋƵŝ ĞŶǀŽŝĞ ƚŽƵƚ ƉŽŝŶƚ – de ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ĚĞ ů͛ĂǆĞ͕ ʹ ƐƵƌ ůĂ ĚƌŽŝƚĞ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ă ů͛ĂǆĞ ƉĂƐƐĂŶƚ ƉĂƌ ĐĞ ƉŽŝŶƚ͕

p.52 B

ʹ ă ƵŶĞ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ĚĞ ů͛ĂǆĞ͘ 4 ŽŶƐƚƌƵŝƐ ůĞƐ ƐǇŵĠƚƌŝƋƵĞƐ ĚĞƐ ƉŽŝŶƚƐ ƉĂƌ ůĂ ƐǇŵĠƚƌŝĞ ŽƌƚŚŽŐŽŶĂůĞ Ě͛ĂǆĞ Ě͕ ƉƵŝƐ ƌĞůŝĞ ůĞƐ ƉŽŝŶƚƐ ƉĂƌ ŽƌĚƌĞ ĂůƉŚĂďĠƚŝƋƵĞ ƉŽƵƌ ĨŽƌŵĞƌ ůĞ ƉŽůǇŐŽŶĞ ŝŶŝƚŝĂů Ğƚ ůĞ ƉŽůǇŐŽŶĞ ŝŵĂŐĞ ƉĂƌ ůĂ ƐǇŵĠƚƌŝĞ ŽƌƚŚŽŐŽŶĂůĞ͘

C D

B B d A

E d

C D

D d

A d

B E

C D

E 107

ACTIVITÉS

Chapitre 5 Transformations du plan

ĐƚŝǀŝƚĠ ϰ ^ǇŵĠƚƌŝĞ ĐĞŶƚƌĂůĞ 1 ĂŶƐ ĐŚĂƋƵĞ ĐĂƐ͕ ĐŽŶƐƚƌƵŝƐ ůĞ ƐǇŵĠƚƌŝƋƵĞ ĚĞ ůĂ ĨŝŐƵƌĞ ƉĂƌ ƌĂƉƉŽƌƚ ĂƵ ĐĞŶƚƌĞ K͘

O O

2 ĂŶƐ ĐŚĂƋƵĞ ĐĂƐ͕ ĐŽůŽƌŝĞ ůĞ ƐǇŵĠƚƌŝƋƵĞ ĚĞƐ ƉŽŝŶƚƐ Ğƚ ƉĂƌ ƌĂƉƉŽƌƚ ĂƵ ĐĞŶƚƌĞ K͘

B3 B2 B1

B A2

A 1 A 2 A3

O A1 A2

O A

B 1 B2

3 ŽŵƉůğƚĞ ůĂ ƉŚƌĂƐĞ ƐƵŝǀĂŶƚĞ͘ hŶĞ ƐǇŵĠƚƌŝĞ ĐĞŶƚƌĂůĞ ĞƐƚ ƵŶĞ ƚƌĂŶƐĨŽƌŵĂƚŝŽŶ ĚƵ ƉůĂŶ ƋƵŝ ĞŶǀŽŝĞ ƚŽƵƚ ƉŽŝŶƚ – de ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ĚƵ ĐĞŶƚƌĞ͕ ʹ ƐƵƌ ƵŶĞ ĚƌŽŝƚĞ ƉĂƐƐĂŶƚ ƉĂƌ ůĞ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ Ğƚ ůĞ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͕

p.53

ʹ ă ƵŶĞ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ĚƵ ĐĞŶƚƌĞ͘ 4 ŽŶƐƚƌƵŝƐ ůĞƐ ƐǇŵĠƚƌŝƋƵĞƐ ĚĞƐ ƉŽŝŶƚƐ ƉĂƌ ůĂ ƐǇŵĠƚƌŝĞ ĐĞŶƚƌĂůĞ ĚĞ ĐĞŶƚƌĞ K͕ ƉƵŝƐ ƌĞůŝĞ ůĞƐ ƉŽŝŶƚƐ ƉĂƌ ŽƌĚƌĞ ĂůƉŚĂďĠƚŝƋƵĞ ƉŽƵƌ ĨŽƌŵĞƌ ůĞ ƉŽůǇŐŽŶĞ ŝŶŝƚŝĂů ;ůĞ ƉŽŝŶƚ K Ŷ͛ĂƉƉĂƌƚŝĞŶƚ ƉĂƐ ĂƵ ƉŽůǇŐŽŶĞͿ Ğƚ ůĞ ƉŽůǇŐŽŶĞ ŝŵĂŐĞ ƉĂƌ ůĂ ƐǇŵĠƚƌŝĞ ĐĞŶƚƌĂůĞ͘

O C

O=D

O B

A D

C A C D

O C B

B A

108

ACTIVITÉS

Chapitre 5 Transformations du plan

ĐƚŝǀŝƚĠ ϱ dƌĂŶƐůĂƚŝŽŶ 1 DĂŶƐ ĐŚĂƋƵĞ ĐĂƐ͕ ĐŽŶƐƚƌƵŝƐ ů͛ŝŵĂŐĞ ĚĞ ůĂ ĨŝŐƵƌĞ ƉĂƌ ůĂ ƚƌĂŶƐůĂƚŝŽŶ ƋƵŝ ĂƉƉůŝƋƵĞ y ƐƵƌ z͘

Y Y

X X

2 ĂŶƐ ĐŚĂƋƵĞ ĐĂƐ͕ ĐŽůŽƌŝĞ ů͛ŝŵĂŐĞ ĚĞƐ ƉŽŝŶƚƐ ͕ Ğƚ ƉĂƌ ůĂ ƚƌĂŶƐůĂƚŝŽŶ ƋƵŝ ĂƉƉůŝƋƵĞ y ƐƵƌ z͘ A A1 A2 C B3 A X X A3 B B B1 B2 A A1 C1 B C A1 C2 Y A2 A3 Y A A Y B 1 B 2 B3 C3 2 3 B1 B2 C1 C2 C3 C X C 1 C 2 C3 B3 3 ŽŵƉůğƚĞ ůĂ ƉŚƌĂƐĞ ƐƵŝǀĂŶƚĞ͘ hŶĞ ƚƌĂŶƐůĂƚŝŽŶ ĞƐƚ ƵŶĞ ƚƌĂŶƐĨŽƌŵĂƚŝŽŶ ĚƵ ƉůĂŶ ƋƵŝ ĚĠƉůĂĐĞ ƚŽƵƚ ƉŽŝŶƚ ʹ ĚĂŶƐ ƵŶĞ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͕ p.53 D

ʹ ĚĂŶƐ ƵŶ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͕ 4

ʹ Ě͛ƵŶĞ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ŽŶƐƚƌƵŝƐ ůĞƐ ŝŵĂŐĞƐ ĚĞƐ ƉŽŝŶƚƐ ƉĂƌ ůĂ ƚƌĂŶƐůĂƚŝŽŶ ƋƵŝ ĂƉƉůŝƋƵĞ y ƐƵƌ z͕ ƉƵŝƐ ƌĞůŝĞ ůĞƐ ƉŽŝŶƚƐ ƉĂƌ ŽƌĚƌĞ ĂůƉŚĂďĠƚŝƋƵĞ ƉŽƵƌ ĨŽƌŵĞƌ ůĞ ƉŽůǇŐŽŶĞ ŝŶŝƚŝĂů Ğƚ ůĞ ƉŽůǇŐŽŶĞ ŝŵĂŐĞ ƉĂƌ ůĂ ƚƌĂŶƐůĂƚŝŽŶ͘

Y X C

D B=X

A D

Y A

Y C

D=X

D F E

A=X

B 109

EXERCICES COMPLÉMENTAIRES

Chapitre 5 Transformations du plan

ŽŶŶĂŠƚƌĞ 1 sŽŝĐŝ ƵŶĞ ƐĠƌŝĞ ĚĞ ĚĠƉůĂĐĞŵĞŶƚƐ ĚĂŶƐ ůΖĞƐƉĂĐĞ͘ YƵĞůůĞƐ ƚƌĂŶƐĨŽƌŵĂƟ ŽŶƐ ĚƵ ƉůĂŶ ĠǀŽƋƵĞŶƚͲŝůƐ ƉŽƵƌ ƚŽŝ ͍

ĂͿ KƵǀƌŝƌ ƵŶ Ɵ ƌŽŝƌ͘ ďͿ ǀĂŶĐĞƌ ů͛ŚĞƵƌĞ Ě͛ƵŶĞ ŚŽƌůŽŐĞ ĚĞ ϯϬ ŵŝŶƵƚĞƐ͘ ĐͿ ^Ğ ƌĞŐĂƌĚĞƌ ĚĂŶƐ ƵŶ ŵŝƌŽŝƌ͘ ĚͿ hŶ ĚĞŵŝͲƚŽƵƌ ă ŐĂƵĐŚĞ͘ ĞͿ >Ğ ĚĠƉůĂĐĞŵĞŶƚ Ě͛ƵŶĞ ďŽŠƚĞ ĚĞ ůĂŝƚ ƐƵƌ ůĞ ƚĂƉŝƐ ƌŽƵůĂŶƚ ă ůĂ ĐĂŝƐƐĞ Ě͛ƵŶ ŐƌĂŶĚ ŵĂŐĂƐŝŶ͘ ĨͿ ZĞƚĂƌĚĞƌ ů͛ŚĞƵƌĞ Ě͛ƵŶĞ ŚŽƌůŽŐĞ ĚĞ ϭϱ ŵŝŶƵƚĞƐ͘ ŐͿ KƵǀƌŝƌ ƵŶĞ ƉŽƌƚĞ ĐŽƵůŝƐƐĂŶƚĞ Ě͛ƵŶĞ ĐƵŝƐŝŶĞ͘ ŚͿ >Ğ ĚĠƉůĂĐĞŵĞŶƚ Ě͛ƵŶ ƚƌĂŝŶ ă ĐƌĠŵĂŝůůğƌĞ͘ ŝͿ hŶĞ ĐĂďĂŶĞ ĚĞ ƉġĐŚĞƵƌ ƋƵŝ ƐĞ ƌĞŇ ğƚĞ ĚĂŶƐ ƵŶ ůĂĐ͘ ũͿ >Ğ ĚĠƉůĂĐĞŵĞŶƚ Ě͛ƵŶ ďĂĐ ĚƵ ƉůĂŶ ŝŶĐůŝŶĠ ĚĞ ZŽŶƋƵŝğƌĞƐ͘ 2 &͛ ĠƚĂŶƚ ů͛ŝŵĂŐĞ ĚĞ & ƉĂƌ ƵŶĞ ƚƌĂŶƐĨŽƌŵĂƟ ŽŶ͕ ƌĞĐŽŶŶĂŝƐͲůĂ Ğƚ ĚĠƚĞƌŵŝŶĞ ƐŽŶ ĠůĠŵĞŶƚ

ĐĂƌĂĐƚĠƌŝƐƟ ƋƵĞ͘ F

F’

F’ F’

F’

F’ F’ F

F’

F’ 3 WŽƵƌ ĐŚĂĐƵŶ ĚĞƐ ĚĞƵǆ ĚĞƐƐŝŶƐ ĐŝͲĚĞƐƐŽƵƐ͕

ʹ ŝŶĚŝƋƵĞ ƉĂƌ ƋƵĞůůĞ ƚƌĂŶƐĨŽƌŵĂƟ ŽŶ ŽŶ ƉĂƐƐĞ ĚĞ ůĂ Į ŐƵƌĞ ă ůĂ Į ŐƵƌĞ ͕ ĚĞ ůĂ Į ŐƵƌĞ ă ůĂ Į ŐƵƌĞ ͕ ĚĞ ůĂ Į ŐƵƌĞ ă ůĂ Į ŐƵƌĞ ͘ ʹ ŶŽƚĞ ƐƵƌ ůĞ ĚĞƐƐŝŶ ůĞƐ ĠůĠŵĞŶƚƐ ĐĂƌĂĐƚĠƌŝƐƟ ƋƵĞƐ ĚĞ ĐĞƐ ƚƌĂŶƐĨŽƌŵĂƟ ŽŶƐ͘ A

D D

B A

4 Ŷ ĠƚĂŶƚ ƚƌğƐ ĂƩ ĞŶƟ Ĩ ĂƵǆ ŶŽŵƐ ĚĞƐ ƉŽŝŶƚƐ͕ ĚĠĐŽƵǀƌĞ ůĞƐ ƚƌĂŶƐĨŽƌŵĂƟ ŽŶƐ ƋƵŝ ĂƉƉůŝƋƵĞŶƚ ͗

ĂͿ ůĞ ƚƌŝĂŶŐůĞ ƐƵƌ ůĞ ƚƌŝĂŶŐůĞ ͛ ͛ ͛͘

ďͿ ůĞ ƌĞĐƚĂŶŐůĞ ƐƵƌ ůĞ ƌĞĐƚĂŶŐůĞ ͛ ͛ ͛ ͛͘

110

B A'

B' B'

A D'

EXERCICES COMPLÉMENTAIRES

Chapitre 5 Transformations du plan

5 ŽůŝŶĞ Ă ĚĞƐƐŝŶĠ ĚĞƐ ŝŵĂŐĞƐ ĚĞ ůĂ Į ŐƵƌĞ ' ƉĂƌ Ěŝī ĠƌĞŶƚĞƐ ƚƌĂŶƐĨŽƌŵĂƟ ŽŶƐ ĚƵ ƉůĂŶ͘

WŽƵƌ ĐŚĂƋƵĞ Į ŐƵƌĞ ĐŽůŽƌĠĞ͕ ĚŽŶŶĞ ůĞ ŶŽŵ ĚĞ ůĂ ƚƌĂŶƐĨŽƌŵĂƟ ŽŶ ĚƵ ƉůĂŶ ƋƵ͛ĞůůĞ Ă ƵƟ ůŝƐĠĞ Ğƚ ƌĞƉƌĠƐĞŶƚĞ ƐŽŶ ĠůĠŵĞŶƚ ĐĂƌĂĐƚĠƌŝƐƟ ƋƵĞ ;ĂǆĞ͕ ĐĞŶƚƌĞ͕ ͙Ϳ͘

B D C

ƉƉůŝƋƵĞƌ 1

ŽŶƐƚƌƵŝƐ ůĞƐ ƐǇŵĠƚƌŝƋƵĞƐ ĚĞƐ ƉŽŝŶƚƐ ƉĂƌ ůĂ ƐǇŵĠƚƌŝĞ ŽƌƚŚŽŐŽŶĂůĞ Ě͛ĂǆĞ Ě͕ ƉƵŝƐ ƌĞůŝĞ ůĞƐ ƉŽŝŶƚƐ ƉĂƌ ŽƌĚƌĞ ĂůƉŚĂďĠƟ ƋƵĞ ƉŽƵƌ ĨŽƌŵĞƌ ůĞ ƉŽůǇŐŽŶĞ ŝŶŝƟ Ăů Ğƚ ůĞ ƉŽůǇŐŽŶĞ ŝŵĂŐĞ ƉĂƌ ůĂ ƐǇŵĠƚƌŝĞ ŽƌƚŚŽŐŽŶĂůĞ͘

B d

C A B d

2 ŽŶƐƚƌƵŝƐ ůĞƐ ƐǇŵĠƚƌŝƋƵĞƐ ĚĞƐ ƉŽŝŶƚƐ ƉĂƌ ůĂ ƐǇŵĠƚƌŝĞ ĐĞŶƚƌĂůĞ ĚĞ ĐĞŶƚƌĞ K͕ ƉƵŝƐ ƌĞůŝĞ ůĞƐ ƉŽŝŶƚƐ ƉĂƌ

ŽƌĚƌĞ ĂůƉŚĂďĠƟ ƋƵĞ ƉŽƵƌ ĨŽƌŵĞƌ ůĞ ƉŽůǇŐŽŶĞ ŝŶŝƟ Ăů ;ůĞ ƉŽŝŶƚ K Ŷ͛ĂƉƉĂƌƟ ĞŶƚ ƉĂƐ ĂƵ ƉŽůǇŐŽŶĞͿ Ğƚ ůĞ ƉŽůǇŐŽŶĞ ŝŵĂŐĞ ƉĂƌ ůĂ ƐǇŵĠƚƌŝĞ ĐĞŶƚƌĂůĞ͘ A B D A D A B O O O C C B C 3 ŽŶƐƚƌƵŝƐ ů͛ŝŵĂŐĞ ĚĞƐ ƉŽŝŶƚƐ ƉĂƌ ůĂ ƚƌĂŶƐůĂƟ ŽŶ ƋƵŝ ĂƉƉůŝƋƵĞ y ƐƵƌ z͕ ƉƵŝƐ ƌĞůŝĞ ůĞƐ ƉŽŝŶƚƐ ƉĂƌ ŽƌĚƌĞ

ĂůƉŚĂďĠƟ ƋƵĞ ƉŽƵƌ ĨŽƌŵĞƌ ůĞ ƉŽůǇŐŽŶĞ ŝŶŝƟ Ăů ;ůĞƐ ƉŽŝŶƚƐ y Ğƚ z ŶΖĂƉƉĂƌƟ ĞŶŶĞŶƚ ƉĂƐ ĂƵ ƉŽůǇŐŽŶĞͿ Ğƚ ůĞ ƉŽůǇŐŽŶĞ ŝŵĂŐĞ ƉĂƌ ůĂ ƚƌĂŶƐůĂƟ ŽŶ͘

X A

C B

Y C

D 111

EXERCICES COMPLÉMENTAIRES

Chapitre 5 Transformations du plan

4 Ŷ ƵƟ ůŝƐĂŶƚ ƵŶĞ ƌğŐůĞ ŶŽŶ ŐƌĂĚƵĠĞ Ğƚ ĞŶ ƚ͛ĂŝĚĂŶƚ ĚƵ ƋƵĂĚƌŝůůĂŐĞ͕ ĐŽŶƐƚƌƵŝƐ ů͛ŝŵĂŐĞ ĚĞƐ Į ŐƵƌĞƐ

ƉƌŽƉŽƐĠĞƐ ĐŝͲĚĞƐƐŽƵƐ ƉĂƌ ůĂ ƚƌĂŶƐĨŽƌŵĂƟ ŽŶ ĚĞŵĂŶĚĠĞ͘ ĂͿ ^ǇŵĠƚƌŝĞ ŽƌƚŚŽŐŽŶĂůĞ Ě͛ĂǆĞ Ě d

ďͿ ^ǇŵĠƚƌŝĞ ŽƌƚŚŽŐŽŶĂůĞ Ě͛ĂǆĞ Ě

d d ĐͿ ^ǇŵĠƚƌŝĞ ĐĞŶƚƌĂůĞ ĚĞ ĐĞŶƚƌĞ K

O O

112

EXERCICES COMPLÉMENTAIRES

Chapitre 5 Transformations du plan

ĚͿ dƌĂŶƐůĂƟ ŽŶ ĚĞ ǀĞĐƚĞƵƌ yz

Y X

X Y X

Y X

dƌĂŶƐĨĠƌĞƌ 1 >Ğ ƉĂǀĂŐĞ ĐŝͲĐŽŶƚƌĞ Ă ĠƚĠ ƌĠĂůŝƐĠ ĂǀĞĐ Ϯϰ ƉŝğĐĞƐ ŝĚĞŶƟ ƋƵĞƐ͘

ĂͿ KďƐĞƌǀĞ ůĞ ƉĂǀĂŐĞ ƉƵŝƐ ĐŽŵƉůğƚĞ ůĞ ƚĂďůĞĂƵ ĐŝͲĚĞƐƐŽƵƐ͘ >Ă ƉŝğĐĞ ĞƐƚ ůĞ ƐǇŵĠƚƌŝƋƵĞ ƉĂƌ ƌĂƉƉŽƌƚ ͘͘͘ ŶΣ ĚĞ ůĂ ƉŝğĐĞ ŶΣ ϭ

ă ůĂ ĚƌŽŝƚĞ

ϭϮ

ĂƵ ƉŽŝŶƚ

ă ůĂ ĚƌŽŝƚĞ ͘͘͘

Ϯϭ

ĂƵ ƉŽŝŶƚ &

ϭϮ

ă ůĂ ĚƌŽŝƚĞ

ĂƵ ƉŽŝŶƚ ͘͘͘

ϭϭ

ă ůĂ ĚƌŽŝƚĞ

ϭϳ

ϭϲ

ĂƵ ƉŽŝŶƚ ͘͘͘

2 1 9

3 A

6 4

13 14 10 D 11 E 18 19 22 17 20 21

16 15

23 24

ďͿ >ĞƐ ƉŝğĐĞƐ ŶΣϱ Ğƚ ŶΣϭϴ ƐŽŶƚ ƐǇŵĠƚƌŝƋƵĞƐ ƉĂƌ ƌĂƉƉŽƌƚ ĂƵ ƉŽŝŶƚ '͘ WůĂĐĞ ůĞ ƉŽŝŶƚ ' ƐƵƌ ůĂ Į ŐƵƌĞ͘ ĐͿ YƵĞůůĞ ƐĞƌĂ ůĞ ŶΣ ĚĞ ůĂ ƉŝğĐĞ ŽďƚĞŶƵĞ ă ƉĂƌƟ ƌ ĚĞ ůĂ ƉŝğĐĞ ϭϴ͕ Ɛŝ ĐĞůůĞͲĐŝ ƐƵďŝƚ ĚΖĂďŽƌĚ ůĂ ƐǇŵĠƚƌŝĞ ĐĞŶƚƌĂůĞ ĚĞ ĐĞŶƚƌĞ ƉƵŝƐ ůĂ ƐǇŵĠƚƌŝĞ ŽƌƚŚŽŐŽŶĂůĞ ĚΖĂǆĞ ͍ 2 DĂǆŝŵĞ ǀŝĞŶƚ ĚĞ ĚĞƐƐŝŶĞƌ ůĞ ƐǇŵĠƚƌŝƋƵĞ ĚƵ ŵĂƐƋƵĞ

ƉĂƌ ƌĂƉƉŽƌƚ ă ůĂ ĚƌŽŝƚĞ Ě͘ ŶƚŽƵƌĞ ůĞƐ ϲ ĞƌƌĞƵƌƐ ĐŽŵŵŝƐĞƐ͘

113

EXERCICES COMPLÉMENTAIRES 3

KŶ Ă ĐŽŶƐƚƌƵŝƚ ůĞ ƉĂǀĂŐĞ ĚĞ ƋƵĂĚƌŝůĂƚğƌĞƐ ƚŽƵƐ ŝĚĞŶƚŝƋƵĞƐ ă ƉĂƌƚŝƌ ĚƵ ƋƵĂĚƌŝůĂƚğƌĞ ĐŽůŽƌĠ͘ ǆƉůŝƋƵĞ ĐŽŵŵĞŶƚ ƌĠĂůŝƐĞƌ ƵŶ ƚĞů ƉĂǀĂŐĞ ĞŶ ƵƚŝůŝƐĂŶƚ ͗ ĂͿ ĚĞƐ ƚƌĂŶƐůĂƟ ŽŶƐ Ğƚ ĚĞƐ ƐǇŵĠƚƌŝĞƐ ĐĞŶƚƌĂůĞƐ͕ ďͿ ƵŶŝƋƵĞŵĞŶƚ ĚĞƐ ƐǇŵĠƚƌŝĞƐ ĐĞŶƚƌĂůĞƐ͘

A D B

Chapitre 5 Transformations du plan

4 ĠƚĞƌŵŝŶĞ ůĞƐ ƉŽŝŶƚƐ ŝŵĂŐĞƐ Ğƚ ůĞ ŵŽƚ ŵǇƐƚğƌĞ ĐŽŶƐƟ ƚƵĠ ĚĞƐ ůĞƩ ƌĞƐ ĚĂŶƐ ůĞ ĚĠƐŽƌĚƌĞ͘

^Y;hͿ

^CH;'Ϳ

^GH;<Ϳ

^N;,Ϳ tYJ ;WͿ

^>;WͿ

^MN;:Ϳ

tLN ; Ϳ

/ŵĂŐĞ DŽƚ 5

>Ă ŐƌĂŶĚĞ ĂŝŐƵŝůůĞ Ě͛ƵŶĞ ŚŽƌůŽŐĞ ƚƌĂŶƐƉĂƌĞŶƚĞ ƐĞ ƚƌŽƵǀĞ ĞŶƚƌĞ ůĞ y// Ğƚ ůĞ ///͘ ŽůŽƌŝĞ ůĞ ĐĞŶƚƌĞ ĚĞ ů͛ŚŽƌůŽŐĞ ĞŶ ƌŽƵŐĞ IX Ɛŝ ĞůůĞ ĞƐƚ ǀƵĞ ĚĞ ĨĂĐĞ Ğƚ ĞŶ ďůĞƵ͕ Ɛŝ ĞůůĞ ĞƐƚ ǀƵĞ ĚĞ ĚŽƐ Ğƚ ŝŶĚŝƋƵĞƐͲǇ ůĞƐ ĐŚŝĨĨƌĞƐ ƌŽŵĂŝŶƐ ŵĂŶƋƵĂŶƚƐ͘ ^ĂĐŚĂŶƚ ƋƵĞ ƐƵƌ ĐŚĂĐƵŶĞ Ě͛ĞŶƚƌĞͲĞůůĞƐ͕ ŽŶ Ă ƌĞƉƌĠƐĞŶƚĠ ůĂ ƚƌĂĐĞ ;ƉŽŝŶƚͿ ůĂŝƐƐĠĞ ƉĂƌ ůĞ ďŽƵƚ ĚĞ ů͛ĂŝŐƵŝůůĞ ĚĞ ůĂ ƉƌĞŵŝğƌĞ ƉŽƐŝƚŝŽŶ͕ ƌĞƉůĂĐĞ ĐĞƚƚĞ ĂŝŐƵŝůůĞ ĚĂŶƐ ůĂ ŵġŵĞ ƉŽƐŝƚŝŽŶ͘

XII

III

XII

IIX

XII 114

XII

Chapitre 6 Figures planes Tableaux de compétences Libre ĂůĐƵů ůŝƩ ĠƌĂů Ğƚ ĠƋƵĂƟ ŽŶƐ 22

DĂŠƚƌŝƐĞƌ ůĞƐ ĐŽŶǀĞŶƟ ŽŶƐ ĚΖĠĐƌŝƚƵƌĞ ŵĂƚŚĠŵĂƟ ƋƵĞ ĚĞƐ ĞǆƉƌĞƐƐŝŽŶƐ ůŝƩ ĠƌĂůĞƐ͘

ĂůĐƵůĞƌ ĚĞƐ ǀĂůĞƵƌƐ ŶƵŵĠƌŝƋƵĞƐ Ě͛ĞǆƉƌĞƐƐŝŽŶƐ ůŝƩ ĠƌĂůĞƐ ;ƉĂƌ ĞǆĞŵƉůĞ ĚĂŶƐ ĚĞƐ ĨŽƌŵƵůĞƐ Ě͛ĂŝƌĞƐ ŽƵ ĚĞ ǀŽůƵŵĞƐͿ͘

Les mouvements dans le plan 36

ŽŵƉƌĞŶĚƌĞ Ğƚ ƵƟ ůŝƐĞƌ͕ ĚĂŶƐ ůĞƵƌ ĐŽŶƚĞǆƚĞ͕ ĚĞƐ ƚĞƌŵĞƐ ƵƐƵĞůƐ ƉƌŽƉƌĞƐ ă ůĂ ŐĠŽŵĠƚƌŝĞ ƉůĂŶĞ͘

:ƵƐƟ Į Ğƌ ƉĂƌ ĚĞƐ ŝŶǀĂƌŝĂŶƚƐ ůĂ ĐŽŶƐĞƌǀĂƟ ŽŶ Ě͛ƵŶĞ ƉƌŽƉƌŝĠƚĠ Ě͛ƵŶĞ Į ŐƵƌĞ ůŽƌƐƋƵ͛ĞůůĞ ƐƵďŝƚ ƵŶĞ ƚƌĂŶƐĨŽƌŵĂƟ ŽŶ͘

Les solides 51

ŽŶƐƚƌƵŝƌĞ͕ ƵƟ ůŝƐĞƌ Ğƚ ƚƌĂŶƐĨŽƌŵĞƌ ĚĞƐ ĞǆƉƌĞƐƐŝŽŶƐ ůŝƩ ĠƌĂůĞƐ ƉŽƵƌ ĐĂůĐƵůĞƌ ůĞ ƉĠƌŝŵğƚƌĞ ŽƵ ů͛ĂŝƌĞ ĚĞ ĨĂĐĞƐ͕ ůĞ ǀŽůƵŵĞ ĚĞ ƐŽůŝĚĞƐ͘

>ĞƐ Į ŐƵƌĞƐ ƉůĂŶĞƐ 55

ŽŵƉƌĞŶĚƌĞ Ğƚ ƵƟ ůŝƐĞƌ͕ ĚĂŶƐ ůĞƵƌ ĐŽŶƚĞǆƚĞ͕ ĚĞƐ ƚĞƌŵĞƐ ƵƐƵĞůƐ ƉƌŽƉƌĞƐ ă ůĂ ŐĠŽŵĠƚƌŝĞ ĚĞƐ Į ŐƵƌĞƐ ƉůĂŶĞƐ͘

ŶŽŶĐĞƌ Ğƚ ĐŽŵƉƌĞŶĚƌĞ ƋƵĞůůĞƐ ƉƌŽƉƌŝĠƚĠƐ ƐƵĸ ƐĞŶƚ ƉŽƵƌ ĐŽŶƐƚƌƵŝƌĞ ĚĞƐ Į ŐƵƌĞƐ ŐĠŽŵĠƚƌŝƋƵĞƐ ƉĂƌƟ ĐƵůŝğƌĞƐ͘

ZĞĐŽŶŶĂŠƚƌĞ͕ ĐŽŵƉĂƌĞƌ͕ Ěŝī ĠƌĞŶĐŝĞƌ Ğƚ ĐůĂƐƐĞƌ ĚĞƐ Į ŐƵƌĞƐ ƉůĂŶĞƐ ;ƋƵĂĚƌŝůĂƚğƌĞƐ Ğƚ ƚƌŝĂŶŐůĞƐͿ͘

ZĞůĞǀĞƌ ĚĞƐ ƌĠŐƵůĂƌŝƚĠƐ ĚĂŶƐ ůĞƐ ĨĂŵŝůůĞƐ ĚĞ Į ŐƵƌĞƐ ƉůĂŶĞƐ Ğƚ ĞŶ Ɵ ƌĞƌ ĚĞƐ ƉƌŽƉƌŝĠƚĠƐ ƌĞůĂƟ ǀĞƐ ĂƵǆ ĂŶŐůĞƐ͕ ĂƵǆ ĚŝƐƚĂŶĐĞƐ Ğƚ ĂƵǆ ĚƌŽŝƚĞƐ ƌĞŵĂƌƋƵĂďůĞƐ͘

dƌĂĐĞƌ ĚĞƐ Į ŐƵƌĞƐ ƐŝŵƉůĞƐ ĂǀĞĐ ĚĞƐ ŝŶƐƚƌƵŵĞŶƚƐ͘

ZĞƉƌŽĚƵŝƌĞ ƵŶĞ Į ŐƵƌĞ ƉůĂŶĞ ĞŶ ǀƌĂŝĞ ŐƌĂŶĚĞƵƌ ŽƵ ă ů͛ĠĐŚĞůůĞ͘

dƌĂĐĞƌ ƵŶĞ ĚƌŽŝƚĞ ƉĞƌƉĞŶĚŝĐƵůĂŝƌĞ ;ƉĂƌĂůůğůĞͿ ă ƵŶĞ ĂƵƚƌĞ͘ 115

ACTIVITÉS

Chapitre 6 Figures planes

dƌĂĐĞƌ ůĂ ŵĠĚŝĂƚƌŝĐĞ Ě͛ƵŶ ƐĞŐŵĞŶƚ͘

dƌĂĐĞƌ ůĂ ďŝƐƐĞĐƚƌŝĐĞ Ě͛ƵŶ ĂŶŐůĞ͘

dƌĂĐĞƌ ůĂ ŚĂƵƚĞƵƌ Ě͛ƵŶ ƚƌŝĂŶŐůĞ ŽƵ Ě͛ƵŶ ƉĂƌĂůůĠůŽŐƌĂŵŵĞ͘

dƌĂĐĞƌ ƵŶĞ ŵĠĚŝĂŶĞ Ě͛ƵŶ ƚƌŝĂŶŐůĞ ŽƵ Ě͛ƵŶ ƋƵĂĚƌŝůĂƚğƌĞ͘

dƌĂĐĞƌ ƵŶ ŚĞǆĂŐŽŶĞ ƌĠŐƵůŝĞƌ Ğƚ ƵŶ ĐĂƌƌĠ ŝŶƐĐƌŝƚƐ ă ƵŶ ĐĞƌĐůĞ͘

ZĠƐŽƵĚƌĞ ĚĞƐ ƉƌŽďůğŵĞƐ ĚĞ ĐŽŶƐƚƌƵĐƟ ŽŶ ă ƉƌŽƉŽƐ ĚĞ ƚƌŝĂŶŐůĞƐ͕ ĚĞ ĐĞƌĐůĞƐ ŽƵ ĚĞ ƋƵĂĚƌŝůĂƚğƌĞƐ͘

ZĠƐŽƵĚƌĞ ĚĞƐ ƉƌŽďůğŵĞƐ ĨĂŝƐĂŶƚ ŝŶƚĞƌǀĞŶŝƌ ĚĞƐ ůŽŶŐƵĞƵƌƐ ŽƵ ĚĞƐ ĂŝƌĞƐ ĚĞ Į ŐƵƌĞƐ ƉůĂŶĞƐ͘

DĞƐƵƌĞ ĚĞƐ ĂŶŐůĞƐ

ZĞĐŽŶŶĂŠƚƌĞ ĚĞƐ ĂŶŐůĞƐ ĂĚũĂĐĞŶƚƐ͕ ĐŽŵƉůĠŵĞŶƚĂŝƌĞƐ͕ ƐƵƉƉůĠŵĞŶƚĂŝƌĞƐ͘

dƌĂĐĞƌ ƵŶ ĂŶŐůĞ Ě͛ĂŵƉůŝƚƵĚĞ ĚŽŶŶĠĞ͘

ZĞƉŽƌƚĞƌ ĚĞƐ ĂŶŐůĞƐ͘

ZĠƐŽƵĚƌĞ ĚĞƐ ƉƌŽďůğŵĞƐ ĚĞ ĐŽŶƐƚƌƵĐƟ ŽŶ ă ƉƌŽƉŽƐ Ě͛ĂŶŐůĞƐ ĚĞ ŵĞƐƵƌĞƐ ƉĂƌƟ ĐƵůŝğƌĞƐ͘

Kĸ ĐŝĞů ǆƉƌĞƐƐŝŽŶƐ ůŝƩ ĠƌĂůĞƐ 48

ĂůĐƵůĞƌ ůĂ ǀĂůĞƵƌ ŶƵŵĠƌŝƋƵĞ Ě͛ƵŶĞ ĞǆƉƌĞƐƐŝŽŶ ůŝƩ ĠƌĂůĞ ĞŶ ĚŽŶŶĂŶƚ ĂƵǆ ǀĂƌŝĂďůĞƐ ĚĞƐ ǀĂůĞƵƌƐ ĞŶƟ ğƌĞƐ͘

^ŽůŝĚĞƐ Ğƚ Į ŐƵƌĞƐ ƉůĂŶĞƐ 56

ZĞĐŽŶŶĂŠƚƌĞ Ğƚ ĐůĂƐƐĞƌ ůĞƐ ƋƵĂĚƌŝůĂƚğƌĞƐ ͗ ƚƌĂƉğǌĞ͕ ƉĂƌĂůůĠůŽŐƌĂŵŵĞ͕ ƌĞĐƚĂŶŐůĞ͕ ůŽƐĂŶŐĞ͕ ĐĂƌƌĠ͘

ZĞĐŽŶŶĂŠƚƌĞ Ğƚ ĐůĂƐƐĞƌ ůĞƐ ƚƌŝĂŶŐůĞƐ ͗ ŝƐŽĐğůĞ͕ ĠƋƵŝůĂƚĠƌĂů͕ ƌĞĐƚĂŶŐůĞ͘

ŽŶŶĂŠƚƌĞ Ğƚ ĠŶŽŶĐĞƌ ůĞƐ ƉƌŽƉƌŝĠƚĠƐ ƌĞůĂƟ ǀĞƐ ĂƵǆ ĐƀƚĠƐ Ğƚ ĂƵǆ ĂŶŐůĞƐ ĚĞƐ ƋƵĂĚƌŝůĂƚğƌĞƐ Ğƚ ĚĞƐ ƚƌŝĂŶŐůĞƐ͘

ŽŶŶĂŠƚƌĞ Ğƚ ĠŶŽŶĐĞƌ ůĞƐ ƉƌŽƉƌŝĠƚĠƐ ĚĞƐ ĚŝĂŐŽŶĂůĞƐ ĚĞƐ ƋƵĂĚƌŝůĂƚğƌĞƐ͘

ĠĐƌŝƌĞ Ěŝī ĠƌĞŶƚƐ ƉŽůǇŐŽŶĞƐ ĞŶ ƵƟ ůŝƐĂŶƚ ůĞƐ ƚĞƌŵĞƐ ĐŽƌƌĞĐƚƐ ͗ ĐƀƚĠ͕ ĂŶŐůĞ͕ ůŽŶŐƵĞƵƌ͕ ĂŵƉůŝƚƵĚĞ ʹ ĂŶŐůĞƐ ĂĚũĂĐĞŶƚƐ ă ƵŶ ŵġŵĞ ĐƀƚĠ͕ ĂŶŐůĞ ŽƉƉŽƐĠ ă ƵŶ ĐƀƚĠ͕ ĂŶŐůĞƐ ŽƉƉŽƐĠƐ Ě͛ƵŶ ƋƵĂĚƌŝůĂƚğƌĞ ʹ ĐƀƚĠƐ ƉĂƌĂůůğůĞƐ͕ ĐƀƚĠƐ ƉĞƌƉĞŶĚŝĐƵůĂŝƌĞƐ͕ ĐƀƚĠƐ ŽƉƉŽƐĠƐ͕ ĐƀƚĠƐ ĐŽŶƐĠĐƵƟ ĨƐ͘

dƌĂĐĞƌ Ğƚ ƌĞƉƌŽĚƵŝƌĞ ůĞƐ ƚƌŝĂŶŐůĞƐ Ğƚ ůĞƐ ƋƵĂĚƌŝůĂƚğƌĞƐ ƉĂƌƟ ĐƵůŝĞƌƐ͘

116

Chapitre 6 Figures planes

ACTIVITÉS

ŽŶƐƚƌƵŝƌĞ ĚĞƐ ƉŽůǇŐŽŶĞƐ ƌĠŐƵůŝĞƌƐ ŝŶƐĐƌŝƚƐ ĚĂŶƐ ƵŶ ĐĞƌĐůĞ ͗ ĐĂƌƌĠ͕ ŽĐƚŽŐŽŶĞ͕ ŚĞǆĂŐŽŶĞ͕ ƚƌŝĂŶŐůĞ ĠƋƵŝůĂƚĠƌĂů͘

ZĞƉƌŽĚƵŝƌĞ ƵŶĞ Į ŐƵƌĞ ƉůĂŶĞ ă ů͛ĠĐŚĞůůĞ͘

ĂůĐƵůĞƌ ĚĞƐ ƉĠƌŝŵğƚƌĞƐ Ğƚ ĚĞƐ ĂŝƌĞƐ͘

&ŝŐƵƌĞƐ ŐĠŽŵĠƚƌŝƋƵĞƐ ĠůĠŵĞŶƚĂŝƌĞƐ Ğƚ ĚŝƐƚĂŶĐĞƐ 66

ŝī ĠƌĞŶĐŝĞƌ ƵŶĞ ĚƌŽŝƚĞ͕ ƵŶĞ ĚĞŵŝͲĚƌŽŝƚĞ Ğƚ ƵŶ ƐĞŐŵĞŶƚ ĚĞ ĚƌŽŝƚĞ͘

ZĞĐŽŶŶĂŠƚƌĞ Ğƚ Ěŝī ĠƌĞŶĐŝĞƌ ĚĞƐ ĚƌŽŝƚĞƐ ƉĂƌĂůůğůĞƐ͕ ĚĞƐ ĚƌŽŝƚĞƐ ƐĠĐĂŶƚĞƐ Ğƚ ĚĞƐ ĚƌŽŝƚĞƐ ƉĞƌƉĞŶĚŝĐƵůĂŝƌĞƐ͘

dƌĂĐĞƌ ƵŶĞ ĚƌŽŝƚĞ ƉĂƌĂůůğůĞ ă ƵŶĞ ĂƵƚƌĞ ĚƌŽŝƚĞ͘

ŽŶŶĂŠƚƌĞ ů͛ĂǆŝŽŵĞ Ě͛ ƵĐůŝĚĞ͘

dƌĂĐĞƌ ƵŶĞ ĚƌŽŝƚĞ ƉĞƌƉĞŶĚŝĐƵůĂŝƌĞ ă ƵŶĞ ĂƵƚƌĞ ĚƌŽŝƚĞ͘

ĠĐŽƵǀƌŝƌ ůĞƐ ƉƌŽƉƌŝĠƚĠƐ ĚĞƐ ĚƌŽŝƚĞƐ ƉĂƌĂůůğůĞƐ Ğƚ ĚĞƐ ĚƌŽŝƚĞƐ ƉĞƌƉĞŶĚŝĐƵůĂŝƌĞƐ͘

dƌĂĐĞƌ Ğƚ ĐĂƌĂĐƚĠƌŝƐĞƌ ůĞƐ ĚƌŽŝƚĞƐ ƌĞŵĂƌƋƵĂďůĞƐ ĚĞƐ ƚƌŝĂŶŐůĞƐ Ğƚ ĚĞƐ ƋƵĂĚƌŝůĂƚğƌĞƐ͘

DĞƐƵƌĞƌ ƵŶ ƐĞŐŵĞŶƚ ĚĞ ĚƌŽŝƚĞ͘

ZĞƉŽƌƚĞƌ ƵŶ ƐĞŐŵĞŶƚ ĚĞ ĚƌŽŝƚĞ ĚŽŶŶĠ͘

ĠĮ Ŷŝƌ ůĞ ŵŝůŝĞƵ Ě͛ƵŶ ƐĞŐŵĞŶƚ͘

dƌĂĐĞƌ Ğƚ ĐĂƌĂĐƚĠƌŝƐĞƌ ůĂ ŵĠĚŝĂƚƌŝĐĞ Ě͛ƵŶ ƐĞŐŵĞŶƚ͘

ŝī ĠƌĞŶĐŝĞƌ ƐŽŵŵĞƚ Ě͛ƵŶĞ Į ŐƵƌĞ Ğƚ ĂŶŐůĞ Ě͛ƵŶĞ Į ŐƵƌĞ͘

ZĞĐŽŶŶĂŠƚƌĞ ĂŶŐůĞ ĚƌŽŝƚ͕ ĂŶŐůĞ ĂŝŐƵ͕ ĂŶŐůĞ ŽďƚƵƐ͕ ĂŶŐůĞƐ ĐŽŵƉůĠŵĞŶƚĂŝƌĞƐ͕ ĂŶŐůĞƐ ƐƵƉƉůĠŵĞŶƚĂŝƌĞƐ͘

DĞƐƵƌĞƌ ƵŶ ĂŶŐůĞ͘

ZĞƉŽƌƚĞƌ ƵŶ ĂŶŐůĞ ĚŽŶŶĠ͘

dƌĂĐĞƌ Ğƚ ĐĂƌĂĐƚĠƌŝƐĞƌ ůĂ ďŝƐƐĞĐƚƌŝĐĞ Ě͛ƵŶ ĂŶŐůĞ͘

dƌĂĐĞƌ ƵŶ ĐĞƌĐůĞ ĚĞ ĐĞŶƚƌĞ Ğƚ ĚĞ ƌĂǇŽŶ ĚŽŶŶĠƐ͘

ŽŵƉĂƌĞƌ ƌĂǇŽŶ Ğƚ ĚŝĂŵğƚƌĞ͘

117

ACTIVITÉS

Chapitre 6 Figures planes

ĐƚŝǀŝƚĠ ϭ ĠĐŽƵǀĞƌƚĞ ĚĞƐ ƋƵĂĚƌŝůĂƚğƌĞƐ ĐƟ ŵĂƚŚǀŝůůĞ ĞƐƚ ƵŶĞ ĐŽŵŵƵŶĞ ĐŽŵƉŽƐĠĞ ƵŶŝƋƵĞŵĞŶƚ ĚĞ ůĂƌŐĞƐ ĂǀĞŶƵĞƐ Ğƚ ĚĞ ƌƵĞƐ ƉůƵƐ ĠƚƌŽŝƚĞƐ ƋƵŝ ƐĞ ĐƌŽŝƐĞŶƚ ƉŽƵƌ ĨŽƌŵĞƌ ĚĞƐ ĐĂƌƌĞĨŽƵƌƐ͘ dŽƵƚĞƐ ůĞƐ ĂǀĞŶƵĞƐ ŽŶƚ ůĂ ŵġŵĞ ůĂƌŐĞƵƌ Ğƚ ƚŽƵƚĞƐ ůĞƐ ƌƵĞƐ ĂƵƐƐŝ͘ 1 ĂŶƐ ĚƵ ĐĂƌƚŽŶ͕ ĚĠĐŽƵƉĞ ƵŶĞ ƌƵĞ ŝĚĞŶƟ ƋƵĞ ă ĐĞůůĞ ƉƌŽƉŽƐĠĞ ĐŝͲĚĞƐƐŽƵƐ͘ ĐŚğǀĞ ůĞƐ ƌĞƉƌĠƐĞŶƚĂƟ ŽŶƐ ƉŽƐƐŝďůĞƐ Ě͛ƵŶ ĐĂƌƌĞĨŽƵƌ ĨŽƌŵĠ ƉĂƌ ͘͘͘ ĂͿ ƵŶĞ ĂǀĞŶƵĞ Ğƚ ƵŶĞ ƌƵĞ͕ ĞŶƐƵŝƚĞ ĚĠƚĞƌŵŝŶĞ ůĂ ŶĂƚƵƌĞ ĚƵ ƋƵĂĚƌŝůĂƚğƌĞ ĂŝŶƐŝ ĨŽƌŵĠ͘

Avenue

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Avenue

ďͿ ĚĞƵǆ ƌƵĞƐ͕ ĞŶƐƵŝƚĞ ĚĠƚĞƌŵŝŶĞ ůĂ ŶĂƚƵƌĞ ĚƵ ƋƵĂĚƌŝůĂƚğƌĞ ĂŝŶƐŝ ĨŽƌŵĠ͘ Rue

Rue

2 ĐƟ ŵĂƚŚǀŝůůĞ͕ ů͛ĂǀĞŶƵĞ ƌĂƚŽƐƚŚğŶĞ Ğƚ ůĂ ƌƵĞ ƵĐůŝĚĞ ƐŽŶƚ ƉĞƌƉĞŶĚŝĐƵůĂŝƌĞƐ ă ů͛ĂǀĞŶƵĞ WǇƚŚĂŐŽƌĞ͘ ŽŵƉůğƚĞ ůĞƐ ƉŚƌĂƐĞƐ͘ Avenue Erat

>Ğ ĐĂƌƌĞĨŽƵƌ ĨŽƌŵĠ ƉĂƌ ůĞƐ ĂǀĞŶƵĞƐ ƌĂƚŽƐƚŚğŶĞ Ğƚ

>Ğ ĐĂƌƌĞĨŽƵƌ ĨŽƌŵĠ ƉĂƌ ůĞƐ ƌƵĞƐ ƵůĞƌ Ğƚ ƵĐůŝĚĞ ĞƐƚ

Eule

r Rue

Eule

thagore

thagore Avenue Py

Avenue Py

Avenue

ƵŶ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Rue

osthène

ƌƵĞ ƵĐůŝĚĞ ĞƐƚ ƵŶ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Rue Euclide

>Ğ ĐĂƌƌĞĨŽƵƌ ĨŽƌŵĠ ƉĂƌ ů͛ĂǀĞŶƵĞ WǇƚŚĂŐŽƌĞ Ğƚ ƉĂƌ ůĂ

Eule

Avenue Erat

ƌƵĞ ƵůĞƌ ĞƐƚ ƵŶ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Rue

Rue Euclide

>Ğ ĐĂƌƌĞĨŽƵƌ ĨŽƌŵĠ ƉĂƌ ů͛ĂǀĞŶƵĞ ƌĂƚŽƐƚŚğŶĞ Ğƚ ƉĂƌ ůĂ

osthène

WǇƚŚĂŐŽƌĞ ĞƐƚ ƵŶ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

WŽƵƌƋƵŽŝ Ŷ͛Ǉ ĂͲƚͲŝů ƉĂƐ ĚĞ ĐĂƌƌĞĨŽƵƌ ĞŶ ĨŽƌŵĞ ĚĞ ƚƌĂƉğǌĞ ͍ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

118

ACTIVITÉS

Chapitre 6 Figures planes

3 ĐƟ ŵĂƚŚǀŝůůĞ ƉŽƐƐğĚĞ ĠŐĂůĞŵĞŶƚ ƵŶ ƌŽŶĚͲƉŽŝŶƚ͘ ĂͿ Ŷ ũŽŝŐŶĂŶƚ ůĞ ƉŽŝŶƚ ă ƚƌŽŝƐ ĂƵƚƌĞƐ ƉŽŝŶƚƐ͕ ƚƌĂĐĞ ͘͘͘ ƵŶ ƚƌĂƉğǌĞ͘ ƵŶ ƌĞĐƚĂŶŐůĞ͘ B

ƵŶ ĐĂƌƌĠ͘

ďͿ YƵĞůůĞ ĞƐƚ ůĂ ƉĂƌƟ ĐƵůĂƌŝƚĠ ĚĞƐ ƉŽŝŶƚƐ ͕ ͕ ͕ ͕ ͕ &͕ ' Ğƚ , ͍ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ƋƵĞůůĞƐ Į ŐƵƌĞƐ ƉŽƵƌƌĂŝĞŶƚͲŝůƐ ĂƉƉĂƌƚĞŶŝƌ ͍ G

4 >ĞƐ Ěŝǆ ŠůŽƚƐ ĚĞ ŵĂŝƐŽŶƐ Ě͛ ĐƟ ŵĂƚŚǀŝůůĞ ŶƵŵĠƌŽƚĠƐ ƐƵƌ ůĞ ƉůĂŶ ĐŝͲĚĞƐƐŽƵƐ ƐŽŶƚ ĚĞƐ ƋƵĂĚƌŝůĂƚğƌĞƐ͘ /ŶĚŝƋƵĞ ůĞ ŶŽŵ ůĞ ƉůƵƐ ƉƌĠĐŝƐ ĚĞƐ ƋƵĂĚƌŝůĂƚğƌĞƐ ĐŽƌƌĞƐƉŽŶĚĂŶƚ ĂƵǆ Ěŝǆ ŠůŽƚƐ͘

6 8 5 7

4 10 3

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϭϬ

119

ACTIVITÉS

Chapitre 6 Figures planes

ĐƚŝǀŝƚĠ Ϯ ĠĨŝŶŝƚŝŽŶ ĚĞƐ ƋƵĂĚƌŝůĂƚğƌĞƐ ĂŶƐ ĐŚĂƋƵĞ ĐĂƐ͕ ĐŽŵƉůğƚĞ ůĂ ƉƌĞŵŝğƌĞ ƉŚƌĂƐĞ ĂǀĞĐ ĚĞƐ ŵŽƚƐ͕ ĨĂŝƐ ĂƉƉĂƌĂŠƚƌĞ ƐƵƌ ůĞ ĚĞƐƐŝŶ ůĞƐ ĠůĠŵĞŶƚƐ ƋƵŝ ƉĞƌŵĞƩ ĞŶƚ ĚĞ ĚĠĮ Ŷŝƌ ůĞ ƋƵĂĚƌŝůĂƚğƌĞ Ğƚ ĐŽŵƉůğƚĞ ůĂ ĚĞƵǆŝğŵĞ ƉŚƌĂƐĞ ĞŶ ůĂŶŐĂŐĞ ŵĂƚŚĠŵĂƟ ƋƵĞ͘ B

ĂͿ hŶ ƚƌĂƉğǌĞ ĞƐƚ ƵŶ ƋƵĂĚƌŝůĂƚğƌĞ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

>Ğ ƋƵĂĚƌŝůĂƚğƌĞ ĞƐƚ ƵŶ ƚƌĂƉğǌĞ ĐĂƌ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ďͿ hŶ ƉĂƌĂůůĠůŽŐƌĂŵŵĞ ĞƐƚ ƵŶ ƋƵĂĚƌŝůĂƚğƌĞ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

>Ğ ƋƵĂĚƌŝůĂƚğƌĞ ĞƐƚ ƵŶ ƉĂƌĂůůĠůŽŐƌĂŵŵĞ ĐĂƌ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ A

ĐͿ hŶ ƌĞĐƚĂŶŐůĞ ĞƐƚ ƵŶ ƋƵĂĚƌŝůĂƚğƌĞ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

>Ğ ƋƵĂĚƌŝůĂƚğƌĞ ĞƐƚ ƵŶ ƌĞĐƚĂŶŐůĞ ĐĂƌ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ĚͿ hŶ ůŽƐĂŶŐĞ ĞƐƚ ƵŶ ƋƵĂĚƌŝůĂƚğƌĞ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

>Ğ ƋƵĂĚƌŝůĂƚğƌĞ ĞƐƚ ƵŶ ůŽƐĂŶŐĞ ĐĂƌ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

C D

ĞͿ hŶ ĐĂƌƌĠ ĞƐƚ ƵŶ ƋƵĂĚƌŝůĂƚğƌĞ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

C p.54 A1 p.62 I

>Ğ ƋƵĂĚƌŝůĂƚğƌĞ ĞƐƚ ƵŶ ĐĂƌƌĠ ĐĂƌ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ĐƚŝǀŝƚĠ ϯ hŶŝĐŝƚĠ ĚĞ ůĂ ƉĂƌĂůůğůĞ Ğƚ ĚĞ ůĂ ƉĞƌƉĞŶĚŝĐƵůĂŝƌĞ dƌĂĐĞ ůĞƐ ĚƌŽŝƚĞƐ ƉĂƌĂůůğůĞƐ ă ůĂ ĚƌŽŝƚĞ Ě ƉĂƐƐĂŶƚ dƌĂĐĞ ůĞƐ ĚƌŽŝƚĞƐ ƉĞƌƉĞŶĚŝĐƵůĂŝƌĞƐ ă ůĂ ĚƌŽŝƚĞ Ě ƌĞƐƉĞĐƟ ǀĞŵĞŶƚ ƉĂƌ ůĞƐ ƉŽŝŶƚƐ ͕ Ğƚ ͘ ƉĂƐƐĂŶƚ ƌĞƐƉĞĐƟ ǀĞŵĞŶƚ ƉĂƌ ůĞƐ ƉŽŝŶƚƐ ͕ Ğƚ ͘ A B

A d

C d

ŽŵƉůğƚĞ ůĂ ƉŚƌĂƐĞ͘ WĂƌ ƵŶ ƉŽŝŶƚ ĞǆƚĠƌŝĞƵƌ ă ƵŶĞ ĚƌŽŝƚĞ͕ ŽŶ ƉĞƵƚ

tracer

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

120

; ǆŝŽŵĞ ĚΖ ƵĐůŝĚĞͿ

ă ĐĞůůĞͲĐŝ͘

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ă ĐĞůůĞͲĐŝ͘

p.55

ACTIVITÉS

Chapitre 6 Figures planes

ĐƚŝǀŝƚĠ ϰ KƌŐĂŶŝŐƌĂŵŵĞ 1 ĂͿ ĐŚğǀĞ ůĂ ĐŽŶƐƚƌƵĐƟ ŽŶ ĚƵ ƌĞĐƚĂŶŐůĞ ĞŶ ƵƟ ůŝƐĂŶƚ ƵŶŝƋƵĞŵĞŶƚ ƐĂ ĚĠĮ ŶŝƟ ŽŶ͘ ;ϭͿ

;ϭͿ

ďͿ hŶ ĠůğǀĞ Ă ŽďƚĞŶƵ ƵŶ ĐĂƌƌĠ͘ ǆƉůŝƋƵĞ ƉŽƵƌƋƵŽŝ Ğƚ ƌĠĂůŝƐĞ ĐĞƩ Ğ ĐŽŶƐƚƌƵĐƟ ŽŶ͘ ;ϮͿ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;ϮͿ

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ŽŵƉůğƚĞ ůĂ ƉŚƌĂƐĞ ͗ ƵŶ ĐĂƌƌĠ ĞƐƚ ƵŶ ƌĞĐƚĂŶŐůĞ ƋƵŝ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

2 ĂͿ ĐŚğǀĞ ůĂ ĐŽŶƐƚƌƵĐƟ ŽŶ ĚƵ ůŽƐĂŶŐĞ ĞŶ ƵƟ ůŝƐĂŶƚ ƵŶŝƋƵĞŵĞŶƚ ƐĂ ĚĠĮ ŶŝƟ ŽŶ͘ ;ϭͿ

;ϭͿ

ďͿ hŶ ĠůğǀĞ Ă ŽďƚĞŶƵ ƵŶ ĐĂƌƌĠ͘ ǆƉůŝƋƵĞ ƉŽƵƌƋƵŽŝ Ğƚ ƌĠĂůŝƐĞ ĐĞƩ Ğ ĐŽŶƐƚƌƵĐƟ ŽŶ͘ ;ϮͿ

;ϮͿ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ŽŵƉůğƚĞ ůĂ ƉŚƌĂƐĞ ͗ ƵŶ ĐĂƌƌĠ ĞƐƚ ƵŶ ůŽƐĂŶŐĞ ƋƵŝ Ă ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

3 ĂͿ ĐŚğǀĞ ůĂ ĐŽŶƐƚƌƵĐƟ ŽŶ ĚƵ ƉĂƌĂůůĠůŽŐƌĂŵŵĞ ĞŶ ƵƟ ůŝƐĂŶƚ ƵŶŝƋƵĞŵĞŶƚ ƐĂ ĚĠĮ ŶŝƟ ŽŶ͘

ďͿ hŶ ĠůğǀĞ Ă ŽďƚĞŶƵ ƵŶ ƌĞĐƚĂŶŐůĞ͘

B A ĐͿ hŶ ĂƵƚƌĞ ĠůğǀĞ Ă ŽďƚĞŶƵ ƵŶ ůŽƐĂŶŐĞ͘

ǆƉůŝƋƵĞ ƉŽƵƌƋƵŽŝ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ZĠĂůŝƐĞ ĐĞƩ Ğ ĐŽŶƐƚƌƵĐƟ ŽŶ͘

B A ŽŵƉůğƚĞ ůĂ ƉŚƌĂƐĞ ͗ ƵŶ ƌĞĐƚĂŶŐůĞ ĞƐƚ ƵŶ ƉĂƌĂůůĠůŽŐƌĂŵŵĞ

B A ŽŵƉůğƚĞ ůĂ ƉŚƌĂƐĞ ͗ ƵŶ ůŽƐĂŶŐĞ ĞƐƚ ƵŶ ƉĂƌĂůůĠůŽŐƌĂŵŵĞ

ƋƵŝ Ă ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

121

ACTIVITÉS

Chapitre 6 Figures planes

4 ĂͿ ĐŚğǀĞ ůĂ ĐŽŶƐƚƌƵĐƟ ŽŶ ĚƵ ƚƌĂƉğǌĞ ĞŶ ƵƟ ůŝƐĂŶƚ ƵŶŝƋƵĞŵĞŶƚ ƐĂ ĚĠĮ ŶŝƟ ŽŶ͘ ;ϭͿ

;ϭͿ

ďͿ hŶ ĠůğǀĞ Ă ŽďƚĞŶƵ ƵŶ ƉĂƌĂůůĠůŽŐƌĂŵŵĞ͘ ǆƉůŝƋƵĞ ƉŽƵƌƋƵŽŝ Ğƚ ƌĠĂůŝƐĞ ĐĞƩ Ğ ĐŽŶƐƚƌƵĐƟ ŽŶ͘ ;ϮͿ

B A

;ϮͿ

ŽŵƉůğƚĞ ůĂ ƉŚƌĂƐĞ ͗ ƵŶ ƉĂƌĂůůĠůŽŐƌĂŵŵĞ ĞƐƚ ƵŶ ƚƌĂƉğǌĞ ƋƵŝ Ă ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

p.54 A2

B A

5 /ŶĚŝƋƵĞ Ɛŝ ůĞƐ ƉƌŽƉŽƐŝƟ ŽŶƐ ƐƵŝǀĂŶƚĞƐ ƐŽŶƚ ǀƌĂŝĞƐ ;sͿ ŽƵ ĨĂƵƐƐĞƐ ;&Ϳ͘ ĂͿ dŽƵƐ ůĞƐ ůŽƐĂŶŐĞƐ ƐŽŶƚ ĚĞƐ ĐĂƌƌĠƐ͘ ďͿ dŽƵƐ ůĞƐ ƉĂƌĂůůĠůŽŐƌĂŵŵĞƐ ƐŽŶƚ ĚĞƐ ƌĞĐƚĂŶŐůĞƐ͘ ĐͿ dŽƵƐ ůĞƐ ĐĂƌƌĠƐ ƐŽŶƚ ĚĞƐ ůŽƐĂŶŐĞƐ͘ ĚͿ dŽƵƐ ůĞƐ ůŽƐĂŶŐĞƐ ƐŽŶƚ ĚĞƐ ƉĂƌĂůůĠůŽŐƌĂŵŵĞƐ͘ ĞͿ dŽƵƐ ůĞƐ ƌĞĐƚĂŶŐůĞƐ ƐŽŶƚ ĚĞƐ ĐĂƌƌĠƐ͘ ĨͿ dŽƵƐ ůĞƐ ƉĂƌĂůůĠůŽŐƌĂŵŵĞƐ ƐŽŶƚ ĚĞƐ ůŽƐĂŶŐĞƐ͘ ŐͿ dŽƵƐ ůĞƐ ƌĞĐƚĂŶŐůĞƐ ƐŽŶƚ ĚĞƐ ƉĂƌĂůůĠůŽŐƌĂŵŵĞƐ͘ ŚͿ dŽƵƐ ůĞƐ ĐĂƌƌĠƐ ƐŽŶƚ ĚĞƐ ƌĞĐƚĂŶŐůĞƐ͘

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ĐƚŝǀŝƚĠ ϱ ĂƌĂĐƚĠƌŝƐƚŝƋƵĞƐ ĚĞƐ ƋƵĂĚƌŝůĂƚğƌĞƐ 1

>Ğ ĐĂƌƌĠ

>Ğ ůŽƐĂŶŐĞ

>Ğ ƌĞĐƚĂŶŐůĞ

>Ğ ƉĂƌĂůůĠůŽŐƌĂŵŵĞ

>Ğ ƚƌĂƉğǌĞ

ĂͿ ^ŝ ůĂ ĚĠĮ ŶŝƟ ŽŶ Ě͛ƵŶ ƋƵĂĚƌŝůĂƚğƌĞ ĐŽŵƉƌĞŶĚ ůĂ ƉŚƌĂƐĞ ƉƌŽƉŽƐĠĞ ĚĂŶƐ ůĞ ƚĂďůĞĂƵ ĐŝͲĚĞƐƐŽƵƐ͕ ŝŶĚŝƋƵĞ ƵŶĞ ĐƌŽŝǆ ƌŽƵŐĞ ;XͿ ĚĂŶƐ ůĂ ĐĂƐĞ ĂĚĠƋƵĂƚĞ͘ ũŽƵƚĞ Ě͛ĂƵƚƌĞƐ ĐƌŽŝǆ ďůĞƵĞƐ ;XͿ ĚĂŶƐ ĐĞ ƚĂďůĞĂƵ ĞŶ ƐĂĐŚĂŶƚ ƋƵĞ ĐĞ ƋƵŝ ĞƐƚ ǀƌĂŝ ƉŽƵƌ ƵŶ ƋƵĂĚƌŝůĂƚğƌĞ ů͛ĞƐƚ ĂƵƐƐŝ ƉŽƵƌ ůĞƐ ƋƵĂĚƌŝůĂƚğƌĞƐ ƐŝƚƵĠƐ ĞŶ ĚĞƐƐŽƵƐ ĚĂŶƐ ů͛ŽƌŐĂŶŝŐƌĂŵŵĞ͘

ƉŽƐƐğĚĞ ĚĞƵǆ ĐƀƚĠƐ ƉĂƌĂůůğůĞƐ͘ ƉŽƐƐğĚĞ ůĞƐ ĐƀƚĠƐ ŽƉƉŽƐĠƐ ƉĂƌĂůůğůĞƐ͘ ƉŽƐƐğĚĞ ůĞƐ ĐƀƚĠƐ ŽƉƉŽƐĠƐ ĚĞ ŵġŵĞ ůŽŶŐƵĞƵƌ͘ ƉŽƐƐğĚĞ ůĞƐ ĐƀƚĠƐ ĚĞ ŵġŵĞ ůŽŶŐƵĞƵƌ͘ ƉŽƐƐğĚĞ ůĞƐ ĂŶŐůĞƐ ŽƉƉŽƐĠƐ ĚĞ ŵġŵĞ ĂŵƉůŝƚƵĚĞ͘ ƉŽƐƐğĚĞ ůĞƐ ĂŶŐůĞƐ ĚĞ ŵġŵĞ ĂŵƉůŝƚƵĚĞ͘

122

p.54 A3

ACTIVITÉS

Chapitre 6 Figures planes

ďͿ dƌĂĐĞ ůĂ ĚŝĂŐŽŶĂůĞ ΀ ΁ ĚĂŶƐ ůĞ ƉƌĞŵŝĞƌ ƉĂƌĂůůĠůŽŐƌĂŵŵĞ Ğƚ ůĂ ĚŝĂŐŽŶĂůĞ ΀ ΁ ĚĂŶƐ ůĞ ƐĞĐŽŶĚ͘ A B A B

YƵĞůůĞ ƚƌĂŶƐĨŽƌŵĂƟ ŽŶ ĚƵ ƉůĂŶ ĂƉƉůŝƋƵĞ ůĞ ƚƌŝĂŶŐůĞ ƐƵƌ ůĞ ƚƌŝĂŶŐůĞ ͍

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Ŷ ƐĂĐŚĂŶƚ ƋƵĞ ůĞƐ ƚƌŝĂŶŐůĞƐ Ğƚ ƐŽŶƚ ƐƵƉĞƌƉŽƐĂďůĞƐ͕ ĐŽŵƉůğƚĞ ůĞƐ ĠŐĂůŝƚĠƐ ĐŝͲĚĞƐƐŽƵƐ͘

ͮ ͮ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͮ ͮ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ^

| ͮ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ͮ ͮ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͮ ͮ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ^

| ͮ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ĐͿ Ŷ ƵƟ ůŝƐĂŶƚ ůĞƐ ĠŐĂůŝƚĠƐ ĚĠĐŽƵǀĞƌƚĞƐ ĂƵ ƉŽŝŶƚ ƉƌĠĐĠĚĞŶƚ͕ ĂũŽƵƚĞ ĚĞƐ ĐƌŽŝǆ ŶŽŝƌĞƐ ;XͿ ĚĂŶƐ ůĂ ĐŽůŽŶŶĞ ĚƵ ƉĂƌĂůůĠůŽŐƌĂŵŵĞ ĚƵ ƚĂďůĞĂƵ ĚĞ ůĂ ƉĂŐĞ ƉƌĠĐĠĚĞŶƚĞ͘ ũŽƵƚĞ ĞŶĮ Ŷ Ě͛ĂƵƚƌĞƐ ĐƌŽŝǆ ǀĞƌƚĞƐ ;XͿ ĞŶ ƐĂĐŚĂŶƚ ƋƵĞ ĐĞ ƋƵŝ ĞƐƚ ǀƌĂŝ ƉŽƵƌ ƵŶ ƋƵĂĚƌŝůĂƚğƌĞ ů͛ĞƐƚ ĂƵƐƐŝ ƉŽƵƌ ůĞƐ ƋƵĂĚƌŝůĂƚğƌĞƐ ƐŝƚƵĠƐ ĞŶͲĚĞƐƐŽƵƐ ĚĂŶƐ ů͛ŽƌŐĂŶŝŐƌĂŵŵĞ͘ 2 Ŷ ƵƟ ůŝƐĂŶƚ ĚĞƐ ĐĂƌĂĐƚĠƌŝƐƟ ƋƵĞƐ Ěŝī ĠƌĞŶƚĞƐ ĚĞ ĐĞůůĞƐ ĚĞ ůĂ ĚĠĮ ŶŝƟ ŽŶ͕ ĐŽŶƐƚƌƵŝƐ ͘͘͘ ĂͿ ƵŶ ĐĂƌƌĠ ĚĞ ϯ Đŵ ĚĞ ĐƀƚĠ͘

ďͿ ƵŶ ƌĞĐƚĂŶŐůĞ ĚŽŶƚ ůĂ ůŽŶŐƵĞƵƌ ŵĞƐƵƌĞ ϱ Đŵ Ğƚ ůĂ ůĂƌŐĞƵƌ ϯϬ ŵŵ͘

ĐͿ ƵŶ ƉĂƌĂůůĠůŽŐƌĂŵŵĞ ĚŽŶƚ ůĞƐ ĐŽƚĠƐ ŵĞƐƵƌĞŶƚ ϯϬ ŵŵ Ğƚ ϰϬ ŵŵ Ğƚ ƵŶ ĂŶŐůĞ ϱϱΣ͘

ĚͿ ƵŶ ůŽƐĂŶŐĞ ĚŽŶƚ ůĞƐ ĐƀƚĠƐ ŵĞƐƵƌĞŶƚ ϰ Đŵ Ğƚ ƵŶ ĂŶŐůĞ ϱϬΣ͘

123

ACTIVITÉS

Chapitre 6 Figures planes

ĐƚŝǀŝƚĠ ϲ ŝĂŐŽŶĂůĞƐ ĚĞƐ ƋƵĂĚƌŝůĂƚğƌĞƐ 1 ĂͿ WŽƵƌ ůĞƐ ĨġƚĞƐ ĚĞ Į Ŷ Ě͛ĂŶŶĠĞ͕ ůĞƐ ĂƵƚŽƌŝƚĠƐ ĐŽŵŵƵŶĂůĞƐ Ě͛ ĐƟ ŵĂƚŚǀŝůůĞ ŽŶƚ ĚĠĐŝĚĠ ĚĞ ƚĞŶĚƌĞ ĚĞƐ ŐƵŝƌůĂŶĚĞƐ ƌĞůŝĂŶƚ ĚĞƵǆ ĐŽŝŶƐ ĚĞ ƌƵĞƐ ŽƉƉŽƐĠƐ ĚĞ ƉůƵƐŝĞƵƌƐ ĐĂƌƌĞĨŽƵƌƐ ĚĞ ůĂ ĐŽŵŵƵŶĞ͘ ů͛ŝŶƚĞƌƐĞĐƟ ŽŶ ĚĞ ĐĞƐ ĚĞƵǆ ŐƵŝƌůĂŶĚĞƐ͕ ŽŶ Ă ĂƩ ĂĐŚĠ ƵŶĞ ĠƚŽŝůĞ ůƵŵŝŶĞƵƐĞ͘ WŽƵƌ ĐŚĂƋƵĞ ĐĂƌƌĞĨŽƵƌ͕ ƚƌĂĐĞ ůĞƐ ŐƵŝƌůĂŶĚĞƐ͕ ŝŶĚŝƋƵĞ ů͛ĞŵƉůĂĐĞŵĞŶƚ ĚĞ ů͛ĠƚŽŝůĞ ; Ϳ ƉƵŝƐ ĐŽŵƉĂƌĞ ůĂ ůŽŶŐƵĞƵƌ ĚĞƐ ĚĞƵǆ ŐƵŝƌůĂŶĚĞƐ Ğƚ ĚĠƚĞƌŵŝŶĞ ůĞƵƌ ƉŽƐŝƟ ŽŶ ƌĞůĂƟ ǀĞ ĞŶ ůĂŶŐĂŐĞ ŵĂƚŚĠŵĂƟ ƋƵĞ͘ ĂƌƌĞĨŽƵƌ ϭ

ĂƌƌĞĨŽƵƌ Ϯ

B A

C D

D ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ĂƌƌĞĨŽƵƌ ϯ

ĂƌƌĞĨŽƵƌ ϰ

B A

6 D

>Ğ ƌĞƐƉŽŶƐĂďůĞ ĚĞ ů͛ŝŶƐƚĂůůĂƟ ŽŶ ƉƌĠƚĞŶĚ ƋƵĞ ĚĂŶƐ ĐŚĂƋƵĞ ĐĂƐ͕ ů͛ĠƚŽŝůĞ ĞƐƚ ƉůĂĐĠĞ ĂƵ ĐĞŶƚƌĞ ĚƵ ĐĂƌƌĞĨŽƵƌ͘ YƵ͛ĞŶ ƉĞŶƐĞƐͲƚƵ ͍ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

p.62

ďͿ ŽŵƉůğƚĞ ůĂ ƉƌĞŵŝğƌĞ ĐŽůŽŶŶĞ ĚƵ ƚĂďůĞĂƵ ĞŶ ĚŽŶŶĂŶƚ ůĂ ŶĂƚƵƌĞ ĚƵ ƋƵĂĚƌŝůĂƚğƌĞ Ğƚ ĞŶ ŵĞƩ ĂŶƚ ƵŶĞ ĐƌŽŝǆ ƋƵĂŶĚ ůĂ ƉƌŽƉƌŝĠƚĠ ĞƐƚ ǀƌĂŝĞ͘ ĞƐƚ ƵŶ ͘͘͘

ͮ ͮ с ͮ ͮ ͮ ͮ с ͮ ͮ Ğƚ ͮ ͮ с ͮ ͮ

|AEBͮ с ϵϬΣ

ĂƌƌĞĨŽƵƌ ϭ ĂƌƌĞĨŽƵƌ Ϯ ĂƌƌĞĨŽƵƌ ϯ ĂƌƌĞĨŽƵƌ ϰ Ŷ ƵƟ ůŝƐĂŶƚ ůĞ ƚĂďůĞĂƵ ĐŝͲĚĞƐƐƵƐ͕ ĐŽŵƉůğƚĞ ůĞƐ ƉŚƌĂƐĞƐ ƐƵŝǀĂŶƚĞƐ͘ >ĞƐ ĚŝĂŐŽŶĂůĞƐ ĚƵ ƉĂƌĂůůĠůŽŐƌĂŵŵĞ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ >ĞƐ ĚŝĂŐŽŶĂůĞƐ ĚƵ ƌĞĐƚĂŶŐůĞ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

>ĞƐ ĚŝĂŐŽŶĂůĞƐ ĚƵ ůŽƐĂŶŐĞ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

>ĞƐ ĚŝĂŐŽŶĂůĞƐ ĚƵ ĐĂƌƌĠ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ 124

p.55 B

ACTIVITÉS

Chapitre 6 Figures planes

2 ŽŵƉůğƚĞ ůĞƐ ƉŚƌĂƐĞƐ͘ ͻ DĞƐ ĚŝĂŐŽŶĂůĞƐ ƐĞ ĐŽƵƉĞŶƚ ĞŶ ůĞƵƌ ŵŝůŝĞƵ Ğƚ ƐŽŶƚ ĚĞ ŵġŵĞ ůŽŶŐƵĞƵƌ͘ :Ğ ƐƵŝƐ ƵŶ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͻ DĞƐ ĚŝĂŐŽŶĂůĞƐ ƐĞ ĐŽƵƉĞŶƚ ƉĞƌƉĞŶĚŝĐƵůĂŝƌĞŵĞŶƚ ĞŶ ůĞƵƌ ŵŝůŝĞƵ͘ :Ğ ƐƵŝƐ ƵŶ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͻ DĞƐ ĚŝĂŐŽŶĂůĞƐ ƐĞ ĐŽƵƉĞŶƚ ĞŶ ůĞƵƌ ŵŝůŝĞƵ͘ :Ğ ƐƵŝƐ ƵŶ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͻ DĞƐ ĚŝĂŐŽŶĂůĞƐ ƐĞ ĐŽƵƉĞŶƚ ƉĞƌƉĞŶĚŝĐƵůĂŝƌĞŵĞŶƚ ĞŶ ůĞƵƌ ŵŝůŝĞƵ Ğƚ ƐŽŶƚ ĚĞ ŵġŵĞ ůŽŶŐƵĞƵƌ͘ :Ğ ƐƵŝƐ ƵŶ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ 3 ŽŶƐƚƌƵŝƐ ƵŶ ĐĂƌƌĠ͕ ƵŶ ůŽƐĂŶŐĞ͕ ƵŶ ƌĞĐƚĂŶŐůĞ Ğƚ ƵŶ ƉĂƌĂůůĠůŽŐƌĂŵŵĞ ĚŽŶƚ ΀ ΁ ĞƐƚ ƵŶĞ ĚŝĂŐŽŶĂůĞ ĚĞ ĐŚĂĐƵŶ ĚĞ ĐĞƐ ƋƵĂĚƌŝůĂƚğƌĞƐ͘ ĂƌƌĠ >ŽƐĂŶŐĞ ZĞĐƚĂŶŐůĞ WĂƌĂůůĠůŽŐƌĂŵŵĞ

ŽŵƉĂƌĞ ƚĞƐ ĚĞƐƐŝŶƐ ĂǀĞĐ ĐĞƵǆ ĚĞ ƚĞƐ ǀŽŝƐŝŶƐ͘ YƵĞů ĞƐƚ ůĞ ƐĞƵů ƋƵĂĚƌŝůĂƚğƌĞ ŝĚĞŶƟ ƋƵĞ ĐŚĞǌ ƚŽƵƐ ůĞƐ ĠůğǀĞƐ ͍ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

YƵĞů;ƐͿ ƌĞŶƐĞŝŐŶĞŵĞŶƚ;ƐͿ ƐƵƉƉůĠŵĞŶƚĂŝƌĞ;ƐͿ ĂƵ ƐƵũĞƚ ĚĞƐ ĚĞƵǆ ĚŝĂŐŽŶĂůĞƐ ĚĞǀĂŝƚͲŽŶ ĚŽŶŶĞƌ ƉŽƵƌ ƋƵĞ ƚŽƵƐ ůĞƐ ƋƵĂĚƌŝůĂƚğƌĞƐ ƐŽŝĞŶƚ ŝĚĞŶƟ ƋƵĞƐ ͍ ʹഩ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹഩ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

4 ΀ ΁ ĞƐƚ ƵŶĞ ĚŝĂŐŽŶĂůĞ ĚƵ ƌĞĐƚĂŶŐůĞ ͘ >Ă ĚŝĂŐŽŶĂůĞ ΀ ΁ ĨŽƌŵĞ ƵŶ ĂŶŐůĞ ĚĞ ϰϬΣ ĂǀĞĐ ůĂ ĚŝĂŐŽŶĂůĞ ΀ ΁͘ dĞƌŵŝŶĞ ůĂ ĐŽŶƐƚƌƵĐƟ ŽŶ ĚĞ ĐĞ ƌĞĐƚĂŶŐůĞ͘

΀ ΁ ĞƐƚ ůĂ ƉĞƟ ƚĞ ĚŝĂŐŽŶĂůĞ Ě͛ƵŶ ůŽƐĂŶŐĞ ĚŽŶƚ ůĂ ŐƌĂŶĚĞ ĚŝĂŐŽŶĂůĞ ĞƐƚ ĚĞƵǆ ĨŽŝƐ ƉůƵƐ ůŽŶŐƵĞ͘ dĞƌŵŝŶĞ ůĂ ĐŽŶƐƚƌƵĐƟ ŽŶ ĚĞ ĐĞ ůŽƐĂŶŐĞ͘

C 125

ACTIVITÉS

Chapitre 6 Figures planes

ĐƚŝǀŝƚĠ ϳ ĠĐŽƵǀĞƌƚĞ ĚĞƐ ƚƌŝĂŶŐůĞƐ 1 WĂƌƚĂŐĞ ůĞƐ ƋƵĂĚƌŝůĂƚğƌĞƐ ĐŝͲĚĞƐƐŽƵƐ ĚĞ ĚĞƵǆ ŵĂŶŝğƌĞƐ Ěŝī ĠƌĞŶƚĞƐ ƉŽƵƌ ŽďƚĞŶŝƌ ĚĞƵǆ ƚƌŝĂŶŐůĞƐ ĚĂŶƐ ĐŚĂƋƵĞ ƋƵĂĚƌŝůĂƚğƌĞ͘ ĂƌƌĠ

ZĞĐƚĂŶŐůĞ

C B

B C

C C

dƌĂƉğǌĞ

D A

WĂƌĂůůĠůŽŐƌĂŵŵĞ

>ŽƐĂŶŐĞ

B C

D A

ĂͿ WŽƵƌ ƋƵĞůƐ ƋƵĂĚƌŝůĂƚğƌĞƐ ůĞƐ ƋƵĂƚƌĞ ƚƌŝĂŶŐůĞƐ ŽďƚĞŶƵƐ ƐŽŶƚͲŝůƐ ĠŐĂƵǆ ͍ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ďͿ Ğ ƋƵĞůůĞ ŶĂƚƵƌĞ ĞƐƚ ůĞ ƚƌŝĂŶŐůĞ ĚĠƚĞƌŵŝŶĠ ƉĂƌ ůĂ ĚŝĂŐŽŶĂůĞ ΀ ΁ ĚƵ ĐĂƌƌĠ ͍ :ƵƐƟ Į Ğ ĞŶ ƵƟ ůŝƐĂŶƚ ůĞ ůĂŶŐĂŐĞ ŵĂƚŚĠŵĂƟ ƋƵĞ͘

C B D

>Ğ ƚƌŝĂŶŐůĞ ĞƐƚ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ car

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ĐͿ Ğ ƋƵĞůůĞ ŶĂƚƵƌĞ ĞƐƚ ůĞ ƚƌŝĂŶŐůĞ ĚĠƚĞƌŵŝŶĠ ƉĂƌ ůĂ ĚŝĂŐŽŶĂůĞ ΀ ΁ ĚƵ ƌĞĐƚĂŶŐůĞ ͍ :ƵƐƟ Į Ğ ĞŶ ƵƟ ůŝƐĂŶƚ ůĞ ůĂŶŐĂŐĞ ŵĂƚŚĠŵĂƟ ƋƵĞ͘

C B D

ĚͿ Ğ ƋƵĞůůĞ ŶĂƚƵƌĞ ĞƐƚ ůĞ ƚƌŝĂŶŐůĞ ĚĠƚĞƌŵŝŶĠ ƉĂƌ ůĂ ĚŝĂŐŽŶĂůĞ ΀ ΁ ĚƵ ůŽƐĂŶŐĞ ͍ :ƵƐƟ Į Ğ ĞŶ ƵƟ ůŝƐĂŶƚ ůĞ ůĂŶŐĂŐĞ ŵĂƚŚĠŵĂƟ ƋƵĞ͘

C B

>Ğ ƚƌŝĂŶŐůĞ ĞƐƚ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ car

ĞͿ Ğ ƋƵĞůůĞ ŶĂƚƵƌĞ ĞƐƚ ůĞ ƚƌŝĂŶŐůĞ ĚĠƚĞƌŵŝŶĠ ƉĂƌ ůĂ ĚŝĂŐŽŶĂůĞ ΀ ΁ ĚƵ ůŽƐĂŶŐĞ ͍ :ƵƐƟ Į Ğ ĞŶ ƵƟ ůŝƐĂŶƚ ůĞ ůĂŶŐĂŐĞ ŵĂƚŚĠŵĂƟ ƋƵĞ͘

A C B

>Ğ ƚƌŝĂŶŐůĞ ĞƐƚ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ car 126

ACTIVITÉS

Chapitre 6 Figures planes

2 ĂͿ dƌĂĐĞ ƵŶĞ ĚŝĂŐŽŶĂůĞ ĚĂŶƐ ĐŚĂƋƵĞ ƋƵĂĚƌŝůĂƚğƌĞ ĂĮ Ŷ ĚĞ ĨĂŝƌĞ ĂƉƉĂƌĂŠƚƌĞ ůĞƐ ƚƌŝĂŶŐůĞƐ ĚĞŵĂŶĚĠƐ͘ ŶƐƵŝƚĞ͕ ĐĂƌĂĐƚĠƌŝƐĞͲůĞƐ ƉĂƌ ĚĞƵǆ ƋƵĂůŝĮ ĐĂƟ ĨƐ͘ WĂƌĂůůĠůŽŐƌĂŵŵĞ dƌĂƉğǌĞ C

D B A

B A

͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ďͿ dŽƵƐ ůĞƐ ƋƵĂůŝĮ ĐĂƟ ĨƐ ƌĞůĂƟ ĨƐ ĂƵǆ ƚƌŝĂŶŐůĞƐ Ŷ͛ŽŶƚ ƉĂƐ ĠƚĠ ƵƟ ůŝƐĠƐ ĚĂŶƐ ůĞƐ ĞǆĞƌĐŝĐĞƐ ƉƌĠĐĠĚĞŶƚƐ͘

ŽŶƐƚƌƵŝƐ ĐĞ ƋƵĂĚƌŝůĂƚğƌĞ͘

/ů ĞŶ ŵĂŶƋƵĞ ƵŶ͘ >ĞƋƵĞů ͍ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ YƵĞů ƋƵĂĚƌŝůĂƚğƌĞ ĂƵƌĂŝƚ ƉƵ ŶŽƵƐ ĚŽŶŶĞƌ ĚĞƵǆ ƚƌŝĂŶŐůĞƐ ĚĞ ĐĞ ƚǇƉĞ ͍

3 ŽŵƉůğƚĞ ůĞƐ Ɵ ƚƌĞƐ ĚĞƐ ůŝŐŶĞƐ Ğƚ ĚĞƐ ĐŽůŽŶŶĞƐ ĚƵ ƚĂďůĞĂƵ ĐŝͲĚĞƐƐŽƵƐ ĞŶ ƵƟ ůŝƐĂŶƚ ĚĞƐ ĂĚũĞĐƟ ĨƐ ƋƵĂůŝĮ ĐĂƟ ĨƐ͘ /ŶĚŝƋƵĞ ůĞ ŶƵŵĠƌŽ ĚĞ ĐŚĂƋƵĞ ƚƌŝĂŶŐůĞ ĚƵ ĚĞƐƐŝŶ ĚĂŶƐ ůĂ ďŽŶŶĞ ĐĂƐĞ ĚƵ ƚĂďůĞĂƵ Ɛŝ ƚƵ ƐĂŝƐ ƋƵĞ ůĞƐ ƐĞŐŵĞŶƚƐ ĚĞ ŵġŵĞ ĐŽƵůĞƵƌ ;ĞǆĐĞƉƚĠ ůĞƐ ŶŽŝƌƐͿ ŽŶƚ ůĂ ŵġŵĞ ůŽŶŐƵĞƵƌ͘ CÔTÉS

1 2

dƌŝĂŶŐůĞ

4 7

ANGLES

5 6

p.56 D1

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

4 dƌĂĚƵŝƐ ĞŶ ůĂŶŐĂŐĞ ŵĂƚŚĠŵĂƟ ƋƵĞ ĐĞ ƋƵĞ ůĞ ĚĞƐƐŝŶ ƚĞ ŵŽŶƚƌĞ Ğƚ ĚŽŶŶĞ ůĂ ŶĂƚƵƌĞ ĚĞ ĐŚĂƋƵĞ ƚƌŝĂŶŐůĞ͘ D K I C B F L A

p.62

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

127

ACTIVITÉS

Chapitre 6 Figures planes

ĐƚŝǀŝƚĠ ϴ ŽŶƐƚƌƵĐƚŝŽŶƐ ĚĞ ƚƌŝĂŶŐůĞƐ ƐĂŶƐ ŵĞƐƵƌĞƐ 1

2 ^Ƶƌ ůĞ ƋƵĂĚƌŝůůĂŐĞ͕ ĐŽŶƐƚƌƵŝƐ ͘͘͘ ĂͿ ůĞ ƚƌŝĂŶŐůĞ ŝƐŽĐğůĞ ĂĐƵƚĂŶŐůĞ ĞŶ ͘ ďͿ ůĞ ƚƌŝĂŶŐůĞ ŝƐŽĐğůĞ ƌĞĐƚĂŶŐůĞ ĞŶ ͘ ĐͿ ůĞ ƚƌŝĂŶŐůĞ ŝƐŽĐğůĞ ŽďƚƵƐĂŶŐůĞ ĞŶ ͘

Ŷ ƵƟ ůŝƐĂŶƚ ů͛ĂƌĐ ĚĞ ĐĞƌĐůĞ Ğƚ ůĞ ƐĞŐŵĞŶƚ ΀ ΁ ĚĠũă ƌĞƉƌĠƐĞŶƚĠ͕ ĐŽŶƐƚƌƵŝƐ ͘͘͘ ĂͿ ůĞ ƚƌŝĂŶŐůĞ ĠƋƵŝůĂƚĠƌĂů͘ ďͿ ůĞ ƚƌŝĂŶŐůĞ ŝƐŽĐğůĞ ƌĞĐƚĂŶŐůĞ ĞŶ ͘ ĐͿ ůĞ ƚƌŝĂŶŐůĞ ĂĐƵƚĂŶŐůĞ Ğƚ ŝƐŽĐğůĞ ĞŶ ͘ ĚͿ ůĞ ƚƌŝĂŶŐůĞ & ŝƐŽĐğůĞ ŽďƚƵƐĂŶŐůĞ ĞŶ ͘

3 ŽŶƐƚƌƵŝƐ ƵŶ ƚƌŝĂŶŐůĞ ĂĐƵƚĂŶŐůĞ Ğƚ ŝƐŽĐğůĞ ĞŶ ͘͘͘ ĂͿ ĂǀĞĐ ƵŶĞ ĠƋƵĞƌƌĞ ƌŝƐƚŽ͘ ďͿ ĂǀĞĐ ƵŶ ĐŽŵƉĂƐ͘

ĐͿ ĂǀĞĐ ƵŶ ĐŽŵƉĂƐ͘

p.57 D2

A B

ĐƚŝǀŝƚĠ ϵ ŽŶƐƚƌƵĐƚŝŽŶƐ ĚĞ ƚƌŝĂŶŐůĞƐ ĂǀĞĐ ŵĞƐƵƌĞƐ 1 dƌŽŝƐ ĐƀƚĠƐ ^ƵŝƐ ƐĐƌƵƉƵůĞƵƐĞŵĞŶƚ ůĞƐ ĐŽŶƐŝŐŶĞƐ͘ ͻ dƌĂĐĞ ƵŶ ƐĞŐŵĞŶƚ ĚĞ ϲ Đŵ͘ ͻ EŽŵŵĞ ƐĞƐ ĞǆƚƌĠŵŝƚĠƐ Ğƚ ͘ ͻ ŽŶƐƚƌƵŝƐ ƵŶ ĂƌĐ ĚĞ ĐĞƌĐůĞ ĚĞ ĐĞŶƚƌĞ Ğƚ ĚĞ ϰ Đŵ ĚĞ ƌĂǇŽŶ͘ ͻ ŽŶƐƚƌƵŝƐ ƵŶ ĂƌĐ ĚĞ ĐĞƌĐůĞ ĚĞ ĐĞŶƚƌĞ Ğƚ ĚĞ ϱ Đŵ ĚĞ ƌĂǇŽŶ͘ ͻ >ĞƐ ĚĞƵǆ ĂƌĐƐ ĚĞ ĐĞƌĐůĞ ƐĞ ĐŽƵƉĞŶƚ ĞŶ ƵŶ ƉŽŝŶƚ͖ ŶŽŵŵĞͲůĞ ͘ ͻ dĞƌŵŝŶĞ ůĞ ƚƌŝĂŶŐůĞ ͘ >Ğ ƚƌŝĂŶŐůĞ ĞƐƚ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ et ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ 128

ACTIVITÉS

Chapitre 6 Figures planes

2 ĞƵǆ ĐƀƚĠƐ Ğƚ ů͛ĂŶŐůĞ ĐŽŵƉƌŝƐ ĞŶƚƌĞ ĐĞƐ ĚĞƵǆ ĐƀƚĠƐ ^ƵŝƐ ƐĐƌƵƉƵůĞƵƐĞŵĞŶƚ ůĞƐ ĐŽŶƐŝŐŶĞƐ͘ ͻ dƌĂĐĞ ƵŶ ƐĞŐŵĞŶƚ ĚĞ ϯϱ ŵŵ͘ ͻ EŽŵŵĞ ƐĞƐ ĞǆƚƌĠŵŝƚĠƐ Ğƚ ͘ ͻ ŽŶƐƚƌƵŝƐ ƵŶ ĂŶŐůĞ ĚĞ ϳϬΣ ĚŽŶƚ ůĞ ƐŽŵŵĞƚ ĞƐƚ ůĞ ƉŽŝŶƚ Ğƚ ĚŽŶƚ ƵŶ ĐƀƚĠ ĞƐƚ ůĂ ĚĞŵŝͲĚƌŽŝƚĞ ΀ ͘ ͻ ^Ƶƌ ůĞ ĚĞƵǆŝğŵĞ ĐƀƚĠ ĚĞ ů͛ĂŶŐůĞ͕ ĐŽŶƐƚƌƵŝƐ ƵŶ ƐĞŐŵĞŶƚ ΀ ΁ ĚĞ ϰϬ ŵŵ͘ ͻ dĞƌŵŝŶĞ ůĞ ƚƌŝĂŶŐůĞ ͘ >Ğ ƚƌŝĂŶŐůĞ ĞƐƚ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ et ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ 3 hŶ ĐƀƚĠ Ğƚ ůĞƐ ĚĞƵǆ ĂŶŐůĞƐ ĂĚũĂĐĞŶƚƐ ă ĐĞ ĐƀƚĠ ^ƵŝƐ ƐĐƌƵƉƵůĞƵƐĞŵĞŶƚ ůĞƐ ĐŽŶƐŝŐŶĞƐ͘ ͻ dƌĂĐĞ ƵŶ ƐĞŐŵĞŶƚ ĚĞ ϰϱ ŵŵ͘ ͻ EŽŵŵĞ ƐĞƐ ĞǆƚƌĠŵŝƚĠƐ Ğƚ ͘ ͻ ŽŶƐƚƌƵŝƐ ƵŶ ĂŶŐůĞ ĚĞ ϰϬΣ ĚŽŶƚ ůĞ ƐŽŵŵĞƚ ĞƐƚ ůĞ ƉŽŝŶƚ Ğƚ ĚŽŶƚ ƵŶ ĐƀƚĠ ĞƐƚ ůĂ ĚĞŵŝͲĚƌŽŝƚĞ ΀ ͖ ƚƵ ǀŝĞŶƐ ĚĞ ƚƌĂĐĞƌ ůĂ ĚĞŵŝͲĚƌŽŝƚĞ ΀ y͘ ͻ ŽŶƐƚƌƵŝƐ ƵŶ ĂŶŐůĞ ĚĞ ϴϬΣ ĚŽŶƚ ůĞ ƐŽŵŵĞƚ ĞƐƚ ůĞ ƉŽŝŶƚ Ğƚ ĚŽŶƚ ƵŶ ĐƀƚĠ ĞƐƚ ůĂ ĚĞŵŝͲĚƌŽŝƚĞ ΀ ͖ ƚƵ ǀŝĞŶƐ ĚĞ ƚƌĂĐĞƌ ůĂ ĚĞŵŝͲĚƌŽŝƚĞ ΀ z͘ ͻ >ĞƐ ĚĞŵŝͲĚƌŽŝƚĞƐ ΀ y Ğƚ ΀ z ƐĞ ĐŽƵƉĞŶƚ ĂƵ ƉŽŝŶƚ ͘ >Ğ ƚƌŝĂŶŐůĞ ĞƐƚ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ et ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

4 >ĞƐ ƚƌŝĂŶŐůĞƐ ĐŝͲĚĞƐƐŽƵƐ ŽŶƚ ĠƚĠ ĚĞƐƐŝŶĠƐ ă ŵĂŝŶ ůĞǀĠĞ͘ ZĞƉƌŽĚƵŝƐͲůĞƐ ĞŶ ƌĞƐƉĞĐƚĂŶƚ ůĞƐ ŵĞƐƵƌĞƐ͘ ĂͿ

ďͿ

ĐͿ

ϯ Đŵ

ϰϬΣ

ϯ Đ

ϱϰΣ

ϱ Đŵ

ϱ Đ

ϰ Đ

ϯϱΣ ϲ Đŵ

129

ACTIVITÉS

Chapitre 6 Figures planes

ĐƚŝǀŝƚĠ ϭϬ ƌŽŝƚĞƐ ƌĞŵĂƌƋƵĂďůĞƐ ĚĞƐ ƚƌŝĂŶŐůĞƐ 1 d2

ĠƚĞƌŵŝŶĞ ůĞƐ ĐĂƌĂĐƚĠƌŝƐƟ ƋƵĞƐ ĚĞƐ ĚƌŽŝƚĞƐ Ěϭ Ğƚ Ě2 ĚƵ ƚƌŝĂŶŐůĞ ĐŝͲĐŽŶƚƌĞ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ĠƚĞƌŵŝŶĞ ůĞƐ ĐĂƌĂĐƚĠƌŝƐƟ ƋƵĞƐ ĚĞƐ ĚƌŽŝƚĞƐ Ě3 Ğƚ Ě4 ĚƵ ƚƌŝĂŶŐůĞ ĐŝͲĐŽŶƚƌĞ͘

d3 p.59 E1

2 Ŷ ƵƟ ůŝƐĂŶƚ ƵŶĞ ƐĞƵůĞ ĨŽŝƐ ĐŚĂĐƵŶ ĚĞƐ ŵŽƚƐ ͨ ŚĂƵƚĞƵƌ ͕ͩ ͨ ŵĠĚŝĂŶĞ ͕ͩ ͨ ŵĠĚŝĂƚƌŝĐĞ ͩ Ğƚ ͨ ďŝƐƐĞĐƚƌŝĐĞ ͕ͩ ĐŽŵƉůğƚĞ ůĞƐ ƉŚƌĂƐĞƐ ĐŝͲĚĞƐƐŽƵƐ͘

>Ă ĚƌŽŝƚĞ , ĞƐƚ ƵŶĞ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ĚƵ ƚƌŝĂŶŐůĞ &͘

E H

>Ă ĚƌŽŝƚĞ : ĞƐƚ ƵŶĞ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ĚƵ ƚƌŝĂŶŐůĞ &͘

>Ă ĚƌŽŝƚĞ ', ĞƐƚ ƵŶĞ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ĚƵ ƚƌŝĂŶŐůĞ &,͘ >Ă ĚƌŽŝƚĞ & ĞƐƚ ƵŶĞ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ĚƵ ƚƌŝĂŶŐůĞ &͘

3 ĂͿ ŽŶƐƚƌƵŝƐ ůĂ ŵĠĚŝĂƚƌŝĐĞ ĚƵ ƐĞŐŵĞŶƚ ΀ ΁ ͘͘͘ ĂǀĞĐ ƵŶĞ ůĂƩ Ğ Ğƚ ƵŶĞ ĠƋƵĞƌƌĞ͘

ĂǀĞĐ ƵŶ ĐŽŵƉĂƐ͘ A

B ͘͘͘ ďͿ ŽŶƐƚƌƵŝƐ ůĂ ďŝƐƐĞĐƚƌŝĐĞ ĚĞ ů͛ĂŶŐůĞ AOB ĂǀĞĐ ƵŶĞ ůĂƩ Ğ Ğƚ ƵŶ ƌĂƉƉŽƌƚĞƵƌ͘

ĂǀĞĐ ƵŶ ĐŽŵƉĂƐ͘

O 130

p.60 E2

p.59 E2

ACTIVITÉS

Chapitre 6 Figures planes

4 WŽƵƌ ƋƵĞů ƚǇƉĞ ĚĞ ƚƌŝĂŶŐůĞ ůĞ ƉŽŝŶƚ Ě͛ŝŶƚĞƌƐĞĐƟ ŽŶ ;yͿ ĚĞƐ ďŝƐƐĞĐƚƌŝĐĞƐ ;ďϭ͕ ď2 Ğƚ ď3Ϳ ĚƵ ƚƌŝĂŶŐůĞ ĂƉƉĂƌƟ ĞŶĚƌĂͲƚͲŝů ă ƵŶĞ ĚĞƐ ŵĠĚŝĂƚƌŝĐĞƐ ;ŵϭ͕ ŵ2 ŽƵ ŵ3Ϳ ͍

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

b3 Y

WŽƵƌ ƋƵĞů ƚǇƉĞ ĚĞ ƚƌŝĂŶŐůĞ͕ ůĞƐ ƉŽŝŶƚƐ Ě͛ŝŶƚĞƌƐĞĐƟ ŽŶ ĚĞƐ ŵĠĚŝĂƚƌŝĐĞƐ Ğƚ ĚĞƐ ďŝƐƐĞĐƚƌŝĐĞƐ ƐĞƌŽŶƚͲŝůƐ ĐŽŶĨŽŶĚƵƐ ͍

b1 X b2

5 ĂŶƐ ĐŚĂƋƵĞ ĐĂƐ͕ ƚƌĂĐĞ ůĂ ŚĂƵƚĞƵƌ ŝƐƐƵĞ ĚƵ ƐŽŵŵĞƚ ͘

➂ C

➀

➁

A A

B C

➃

➄

A C

➅ C

➆ C

C A

➇ C

➈ A

➉ A

B C

B 131

ACTIVITÉS

Chapitre 6 Figures planes

6 WƌĠĐŝƐĞ͕ ĞŶ ĐŽŵƉůĠƚĂŶƚ ůĞ ƚĂďůĞĂƵ͕ ůĂ ƉŽƐŝƟ ŽŶ ĚƵ ƉŽŝŶƚ Ě͛ŝŶƚĞƌƐĞĐƟ ŽŶ ĚĞƐ ĚƌŽŝƚĞƐ ƌĞŵĂƌƋƵĂďůĞƐ ĚƵ ƚƌŝĂŶŐůĞ ĞŶ ĨŽŶĐƟ ŽŶ ĚĞ ƐĂ ŶĂƚƵƌĞ͘

>ĞƐ ŚĂƵƚĞƵƌƐ

>ĞƐ ŵĠĚŝĂŶĞƐ

>ĞƐ ďŝƐƐĞĐƚƌŝĐĞƐ

dƌŝĂŶŐůĞ ĂĐƵƚĂŶŐůĞ

dƌŝĂŶŐůĞ ƌĞĐƚĂŶŐůĞ

dƌŝĂŶŐůĞ ŽďƚƵƐĂŶŐůĞ

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ă ů͛ŝŶƚĠƌŝĞƵƌ ĚƵ ƚƌŝĂŶŐůĞ͘

>Ğ ƉŽŝŶƚ Ě͛ŝŶƚĞƌƐĞĐƟ ŽŶ ĚĞƐ ŵĠĚŝĂƚƌŝĐĞƐ ĞƐƚ ͙

ă ů͛ŝŶƚĠƌŝĞƵƌ ĚƵ ƚƌŝĂŶŐůĞ͘

>Ğ ƉŽŝŶƚ Ě͛ŝŶƚĞƌƐĞĐƟ ŽŶ ĚĞƐ ďŝƐƐĞĐƚƌŝĐĞƐ ĞƐƚ ͙

>ĞƐ ŵĠĚŝĂƚƌŝĐĞƐ

>Ğ ƉŽŝŶƚ Ě͛ŝŶƚĞƌƐĞĐƟ ŽŶ ĚĞƐ ŚĂƵƚĞƵƌƐ ĞƐƚ ͙

>Ğ ƉŽŝŶƚ Ě͛ŝŶƚĞƌƐĞĐƟ ŽŶ ĚĞƐ ŵĠĚŝĂŶĞƐ ĞƐƚ ͙

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ă ů͛ŝŶƚĠƌŝĞƵƌ ĚƵ ƚƌŝĂŶŐůĞ͘

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ă ů͛ŝŶƚĠƌŝĞƵƌ ĚƵ ƚƌŝĂŶŐůĞ͘

7 ĞƐƚ ƵŶ ƚƌŝĂŶŐůĞ ƌĞĐƚĂŶŐůĞ ĞŶ ͘ dƌĂĐĞ ůĂ ŵĠĚŝĂŶĞ D Ğƚ ĐŽŵƉůğƚĞ ůĞ ƚĞǆƚĞ ĐŝͲĚĞƐƐŽƵƐ͘ + |AMBͮ с B |AMC| ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ et AMB ĨŽƌŵĞŶƚ ƵŶ ĂŶŐůĞ >ĞƐ ĂŶŐůĞƐ AMC ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ /ůƐ ƐŽŶƚ ĂƉƉĞůĠƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ + |MACͮ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ |BAM| et MAC ĨŽƌŵĞŶƚ ƵŶ ĂŶŐůĞ >ĞƐ ĂŶŐůĞƐ BAM ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ /ůƐ ƐŽŶƚ ĂƉƉĞůĠƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

p.60 G - 61

ĐƚŝǀŝƚĠ ϭϭ &ŝŐƵƌĞƐ ŝŶƐĐƌŝƚĞƐ ĚĂŶƐ ƵŶ ĐĞƌĐůĞ 1 ŽŶƐƚƌƵŝƐ ƵŶ ĐĂƌƌĠ ĚŽŶƚ ůĞƐ ƋƵĂƚƌĞ ƐŽŵŵĞƚƐ ĂƉƉĂƌƟ ĞŶŶĞŶƚ ĂƵ ĐĞƌĐůĞ ĚĞ ĐĞŶƚƌĞ K͘ ŶƐƵŝƚĞ͕ ĐŽŶƐƚƌƵŝƐ ƵŶ ŽĐƚŽŐŽŶĞ ƌĠŐƵůŝĞƌ & ' , ŝŶƐĐƌŝƚ ĂƵ ĐĞƌĐůĞ Ğƚ ĐŽŵƉůğƚĞ ůĞƐ ƉŚĂƐĞƐ ĐŝͲĚĞƐƐŽƵƐ͘

>Ğ ĐĂƌƌĠ ĞƐƚ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ĂƵ ĐĞƌĐůĞ͘ Le cercle est ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ĂƵ ĐĂƌƌĠ ͘

132

p.60

ACTIVITÉS

Chapitre 6 Figures planes

2 Ŷ ƵƟ ůŝƐĂŶƚ ƵŶŝƋƵĞŵĞŶƚ ƚŽŶ ĐŽŵƉĂƐ͕ ĚĠƚĞƌŵŝŶĞ ůĞƐ ƐŽŵŵĞƚƐ ͕ ͕ ͕ Ğƚ & ĚĞ ůĂ ƐĞĐŽŶĚĞ ƌŽƐĂĐĞ͘ F A A E

O D

dƌĂĐĞ ůĞ ƉŽůǇŐŽŶĞ &͘ Ğ ƉŽůǇŐŽŶĞ ĐŽŵƉƚĞ ͘ ͘ ͘ ͘ ͘ ͘ ĐƀƚĠƐ͕ ŝů Ɛ͛ĂŐŝƚ Ě͛ƵŶ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ Ğ ƋƵĞůůĞ ŶĂƚƵƌĞ ĞƐƚ ůĞ ƚƌŝĂŶŐůĞ ͍ :ƵƐƟ Į Ğ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ĐƚŝǀŝƚĠ ϭϮ WƌŽďůğŵĞƐ ĚĞ ƉĠƌŝŵğƚƌĞƐ Ğƚ Ě͛ĂŝƌĞƐ 1

ĂŶƐ ĐŚĂƋƵĞ ĐĂƐ͕ ĐŽůŽƌŝĞ ĚĂŶƐ ůĂ ŵġŵĞ ĐŽƵůĞƵƌ ůĞƐ ƉŽůǇŐŽŶĞƐ ĚĞ ŵġŵĞ ĂŝƌĞ͘ ĂͿ

ďͿ

p.61 H

2 >Ğ ƋƵĂĚƌŝůĂƚğƌĞ ĞƐƚ ƵŶ ƌĞĐƚĂŶŐůĞ͘ ŽŵƉĂƌĞ ů͛ĂŝƌĞ ĚĞƐ ƚƌŝĂŶŐůĞƐ ϭ Ğƚ Ϯ͘ :ƵƐƟ Į Ğ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

2 E

C 133

ACTIVITÉS

Chapitre 6 Figures planes

3 DĂŶŽŶ ĚŽŝƚ ĞŵďĂůůĞƌ ƵŶ ĐĂĚĞĂƵ ƉŽƵƌ ů͛ĂŶŶŝǀĞƌƐĂŝƌĞ ĚĞ ƐŽŶ ŐƌĂŶĚͲƉğƌĞ͕ ŵĂŝƐ ĞůůĞ ŶĞ ĚŝƐƉŽƐĞ ƋƵĞ ĚĞ ϯ ŵ ĚĞ ĐŽƌĚŽŶŶĞƚ͘ Ŷ ƚĞŶĂŶƚ ĐŽŵƉƚĞ ƋƵ͛ŝů ůƵŝ ĨĂƵƚ ϯϬ Đŵ ĚĞ ĐŽƌĚŽŶŶĞƚ ƉŽƵƌ ƌĠĂůŝƐĞƌ ůĞ ŶƈƵĚ͕ ĞůůĞ ƐĞ ĚĞŵĂŶĚĞ ƋƵĞů ƚǇƉĞ Ě͛ĞŵďĂůůĂŐĞ ĞůůĞ ǀĂ ƵƟ ůŝƐĞƌ͘ ŝĚĞͲůĂ ĚĂŶƐ ƐŽŶ ĐŚŽŝǆ͘ >ĞƐ ĚŝŵĞŶƐŝŽŶƐ ĚƵ ƉĂƋƵĞƚ ƐŽŶƚ ͗ ŚĂƵƚĞƵƌ ϮϬ Đŵ͕ ůĂƌŐĞƵƌ ϯϬ Đŵ Ğƚ ůŽŶŐƵĞƵƌ ϲϬ Đŵ͘

4 hŶ ũĂƌĚŝŶ ĂǇĂŶƚ ůĂ ĨŽƌŵĞ Ě͛ƵŶ ƉĂƌĂůůĠůŽŐƌĂŵŵĞ ĞƐƚ ĐŽƵƉĠ ƉĂƌ ĚĞƵǆ ĂůůĠĞƐ͘

ĂůĐƵůĞ ů͛ĂŝƌĞ ƚŽƚĂůĞ ĚĞƐ ĂůůĠĞƐ Ğƚ ĐĞůůĞ ĚĞƐ ƋƵĂƚƌĞ ƉĞůŽƵƐĞƐ ƌĠƵŶŝĞƐ͘

8 A

B 8 32

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

D 50

5 hŶ ĠƚĂŶŐ ĐŝƌĐƵůĂŝƌĞ ĚĞ ϰ ŵ ĚĞ ƌĂǇŽŶ ĞƐƚ ďŽƌĚĠ ƉĂƌ ƵŶĞ ĂůůĠĞ ĚĞ Ϯ ŵ ĚĞ ůĂƌŐĞ͕ ůĞ ƚŽƵƚ ĠƚĂŶƚ ĐůƀƚƵƌĠ ƉĂƌ ƵŶ ƚƌĞŝůůŝƐ͘ ĂͿ ŽŵƉůğƚĞ ůĂ Į ŐƵƌĞ ĐŝͲĐŽŶƚƌĞ ĞŶ ƚƌĂĕĂŶƚ ůΖĂůůĠĞ ă ůΖĠĐŚĞůůĞ͘ ďͿ /ŶĚŝƋƵĞ ůĞƐ ĚŽŶŶĠĞƐ ĚƵ ƉƌŽďůğŵĞ ƐƵƌ ĐĞƩ Ğ Į ŐƵƌĞ͘ ĐͿ ,ĂĐŚƵƌĞ ůĂ ƐƵƌĨĂĐĞ ĚĞ ů͛ĂůůĠĞ͘ ĚͿ ĂůĐƵůĞ ů͛ĂŝƌĞ ĚĞ ĐĞƩ Ğ ĂůůĠĞ͘ ĞͿ ĂůĐƵůĞ ůĂ ůŽŶŐƵĞƵƌ ĚƵ ƚƌĞŝůůŝƐ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

6 ĂůĐƵůĞ ůĞ ƉĠƌŝŵğƚƌĞ Ğƚ ů͛ĂŝƌĞ ĚĞ ůĂ Į ŐƵƌĞ ĐŝͲĐŽŶƚƌĞ ƐĂĐŚĂŶƚ ƋƵĞ ůĞƐ ƋƵĂƚƌĞ ƌĂǇŽŶƐ Ğƚ ůĞƐ ƋƵĂƚƌĞ ƐĞŐŵĞŶƚƐ ŵĞƐƵƌĞŶƚ Ϯ Đŵ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

134

2 cm

Chapitre 6 Figures planes

ACTIVITÉS

7 hŶ ŵĞŶƵŝƐŝĞƌ Ă ƵƟ ůŝƐĠ ϭϴ ŵğƚƌĞƐ ĚĞ ƉůŝŶƚŚĞƐ ĞŶ ďŽŝƐ ƉŽƵƌ ƚĞƌŵŝŶĞƌ ů͛ŝŶƐƚĂůůĂƟ ŽŶ ĚƵ ƉůĂŶĐŚĞƌ Ě͛ƵŶĞ ƐĂůůĞ ĚĞ ũĞƵǆ͘ ĞƩ Ğ ƉŝğĐĞ ĞƐƚ ĚĞ ĨŽƌŵĞ ĐĂƌƌĠĞ Ğƚ ƉŽƐƐğĚĞ ĚĞƵǆ ƉŽƌƚĞƐ Ě͛ĂĐĐğƐ ĚĞ ϭ ŵğƚƌĞ ĚĞ ůĂƌŐĞ͘ ĂͿ YƵĞůůĞ ƐƵƌĨĂĐĞ ĚĞ ƉĂƌƋƵĞƚ ůĞ ŵĞŶƵŝƐŝĞƌ ĂͲƚͲŝů ŝŶƐƚĂůůĠĞ ͍ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ZĠĂůŝƐĞ ƵŶ ĐƌŽƋƵŝƐ ĚĞ ůĂ ƐŝƚƵĂƟ ŽŶ͘

ďͿ sŽŝĐŝ ůĞƐ ĚĞƵǆ ĚĞǀŝƐ ƉƌŽƉŽƐĠƐ ƉĂƌ ůĞ ŵĞŶƵŝƐŝĞƌ ͗ Devis A Wƌŝǆ ĚƵ ƉĂƌƋƵĞƚ ͗ ϰϵ €ͬŵ2 Wƌŝǆ ĚĞ ůĂ ƉŽƐĞ ĚƵ ƉĂƌƋƵĞƚ ͗ Ϯϰ €ͬŵ2 >ĞƐ ƉůŝŶƚŚĞƐ Ğƚ ůĞƵƌ ƉŽƐĞ ƐŽŶƚ Žī ĞƌƚĞƐ͘

ĞǀŝƐ Wƌŝǆ ĚƵ ƉĂƌƋƵĞƚ ͗ ϱϵ €ͬŵ2 Wƌŝǆ ĚĞƐ ƉůŝŶƚŚĞƐ ͗ ϴ €ͬŵ hŶ ĨŽƌĨĂŝƚ ĚĞ ϭϱϬ € ĞƐƚ ĚĞŵĂŶĚĠ ƉŽƵƌ ůĂ ƉŽƐĞ ĚƵ ƉĂƌƋƵĞƚ Ğƚ ĚĞƐ ƉůŝŶƚŚĞƐ͘

>ĞƋƵĞů ĞƐƚ ůĞ ƉůƵƐ ĠĐŽŶŽŵŝƋƵĞ ͍ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

8 hŶ ĨĞƌŵŝĞƌ ƉŽƐƐğĚĞ ƵŶĞ ƉƌĂŝƌŝĞ ĐĂƌƌĠĞ ĚĞ ϭϱϬ ŵ ĚĞ ĐƀƚĠ ĐůƀƚƵƌĠĞ ƉĂƌ ƚƌŽŝƐ ƌĂŶŐĠĞƐ ĚĞ Į ů ďĂƌďĞůĠ͘ ^ƵŝƚĞ ă ƵŶĞ ŵŽĚŝĮ ĐĂƟ ŽŶ ĚƵ ƉůĂŶ ĚĞ ů͛ĂŵĠŶĂŐĞŵĞŶƚ ĚƵ ƚĞƌƌŝƚŽŝƌĞ͕ ƐŽŶ ƚĞƌƌĂŝŶ Ă ĠƚĠ ƌĞĚĠĐŽƵƉĠ Ğƚ ƐĞ ƉƌĠƐĞŶƚĞ ŵĂŝŶƚĞŶĂŶƚ ƐŽƵƐ ůĂ ĨŽƌŵĞ Ě͛ƵŶ ƌĞĐƚĂŶŐůĞ͘ ^ŝ ƚƵ ƐĂŝƐ ƋƵĞ ůĞ ŶŽƵǀĞĂƵ ƚĞƌƌĂŝŶ Ă ůĂ ŵġŵĞ ĂŝƌĞ ƋƵĞ ůĞ ƉƌĠĐĠĚĞŶƚ Ğƚ ƋƵĞ ƐĂ ůĂƌŐĞƵƌ ŵĞƐƵƌĞ ϭϬϬ ŵ͕ ĚĠƚĞƌŵŝŶĞ ůĂ ůŽŶŐƵĞƵƌ ĚƵ ŶŽƵǀĞĂƵ ƚĞƌƌĂŝŶ ĂŝŶƐŝ ƋƵĞ ůĂ ƋƵĂŶƟ ƚĠ ĚĞ Į ů ďĂƌďĞůĠ ƋƵĞ ůĞ ĨĞƌŵŝĞƌ ĚĞǀƌĂ ĂĐŚĞƚĞƌ ƉŽƵƌ ůĞ ĐůƀƚƵƌĞƌ Ɛ͛ŝů ƌĠĐƵƉğƌĞ ůĞ Į ů ĚĞ ů͛ĂŶĐŝĞŶ ƚĞƌƌĂŝŶ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ZĠĂůŝƐĞ ƵŶ ĐƌŽƋƵŝƐ ĚĞ ůĂ ƐŝƚƵĂƟ ŽŶ͘

........................................................................................................................................................

135

EXERCICES COMPLÉMENTAIRES

Chapitre 6 Figures planes

ŽŶŶĂŠƚƌĞ 1

ŽŶŶĞ ůĂ ŶĂƚƵƌĞ ĚĞƐ ƋƵĂĚƌŝůĂƚğƌĞƐ ƋƵŝ ĐŽŵƉŽƐĞŶƚ ůĞ ͨ ĐĂŶĂƌĚ ƐƚǇůŝƐĠ ͩ͘

ŽŶŶĞ ůĂ ŶĂƚƵƌĞ ĚĞƐ ƚƌŝĂŶŐůĞƐ ƋƵŝ ĐŽŵƉŽƐĞŶƚ ůĞ ͨ ĐŚŝĞŶ ƐƚǇůŝƐĠ ͩ͘

3 1

2 4

5 4

6 9

10 11

13 15

8 12

ŽŵƉůğƚĞ͘ ĂͿ hŶ ƌĞĐƚĂŶŐůĞ ƋƵŝ ƉŽƐƐğĚĞ ĚĞƐ ĐƀƚĠƐ ĚĞ ŵġŵĞ ůŽŶŐƵĞƵƌ ĞƐƚ ƵŶ ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ďͿ hŶ ƉĂƌĂůůĠůŽŐƌĂŵŵĞ ƋƵŝ ƉŽƐƐğĚĞ ƵŶ ĂŶŐůĞ ĚƌŽŝƚ ĞƐƚ ƵŶ ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ĐͿ hŶ ůŽƐĂŶŐĞ ƋƵŝ ƉŽƐƐğĚĞ ƵŶ ĂŶŐůĞ ĚƌŽŝƚ ĞƐƚ ƵŶ ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ĚͿ hŶ ƉĂƌĂůůĠůŽŐƌĂŵŵĞ ƋƵŝ ƉŽƐƐğĚĞ ĚĞƐ ĐƀƚĠƐ ĚĞ ŵġŵĞ ůŽŶŐƵĞƵƌ ĞƐƚ ƵŶ ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ĞͿ hŶ ƚƌŝĂŶŐůĞ ŝƐŽĐğůĞ ƋƵŝ ƉŽƐƐğĚĞ ƵŶ ĂŶŐůĞ ŽďƚƵƐ ĞƐƚ ĂƵƐƐŝ ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ĨͿ hŶ ƚƌŝĂŶŐůĞ ƌĞĐƚĂŶŐůĞ ƋƵŝ ƉŽƐƐğĚĞ ĚĞƵǆ ĐƀƚĠƐ ĚĞ ŵġŵĞ ůŽŶŐƵĞƵƌ ĞƐƚ ĚĞ ƉůƵƐ ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘

ĐƌŝƐ ĞŶ ůĂŶŐĂŐĞ ŵĂƚŚĠŵĂƚŝƋƵĞ ĐĞ ƋƵĞ ƚƵ ƉĞƵǆ ĚĠĚƵŝƌĞ ĚĞƐ ĂĨĨŝƌŵĂƚŝŽŶƐ ƐƵŝǀĂŶƚĞƐ͘ ĂͿ dƵ ƐĂŝƐ ƋƵĞ ůĞ ƚƌŝĂŶŐůĞ ĞƐƚ ƌĞĐƚĂŶŐůĞ ĞŶ ͘ ďͿ dƵ ƐĂŝƐ ƋƵĞ ůĞ ƚƌŝĂŶŐůĞ yz ĞƐƚ ŝƐŽĐğůĞ ĞŶ y͘ ĐͿ dƵ ƐĂŝƐ ƋƵĞ ůĞ ƚƌŝĂŶŐůĞ & ĞƐƚ ĠƋƵŝůĂƚĠƌĂů͘ ĚͿ dƵ ƐĂŝƐ ƋƵĞ ůĞ ƚƌŝĂŶŐůĞ WYZ ĞƐƚ ŝƐŽĐğůĞ ƌĞĐƚĂŶŐůĞ ĞŶ Z͘ ĞͿ dƵ ƐĂŝƐ ƋƵĞ ůĞ ƋƵĂĚƌŝůĂƚğƌĞ ĞƐƚ ƵŶ ůŽƐĂŶŐĞ͘ ĨͿ dƵ ƐĂŝƐ ƋƵĞ ůĞ ƋƵĂĚƌŝůĂƚğƌĞ &', ĞƐƚ ƵŶ ƉĂƌĂůůĠůŽŐƌĂŵŵĞ͘

ŽŵƉůğƚĞ ůĞƐ ƉŚƌĂƐĞƐ ƐƵŝǀĂŶƚĞƐ͘ ĂͿ ^ŝ ͮ ͮ с ͮ ͕ͮ ĂůŽƌƐ ůĞ ƚƌŝĂŶŐůĞ ĞƐƚ ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ďͿ ^ŝ ͕͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ĂůŽƌƐ ůĞ ƚƌŝĂŶŐůĞ yz ĞƐƚ ƌĞĐƚĂŶŐůĞ ĞŶ y͘ ^ ĐͿ ^ŝ ͮ ͮ х ϵϬΣ͕ ĂůŽƌƐ ůĞ ƚƌŝĂŶŐůĞ & ĞƐƚ ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ĚͿ ^ŝ ͮ ͮ с ͮ ͮ Ğƚ ΀ ΁ ^ ΀ ΁͕ ĂůŽƌƐ ůĞ ƉĂƌĂůůĠůŽŐƌĂŵŵĞ ĞƐƚ ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ĞͿ ^ŝ ͕͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ĂůŽƌƐ ůĞ ƉĂƌĂůůĠůŽŐƌĂŵŵĞ DEWY ĞƐƚ ƵŶ ůŽƐĂŶŐĞ͘

Ŷ ƐĞ ďĂůĂĚĂŶƚ ĚĂŶƐ ůĞ ũĂƌĚŝŶ͕ ,ĠůğŶĞ Ğƚ DĂƌŝĞ ƐŽŶƚ ƚŽŵďĠĞƐ ƐƵƌ ƵŶĞ ƚŽŝůĞ Ě͛ĂƌĂŝŐŶĠĞ ĞŶ ĨŽƌŵĞ ĚĞ ĚŽĚĠĐĂŐŽŶĞ ƌĠŐƵůŝĞƌ͘ Ŷ Ŷ͛ƵƚŝůŝƐĂŶƚ ƋƵĞ ůĞƐ ƉŽŝŶƚƐ ŶŽŵŵĠƐ͕ ŝŶĚŝƋƵĞ ƐƵƌ ĐŚĂƋƵĞ ĚĞƐƐŝŶ͕ ƵŶ ĐŚĞŵŝŶ ƉĂƌĐŽƵƌƵ ƉĂƌ ů͛ĂƌĂŝŐŶĠĞ ƉŽƵƌ ƚƌĂĐĞƌ ͗ hŶ ĐĂƌƌĠ ĞŶ ƉĂƌƚĂŶƚ hŶ ƌĞĐƚĂŶŐůĞ ĞŶ hŶ ůŽƐĂŶŐĞ ĞŶ hŶ ƉĂƌĂůůĠůŽŐƌĂŵŵĞ ĚƵ ƉŽŝŶƚ ƉĂƌƚĂŶƚ ĚƵ ƉŽŝŶƚ < ƉĂƌƚĂŶƚ ĚƵ ƉŽŝŶƚ ĞŶ ƉĂƌƚĂŶƚ ĚƵ ƉŽŝŶƚ '

A M

N C

U Q R

S G

U Q R F

S G

I E

K C

U R F

S G

K W

D E

E H

N C

136

K W

U Q R F

S G

T H

EXERCICES COMPLÉMENTAIRES

Chapitre 6 Figures planes

1D 7 17

ŽŵƉůğƚĞ ůĞƐ ƉŚƌĂƐĞƐ ĐŝͲĚĞƐƐŽƵƐ ƉĂƌ ƵŶ ĚĞƐ ŵŽƚƐ ƐƵŝǀĂŶƚƐ ͗ ŚĂƵƚĞƵƌ͕ ŵĠĚŝĂŶĞ͕ ŵĠĚŝĂƚƌŝĐĞ͕ ďŝƐƐĞĐƚƌŝĐĞ͕ ĚŝĂŐŽŶĂůĞ͘ A E B ĂͿ >Ă ĚƌŽŝƚĞ ĞƐƚ ƵŶĞ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ĚƵ ƌĞĐƚĂŶŐůĞ ͘ ďͿ >Ă ĚƌŽŝƚĞ , ĞƐƚ ƵŶĞ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ĚƵ ƚƌŝĂŶŐůĞ ͘ H ĐͿ >Ă ĚĞŵŝͲĚƌŽŝƚĞ ΀,d ĞƐƚ ƵŶĞ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ĚƵ ƚƌŝĂŶŐůĞ , ͘ ĚͿ >Ğ ƐĞŐŵĞŶƚ ΀' ΁ ĞƐƚ ƵŶĞ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ĚƵ ƚƌŝĂŶŐůĞ ͘ G ĞͿ >Ă ĚƌŽŝƚĞ & ĞƐƚ ƵŶĞ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ĚƵ ƚƌŝĂŶŐůĞ d,͘ D

1D 9 15

hŶ ŚĞǆĂŐŽŶĞ ƌĠŐƵůŝĞƌ & ĞƐƚ ŝŶƐĐƌŝƚ ĚĂŶƐ ƵŶ ĐĞƌĐůĞ ĚĞ ĐĞŶƚƌĞ K͘ DÉTERMINE ůĂ ŶĂƚƵƌĞ ĚƵ ƚƌŝĂŶŐůĞ ĞŶ ĠĐƌŝǀĂŶƚ ů͛ĂĚũĞĐƚŝĨ ƋƵŝ ůĞ ĐĂƌĂĐƚĠƌŝƐĞ ĂƵ ŵŝĞƵǆ͘ F ĞƐƚ ƵŶ ƚƌŝĂŶŐůĞ ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ DÉTERMINE ůĂ ŶĂƚƵƌĞ ĚƵ ƋƵĂĚƌŝůĂƚğƌĞ ĞŶ ĠĐƌŝǀĂŶƚ ůĞ ŶŽŵ ƋƵŝ ůĞ ĐĂƌĂĐƚĠƌŝƐĞ ĂƵ ŵŝĞƵǆ͘ ĞƐƚ ƵŶ ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘

ĞƐƚ ƵŶ ƌĞĐƚĂŶŐůĞ ĚŽŶƚ ůĞƐ ĚŝĂŐŽŶĂůĞƐ ƐĞ ĐŽƵƉĞŶƚ ĞŶ ͘

8 cm

JUSTIFIE͕ ă ůΖĂŝĚĞ ĚĞ ƉƌŽƉƌŝĠƚĠƐ͕ ƋƵĞ ůĞ ƉĠƌŝŵğƚƌĞ ĚƵ ƚƌŝĂŶŐůĞ ŵĞƐƵƌĞ Ϯϰ Đŵ͘

m C

6 cm

ƉƉůŝƋƵĞƌ >ĞƐ ƚƌŝĂŶŐůĞƐ Ğƚ ůĞƐ ƋƵĂĚƌŝůĂƚğƌĞƐ ĐŝͲĚĞƐƐŽƵƐ ŽŶƚ ĠƚĠ ĚĞƐƐŝŶĠƐ ă ŵĂŝŶ ůĞǀĠĞ͘ ZĞƉƌŽĚƵŝƐͲůĞƐ ĞŶ ƌĞƐƉĞĐƚĂŶƚ ůĞƐ ŵĞƐƵƌĞƐ͘

2 cm

60°

ƌĞĐƚĂŶŐůĞ ĐͿ

m 120°

ƌĞĐƚĂŶŐůĞ

6 cm

80°

55° 4 cm

3 cm

5 cm

ƉĂƌĂůůĠůŽŐƌĂŵŵĞ

ƚƌĂƉğǌĞ

2 cm

ĐĂƌƌĠ

ůŽƐĂŶŐĞ m

ďͿ

7 cm

40°

5 cm

15 m

40°

4 cm 30° 6 cm

4 cm

ĂͿ

3 cm

ůŽƐĂŶŐĞ

137

EXERCICES COMPLÉMENTAIRES

3 cm

Chapitre 6 Figures planes

25°

ƌĞĐƚĂŶŐůĞ

60°

3 cm 30°

ůŽƐĂŶŐĞ

3 cm 2c m

ƉĂƌĂůůĠůŽŐƌĂŵŵĞ ^

ĂͿ ŽŶƐƚƌƵŝƐ ƵŶ ƉĂƌĂůůĠůŽŐƌĂŵŵĞ ƐĂĐŚĂŶƚ ƋƵĞ ͮ ͮ с ϱ Đŵ͕ ͮ ͮ с ϲϬΣ Ğƚ ͮ ͮ с ϰ Đŵ͘ ^ ďͿ ŽŶƐƚƌƵŝƐ ƵŶ ůŽƐĂŶŐĞ ƐĂĐŚĂŶƚ ƋƵĞ ͮ ͮ с Ϯ͕ϱ Đŵ Ğƚ ͮ ͮ с ϲϬΣ͘ ĐͿ ŽŶƐƚƌƵŝƐ ƵŶ ƌĞĐƚĂŶŐůĞ ƐĂĐŚĂŶƚ ƋƵĞ ͮ ͮ с ϱ Đŵ Ğƚ ͮ ͮ с ϯ Đŵ͘ ĚͿ ŽŶƐƚƌƵŝƐ ƵŶ ĐĂƌƌĠ ƐĂĐŚĂŶƚ ƋƵĞ ͮ ͮ с ϰ Đŵ͘

ĂͿ D ĠƚĂŶƚ ůΖŝŶƚĞƌƐĞĐƚŝŽŶ ĚĞ ƐĞƐ ĚŝĂŐŽŶĂůĞƐ͕ ĐŽŶƐƚƌƵŝƐ ƵŶ ƉĂƌĂůůĠůŽŐƌĂŵŵĞ Ɛŝ ƚƵ ƐĂŝƐ ƋƵĞ ͮ ͮ с ϲ Đŵ͕ ͮ ͮ с ϰ Đŵ Ğƚ ͮDMAͮ с ϳϬΣ͘ ďͿ ŽŶƐƚƌƵŝƐ ƵŶ ůŽƐĂŶŐĞ ƐĂĐŚĂŶƚ ƋƵĞ ͮ ͮ с ϱ Đŵ Ğƚ ͮ ͮ с ϯ Đŵ͘ ĐͿ ŽŶƐƚƌƵŝƐ ƵŶ ƌĞĐƚĂŶŐůĞ ƐĂĐŚĂŶƚ ƋƵĞ ͮ ͮ с ϱ Đŵ Ğƚ ů͛ĂŵƉůŝƚƵĚĞ ĚĞ ů͛ĂŶŐůĞ ĂŝŐƵ ĨŽƌŵĠ ƉĂƌ ůĞƐ ĚĞƵǆ ĚŝĂŐŽŶĂůĞƐ ǀĂƵƚ ϲϬΣ͘

^ƵŝƐ ůĞƐ ĐŽŶƐŝŐŶĞƐ͘

1D 5 16

ʹ ŽŶƐƚƌƵŝƐ ƵŶ ƌĞĐƚĂŶŐůĞ ƚĞů ƋƵĞ ͮ ͮ с ϰ Đŵ Ğƚ ͮ ͮ с ϴ Đŵ͘ ʹ DĂƌƋƵĞ ůĞ ŵŝůŝĞƵ D ĚĞ ΀ ΁ Ğƚ ůĞ ŵŝůŝĞƵ E ĚĞ ΀ ΁͘ ʹ EŽŵŵĞ / ůĞ ƉŽŝŶƚ Ě͛ŝŶƚĞƌƐĞĐƚŝŽŶ ĚĞ ΀ E΁ Ğƚ ΀ D΁ Ğƚ : ůĞ ƉŽŝŶƚ Ě͛ŝŶƚĞƌƐĞĐƚŝŽŶ ĚĞ ΀D ΁ Ğƚ ΀ E΁͘ ʹ EŽŵŵĞ W ůĞ ƉŽŝŶƚ Ě͛ŝŶƚĞƌƐĞĐƚŝŽŶ ĚĞƐ ĚƌŽŝƚĞƐ E Ğƚ ͘ ʹ dƌĂĐĞ ůĞ ƉŽůǇŐŽŶĞ EW : D/ Ğƚ ĐŽůŽƌŝĞͲůĞ͘

NUMÉROTE ůĞƐ ĠƚĂƉĞƐ ƋƵŝ ĐŽƌƌĞƐƉŽŶĚĞŶƚ ă ů͛ŽƌĚƌĞ ƐƵŝǀŝ ƉŽƵƌ ƌĠĂůŝƐĞƌ ůĂ ĐŽŶƐƚƌƵĐƚŝŽŶ ĚĞƐ ůƵŶƵůĞƐ Ě͛,ŝƉƉŽĐƌĂƚĞ ƚƌĂĐĠĞƐ ĐŝͲĚĞƐƐŽƵƐ͘ >Ğ ϱ ĞƐƚ ĚĠũă ƉůĂĐĠ͘ ͘͘͘͘͘

ŽŶƐƚƌƵŝƐ ă ůΖĞǆƚĠƌŝĞƵƌ ĚƵ ĐĞƌĐůĞ C͕ ƋƵĂƚƌĞ ĚĞŵŝͲĐĞƌĐůĞƐ ĚĞ ĚŝĂŵğƚƌĞ ͮ &ͮ Ğƚ ĚĞ ĐĞŶƚƌĞƐ :͕ <͕ >͕ D͘

E L

͘͘͘͘͘ dƌĂĐĞ ƵŶ ĐĞƌĐůĞ C ĚĞ ĐĞŶƚƌĞ K͘ ͘͘͘͘͘

WůĂĐĞ D ůĞ ŵŝůŝĞƵ ĚĞ ΀ &΁͕ : ůĞ ŵŝůŝĞƵ ĚĞ ΀&'΁͕ < ůĞ ŵŝůŝĞƵ ĚĞ ΀',΁ Ğƚ > ůĞ ŵŝůŝĞƵ ĚĞ ΀ ,΁͘

͘͘͘͘͘ ŽŶƐƚƌƵŝƐ ƵŶ ĐĂƌƌĠ &', ŝŶƐĐƌŝƚ ĚĂŶƐ ůĞ ĐĞƌĐůĞ C͘ 5

ŽůŽƌŝĞ ůĞƐ ϰ ƉĂƌƚŝĞƐ ĐŽŵƉƌŝƐĞƐ ĞŶƚƌĞ ůĞ ĐĞƌĐůĞ Ğƚ ůĞƐ ϰ ĚĞŵŝͲĐĞƌĐůĞƐ͘ Ğ ƐŽŶƚ ůĞƐ ůƵŶƵůĞƐ Ě͛,ŝƉƉŽĐƌĂƚĞ͘

H O

K J G

dƌĂĐĞ ƵŶĞ ĚƌŽŝƚĞ Ě Ğƚ ŶŽŵŵĞ ƵŶ ƉŽŝŶƚ ƋƵĞůĐŽŶƋƵĞ Ŷ͛ĂƉƉĂƌƚĞŶĂŶƚ ƉĂƐ ă ůĂ ĚƌŽŝƚĞ Ě͘ dƌĂĐĞ ƵŶ ĂƌĐ ĚĞ ĐĞƌĐůĞ ĚĞ ĐĞŶƚƌĞ ĐŽƵƉĂŶƚ ůĂ ĚƌŽŝƚĞ Ě ĞŶ ĚĞƵǆ ƉŽŝŶƚƐ W Ğƚ Y͘ ŽŵƉůğƚĞ ůĂ ĨŝŐƵƌĞ ;ĂǀĞĐ ƌğŐůĞ Ğƚ ĐŽŵƉĂƐͿ ĂĨŝŶ Ě͛ŽďƚĞŶŝƌ ƵŶ ůŽƐĂŶŐĞ W Y͘

ĂͿ ŽŶƐƚƌƵŝƐ ƵŶ ƚƌŝĂŶŐůĞ ƐĂĐŚĂŶƚ ƋƵĞ ƐĞƐ ĐƀƚĠƐ ŵĞƐƵƌĞŶƚ ϰ Đŵ͕ ϱ Đŵ Ğƚ ϲ Đŵ͘ ďͿ ŽŶƐƚƌƵŝƐ ƵŶ ƚƌŝĂŶŐůĞ ƐĂĐŚĂŶƚ ƋƵĞ ƐĞƐ ĐƀƚĠƐ ŵĞƐƵƌĞŶƚ ϯ Đŵ͕ ϱ Đŵ Ğƚ ϰ Đŵ͘ ĐͿ ŽŶƐƚƌƵŝƐ ƵŶ ƚƌŝĂŶŐůĞ ƐĂĐŚĂŶƚ ƋƵ͛ƵŶ ĚĞ ƐĞƐ ĐƀƚĠƐ ŵĞƐƵƌĞ ϴ Đŵ Ğƚ ƋƵĞ ůĞƐ ĂŶŐůĞƐ ĂĚũĂĐĞŶƚƐ ă ĐĞ ĐƀƚĠ ŵĞƐƵƌĞŶƚ ϱϬΣ Ğƚ ϯϬΣ͘ ĚͿ ŽŶƐƚƌƵŝƐ ƵŶ ƚƌŝĂŶŐůĞ ƐĂĐŚĂŶƚ ƋƵ͛ƵŶ ĚĞ ƐĞƐ ĐƀƚĠƐ ŵĞƐƵƌĞ ϳ Đŵ Ğƚ ƋƵĞ ůĞƐ ĂŶŐůĞƐ ĂĚũĂĐĞŶƚƐ ă ĐĞ ĐƀƚĠ ŵĞƐƵƌĞŶƚ ϰϱΣ Ğƚ ϲϬΣ͘ ĞͿ ŽŶƐƚƌƵŝƐ ƵŶ ƚƌŝĂŶŐůĞ ƐĂĐŚĂŶƚ ƋƵ͛ƵŶ ĚĞ ƐĞƐ ĂŶŐůĞƐ ŵĞƐƵƌĞ ϴϬΣ Ğƚ ƋƵĞ ůĞƐ ĐƀƚĠƐ ƋƵŝ ĨŽƌŵĞŶƚ ĐĞƚ ĂŶŐůĞ ŵĞƐƵƌĞŶƚ ϰ Đŵ Ğƚ ϲ Đŵ͘ ĨͿ ŽŶƐƚƌƵŝƐ ƵŶ ƚƌŝĂŶŐůĞ ƐĂĐŚĂŶƚ ƋƵ͛ƵŶ ĚĞ ƐĞƐ ĂŶŐůĞƐ ŵĞƐƵƌĞ ϭϬϬΣ Ğƚ ƋƵĞ ůĞƐ ĐƀƚĠƐ ƋƵŝ ĨŽƌŵĞŶƚ ĐĞƚ ĂŶŐůĞ ŵĞƐƵƌĞŶƚ ϳ Đŵ Ğƚ ϱ Đŵ͘

138

Chapitre 6 Figures planes

8 ŽŶƐƚƌƵŝƐ ĐŚĂƋƵĞ ƚƌŝĂŶŐůĞ Ğƚ ƚƌĂĐĞ ƐĞƐ

ŚĂƵƚĞƵƌƐ͘ ĂͿ ͮ ͮ с ͮ ͮ с ͮ ͮ с ϱϮ ŵŵ ďͿ ͮ ͮ с ͮ ͮ с ϰϱ ŵŵ Ğƚ ͮ ͮ с ϯϬ ŵŵ ĐͿ ͮ ͮ с ϰϰ ŵŵ͕ ͮ ͮ с ϯϱ ŵŵ Ğƚ ͮ ͮ с ϲϱ ŵŵ

10 ŽŶƐƚƌƵŝƐ ĐŚĂƋƵĞ ƚƌŝĂŶŐůĞ Ğƚ ƚƌĂĐĞ ƐĞƐ

EXERCICES COMPLÉMENTAIRES

ŽŶƐƚƌƵŝƐ ĐŚĂƋƵĞ ƚƌŝĂŶŐůĞ Ğƚ ƚƌĂĐĞ ƐĞƐ ŵĠĚŝĂƚƌŝĐĞƐ͘ ĂͿ ͮ ͮ с ϲϬ ŵŵ͕ ͮ ͮ с ϰϱ ŵŵ Ğƚ ͮ ͮ с ϱϬ ŵŵ ďͿ ͮ ͮ с ϲϱ ŵŵ͕ ͮ ͮ с ϯϱ ŵŵ Ğƚ ͮ ͮ с ϱϬ ŵŵ ^ ĐͿ ͮ ͮ с ϯϱ ŵŵ͕ ͮ ͮ с ϵϬΣ Ğƚ ͮ ͮ с ϱϬ ŵŵ

11 ŽŶƐƚƌƵŝƐ ĐŚĂƋƵĞ ƚƌŝĂŶŐůĞ Ğƚ ƚƌĂĐĞ ƐĞƐ

ŵĠĚŝĂŶĞƐ͘ ĂͿ ͮ ͮ с ϲϴ ŵŵ͕ ͮ ͮ с ϯϰ ŵŵ Ğƚ ͮ ͮ с ϱϬ ŵŵ ďͿ ͮ ͮ с ϰϱ ŵŵ͕ ͮ ͮ с ϱϱ ŵŵ Ğƚ ͮ ͮ с ϲϬ ŵŵ

1D 12 TERMINE ůĂ ĐŽŶƐƚƌƵĐƚŝŽŶ ĚƵ ƚƌŝĂŶŐůĞ ŝƐŽĐğůĞ 17 ĚŽŶƚ ΀ ΁ ĞƐƚ ůĂ ďĂƐĞ͘

ďŝƐƐĞĐƚƌŝĐĞƐ͘ ĂͿ ͮ ͮ с ϱϬ ŵŵ͕ ͮ ͮ с ϰϬ ŵŵ Ğƚ ͮ ͮ с ϳϬ ŵŵ ďͿ ͮ ͮ с ϲϱ ŵŵ͕ ͮ ͮ с ϱϱ ŵŵ Ğƚ ͮ ͮ с ϰϴ ŵŵ

LAISSE ƚĞƐ ĐŽŶƐƚƌƵĐƚŝŽŶƐ ǀŝƐŝďůĞƐ͘

A 13 sŽŝĐŝ ĚĂŶƐ ůĞ ĚĠƐŽƌĚƌĞ͕ ůĞƐ ĠƚĂƉĞƐ ĚĞ ůĂ ĐŽŶƐƚƌƵĐƚŝŽŶ ĚĞ ůĂ ĨŝŐƵƌĞ ĐŝͲĚĞƐƐŽƵƐ͘ ZĞĐŽƉŝĞͲůĞƐ ĚĂŶƐ

ů͛ŽƌĚƌĞ Ě͛ĞǆĠĐƵƚŝŽŶ͘ G D ϭΣ dƌĂĐĞƌ ůĂ ĚŝĂŐŽŶĂůĞ ΀ ΁͘ ϮΣ ŽŶƐƚƌƵŝƌĞ ůĞ ƌĞĐƚĂŶŐůĞ ,' ͘ ϯΣ ŽŶƐƚƌƵŝƌĞ ůĞ ƌĞĐƚĂŶŐůĞ ͘ ϰΣ EŽŵŵĞƌ '͕ ůĞ ŵŝůŝĞƵ ĚƵ ƐĞŐŵĞŶƚ ΀ &΁͘ A H ϱΣ ŽŶƐƚƌƵŝƌĞ ď͕ ůĂ ďŝƐƐĞĐƚƌŝĐĞ ĚĞ ů͛ĂŶŐůĞ ACB͘ ϲΣ EŽŵŵĞƌ ͕ ůĞ ƉŽŝŶƚ ă ů͛ŝŶƚĞƌƐĞĐƚŝŽŶ ĚĞ ůĂ ĚƌŽŝƚĞ ď Ğƚ ĚƵ ĐƀƚĠ ΀ ΁͘ ϳΣ EŽŵŵĞƌ &͕ ůĞ ƉŽŝŶƚ ă ů͛ŝŶƚĞƌƐĞĐƚŝŽŶ ĚĞ ůĂ ĚƌŽŝƚĞ Ɖ Ğƚ ĚƵ ĐƀƚĠ ΀ ΁͘ ϴΣ ŽŶƐƚƌƵŝƌĞ Ɖ͕ ůĂ ĚƌŽŝƚĞ ƉĞƌƉĞŶĚŝĐƵůĂŝƌĞ ă ΀ ΁ ƉĂƐƐĂŶƚ ƉĂƌ ůĞ ƉŽŝŶƚ ͘

E b

dƌĂŶƐĨĠƌĞƌ 1

ŽŶƐƚƌƵŝƐ ƵŶ ůŽƐĂŶŐĞ ƐĂĐŚĂŶƚ ƋƵĞ ͘͘͘ ^ ĂͿ ͮ ͮ с ϲϬΣ Ğƚ ůĞ ƉĠƌŝŵğƚƌĞ ŵĞƐƵƌĞ ϭϲ Đŵ͘ ďͿ ͮ ͮ с ϴ Đŵ Ğƚ ů͛ĂŝƌĞ ŵĞƐƵƌĞ ϮϬ Đŵ2͘ ĐͿ ͮ ͮ с ϲ Đŵ Ğƚ ůĞ ƉĠƌŝŵğƚƌĞ ŵĞƐƵƌĞ ϭϰ Đŵ͘

ŽŶƐƚƌƵŝƐ ƵŶ ĐĂƌƌĠ ƐĂĐŚĂŶƚ ƋƵĞ ͘͘͘ ĂͿ ƐŽŶ ƉĠƌŝŵğƚƌĞ ŵĞƐƵƌĞ ϭϮ Đŵ͘ ďͿ ĐĞ ĐĂƌƌĠ ĞƐƚ ŝŶƐĐƌŝƚ ĚĂŶƐ ƵŶ ĐĞƌĐůĞ ĚĞ Ϯ͕ϱ Đŵ ĚĞ ƌĂǇŽŶ͘

sŽŝĐŝ ƵŶĞ ͨ ĨƵƐĠĞ ͩ͘ ^ŝ | | с ϰ Đŵ͕ ĐŽŶƐƚƌƵŝƐͲůĂ ĞŶ ŐƌĂŶĚĞƵƌ ƌĠĞůůĞ ĞŶ ƐĂĐŚĂŶƚ A ƋƵĞ ĞƐƚ ƵŶ ĐĂƌƌĠ͘

ŽŶƐƚƌƵŝƐ ƵŶ ƌĞĐƚĂŶŐůĞ ƐĂĐŚĂŶƚ ƋƵĞ ͘͘͘ ĂͿ ͮ ͮ с ϲ Đŵ Ğƚ ů͛ĂŝƌĞ ǀĂƵƚ Ϯϰ Đŵ2͘ ďͿ ͮ ͮ с 2 . ͮ ͮ Ğƚ ůĞ ƉĠƌŝŵğƚƌĞ ǀĂƵƚ ϭϴ Đŵ͘ ĐͿ ͮ ͮ с ϲ Đŵ Ğƚ ͮ ͮ с Ϯ . ͮ ͮ͘

139

EXERCICES COMPLÉMENTAIRES 5

ĂͿ ŽŶƐƚƌƵŝƐ ůĞ ĐĂƌƌĠ ƐĂĐŚĂŶƚ ƋƵĞ ŵ ĞƐƚ ůĂ ŵĠĚŝĂƚƌŝĐĞ ĚĞ ΀ ΁͘

Chapitre 6 Figures planes

ďͿ ŽŶƐƚƌƵŝƐ ůĞ ůŽƐĂŶŐĞ ƐĂĐŚĂŶƚ ƋƵĞ ŵ ĞƐƚ ůĂ ŵĠĚŝĂƚƌŝĐĞ ĚĞ ΀ ΁ Ğƚ ď ůĂ ^ ďŝƐƐĞĐƚƌŝĐĞ ĚĞ ͘

ĐͿ ŽŶƐƚƌƵŝƐ ůĞ ƉĂƌĂůůĠůŽŐƌĂŵŵĞ ƐĂĐŚĂŶƚ ƋƵĞ ŵ ĞƐƚ ůĂ ŵĠĚŝĂƚƌŝĐĞ ĚĞ ΀ ΁͘

A A 6

ĂͿ ŽŶƐƚƌƵŝƐ ůĞ ƚƌŝĂŶŐůĞ ďͿ ŽŶƐƚƌƵŝƐ ůĞ ƚƌŝĂŶŐůĞ ĐͿ ŽŶƐƚƌƵŝƐ ůĞ ƚƌŝĂŶŐůĞ ƐĂĐŚĂŶƚ ƋƵĞ ŵ Ğƚ Ŷ ƐĂĐŚĂŶƚ ƋƵĞ ďϭ Ğƚ ď2 sont ŝƐŽĐğůĞ ĞŶ ƐĂĐŚĂŶƚ ƋƵĞ ŵ ƐŽŶƚ ůĞƐ ŵĠĚŝĂƚƌŝĐĞƐ ĞƐƚ ůĂ ŵĠĚŝĂƚƌŝĐĞ ĚƵ ĐƀƚĠ ůĞƐ ďŝƐƐĞĐƚƌŝĐĞƐ ĚĞƐ ĂŶŐůĞƐ ^ ^ ƌĞƐƉĞĐƚŝǀĞƐ ĚĞƐ ĐƀƚĠƐ ΀ ΁ A et ͘ ΀ ΁ Ğƚ ď ůĂ ďŝƐƐĞĐƚƌŝĐĞ ĚĞ ^ Ğƚ ΀ ΁͘ ů͛ĂŶŐůĞ ͘

b A

b1 m

>Ğ ƐĐŚĠŵĂ ĐŝͲĐŽŶƚƌĞ ƌĞƉƌĠƐĞŶƚĞ ƵŶ ƉĠƚƌŝŶ ĚĞ ů͛ĂƌƚŝƐĂŶ ďŽƵůĂŶŐĞƌ ĚƵ ƐŝğĐůĞ ĚĞƌŶŝĞƌ͘ ĨŝŶ ĚĞ ůĞ ƌĂĨƌĂŠĐŚŝƌ͕ ŽŶ ĚĠĐŝĚĞ ĚĞ ƌĞĐŽƵǀƌŝƌ ů͛ĞǆƚĠƌŝĞƵƌ Ě͛ƵŶ ǀĞƌŶŝƐ͘ ^ĂĐŚĂŶƚ ƋƵĞ ů͛ŽŶ ƌĞĐŽƵǀƌĞ ƵŶĞ ƐƵƌĨĂĐĞ ĚĞ ϭ ŵ2 ĂǀĞĐ ĞŶǀŝƌŽŶ ϴϬ ŵů ĚĞ ĐĞ ƉƌŽĚƵŝƚ͕ ĐĂůĐƵůĞ ůĂ ƋƵĂŶƚŝƚĠ ŶĠĐĞƐƐĂŝƌĞ ĂƵ ƌĞĐŽƵǀƌĞŵĞŶƚ ĚƵ ƉĠƚƌŝŶ͘ ƚƚĞŶƚŝŽŶ͕ ĞŶ ƌĂŝƐŽŶ ĚĞ ůĞƵƌ ŝŶĐůŝŶĂŝƐŽŶ͕ ůĞƐ ƉĂƌŽŝƐ ƐŽŶƚ ĚĞƐ ƚƌĂƉğǌĞƐ ĚŽŶƚ ůĞƐ ŚĂƵƚĞƵƌƐ ŵĞƐƵƌĞŶƚ ϰϱ Đŵ͘

1D 9 16

cm 40 cm

100

EĂƚŚĂůŝĞ ǀĞƵƚ ƌĞƉĞŝŶĚƌĞ ůĞƐ ŵƵƌƐ Ğƚ ůĞ ƉůĂĨŽŶĚ Ě͛ƵŶĞ ƉŝğĐĞ ƌĞĐƚĂŶŐƵůĂŝƌĞ ƋƵŝ ŵĞƐƵƌĞ ϲ ŵ ĚĞ ůŽŶŐ͕ ϰ ŵ ĚĞ ůĂƌŐĞ Ğƚ Ϯ͕ϱϬ ŵ ĚĞ ŚĂƵƚ͘ >ĞƐ ĚĞƵǆ ƉŽƌƚĞƐ ŵĞƐƵƌĞŶƚ Ϯ͕ϮϬ ŵ ƐƵƌ Ϭ͕ϴϬ ŵ Ğƚ ůĂ ďĂŝĞ ǀŝƚƌĠĞ Ϯ͕ϱϬ ŵ ƐƵƌ Ϯ͕ϯϬ ŵ͘ ŽŵďŝĞŶ ĚŽŝƚͲĞůůĞ ĚĠďŽƵƌƐĞƌ Ɛŝ ƵŶ ůŝƚƌĞ ĚĞ ƉĞŝŶƚƵƌĞ ĐŽƵǀƌĞ ϭϯ ŵ2 et Ɛŝ ůĞ ƉŽƚ ĚĞ Ϯ͕ϱ ůŝƚƌĞƐ ĚĞ ƉĞŝŶƚƵƌĞ ĐŽƸƚĞ ϰϬ € ͍

>Ğ ƌĞĐƚĂŶŐůĞ ŶΖĞƐƚ ƉĂƐ ĞŶ ǀƌĂŝĞ ŐƌĂŶĚĞƵƌ͘

CALCULE ů͛ĂŝƌĞ ĚƵ ƚƌĂƉğǌĞ ƌĞĐƚĂŶŐůĞ ͘

C 3 cm

ŝƌĞ ĚĞ с ͘͘͘ Đŵ2 E

140

8 cm

Chapitre 6 Figures planes

EXERCICES COMPLÉMENTAIRES

10 :ĞĂŶ ĚŽŝƚ ĠƉĂŶĚƌĞ ĚƵ ĚĠƐŚĞƌďĂŶƚ ŶĂƚƵƌĞů ƐƵƌ ůĞ

ŐƌĂǀŝĞƌ ĚĞƐ ĐŚĞŵŝŶƐ ĚĞ ƐŽŶ ƉŽƚĂŐĞƌ͘ /ů Ă ĚĞƐƐŝŶĠ ĚŝĨĨĠƌĞŶƚĞƐ ĨŽƌŵĞƐ ŐĠŽŵĠƚƌŝƋƵĞƐ ƉŽƵƌ ĚĠůŝŵŝƚĞƌ ƐĞƐ ĐƵůƚƵƌĞƐ͘ hŶ ůŝƚƌĞ ĚĞ ƉƌŽĚƵŝƚ Ɖƌġƚ ă ů͛ĞŵƉůŽŝ ĐŽŶƚĞŶĂŶƚ ĚƵ ĚĠƐŚĞƌďĂŶƚ ŶĂƚƵƌĞů ƚƌĂŝƚĞ ϭϱ ŵ2͘ ĂůĐƵůĞ ůĂ ƋƵĂŶƚŝƚĠ ĚĞ ĚĠƐŚĞƌďĂŶƚ ŶĂƚƵƌĞů ƋƵ͛ŝů ůƵŝ ĨĂƵĚƌĂ Ɛŝ ƚƵ ƐĂŝƐ ƋƵĞ ůĞ ůŽƉŝŶ ĚĞ ƚĞƌƌĞ ĚĞ ĨŽƌŵĞ ĐĂƌƌĠĞ Ă ĚĞƵǆ ŵğƚƌĞƐ ĚĞ ƀƚĠ͘

11 hŶ ŽƉƚŝĐŝĞŶ Ă ĐƌĠĠ ƐŽŶ ƉƌŽƉƌĞ ůŽŐŽ͘ ĞůƵŝͲ

12 ů͛ĂƉƉƌŽĐŚĞ ĚĞ ů͛ŚŝǀĞƌ͕ ƌƵŶŽ Ă ů͛ŝŶƚĞŶƚŝŽŶ

ĚĞ ŵĞƚƚƌĞ ĚĞƵǆ ĐŽƵĐŚĞƐ ĚĞ ůĂƐƵƌĞ ƐƵƌ ůĂ ƉŽƌƚĞ ĚĞ ƐŽŶ ĞŶƚƌĞƉƀƚ ƋƵ͛ŝů Ă ĚĠĐŽƌĠ ĞŶ ƉůĂĕĂŶƚ ĚĞƵǆ ŐƌĂŶĚƐ ůŽƐĂŶŐĞƐ͘ /ů Ă ĚĠĐŝĚĠ Ě͛ƵƚŝůŝƐĞƌ ƚƌŽŝƐ ƚŽŶƐ ĚŝĨĨĠƌĞŶƚƐ͘ ĂůĐƵůĞ ƉŽƵƌ ĐŚĂƋƵĞ ƚŽŶ ůĂ ƋƵĂŶƚŝƚĠ ƋƵ͛ŝů ĚĞǀƌĂ ĂĐŚĞƚĞƌ Ɛŝ ƚƵ ƐĂŝƐ ƋƵ͛ƵŶ ůŝƚƌĞ ĚĞ ůĂƐƵƌĞ ĐŽƵǀƌĞ ϴ ŵ2͘ 1m

Đŝ ĞƐƚ ĐŽŵƉŽƐĠ Ě͛ƵŶ ƈŝů ŝŶƐĐƌŝƚ ĚĂŶƐ ƵŶ ĐĂƌƌĠ ĚĞ ϲ Đŵ ĚĞ ĐƀƚĠ͘ ĂůĐƵůĞ ů͛ĂŝƌĞ ĚĞ ůĂ ƉĂƌƚŝĞ ŵĂƵǀĞ͕ ĚĞ ůĂ ƉĂƌƚŝĞ ǀĞƌƚĞ Ğƚ ĚĞ ůĂ ƉĂƌƚŝĞ ũĂƵŶĞ ĞŶ ƵƚŝůŝƐĂŶƚ p ĂƌƌŽŶĚŝ ĂƵ ĐĞŶƚŝğŵĞ ƉƌğƐ͘

1m 6m

13 ^ŝ ƚƵ ƐĂŝƐ ƋƵĞ ů͛ĂŝƌĞ ĚƵ ĐĂƌƌĠ D Z ǀĂƵƚ

ϯϲ Đŵ2͕ ĐĂůĐƵůĞ ĐĞůůĞ ĚƵ ƋƵĂĚƌŝůĂƚğƌĞ D d,͘ M

ƉĂƌƚŝĞ ĐŽůŽƌĠĞ͘ ;hƚŝůŝƐĞ ƵŶĞ ǀĂůĞƵƌ ĚĞ p ĂƌƌŽŶĚŝĞ ă ĚĞƵǆ ĚĠĐŝŵĂůĞƐ͘Ϳ ĂͿ ďͿ

1 cm

15 ĂůĐƵůĞ ůĞ ƉĠƌŝŵğƚƌĞ Ğƚ ů͛ĂŝƌĞ ĚĞ ĐŚĂƋƵĞ

4 cm

ƚƵ ƐĂŝƐ ƋƵĞ ͮZ ͮ с ϭ͕ϱ Đŵ Ğƚ ͮ dͮ с ϰ Đŵ͘

14 ĂůĐƵůĞ ů͛ĂŝƌĞ ĚĞƐ ĨŝŐƵƌĞƐ Z d^ Ğƚ Zh^ ͕ Ɛŝ

16 ĂŶƐ ĐŚĂƋƵĞ ĐĂƐ͕ ƋƵĞůůĞ ĞƐƚ ů͛ĂŝƌĞ ůĂ ƉůƵƐ

ŐƌĂŶĚĞ ͗ ů͛ĂŝƌĞ ĐŽůŽƌĠĞ ŽƵ ů͛ĂƵƚƌĞ ͍ ĂůĐƵůĞ ĂǀĞĐ ƵŶĞ ǀĂůĞƵƌ ĚĞ p ĂƌƌŽŶĚŝĞ ă ĚĞƵǆ ĚĠĐŝŵĂůĞƐ͘ ĂͿ ďͿ

3 cm

141

EXERCICES COMPLÉMENTAIRES

Chapitre 6 Figures planes

17 Ŷ ƵƚŝůŝƐĂŶƚ ůĞƐ ƌĞŶƐĞŝŐŶĞŵĞŶƚƐ ĨŽƵƌŶŝƐ ƉĂƌ ůĞ ĚĞƐƐŝŶ͕ ĐĂůĐƵůĞ ůĞ ƉĠƌŝŵğƚƌĞ

A 12 m2

Ğƚ ů͛ĂŝƌĞ ĚĞ ůĂ ĨŝŐƵƌĞ ͘

B 36 m2

18 ŽŶƐƚƌƵŝƐ ƵŶ ƚƌŝĂŶŐůĞ D/ ŝƐŽĐğůĞ ĞŶ D͕ Ɛŝ ƵŶ ĚĞƐ ĐƀƚĠƐ ŵĞƐƵƌĞ ϯ Đŵ Ğƚ ůĞ ƉĠƌŝŵğƚƌĞ ϭϭ Đŵ͘

ŶǀŝƐĂŐĞ ƚŽƵƚĞƐ ůĞƐ ƐŽůƵƚŝŽŶƐ͘ ƉĂƌƚŝƌ ĚĞ ĐĞ ƚƌŝĂŶŐůĞ͕ ĐŽŶƐƚƌƵŝƐ ůĞ ůŽƐĂŶŐĞ D/^ Ğƚ ĐĂůĐƵůĞ ƐŽŶ ƉĠƌŝŵğƚƌĞ͘ 19 ^ŝ ƚƵ ƐĂŝƐ ƋƵĞ ůĞƐ ƋƵĂĚƌŝůĂƚğƌĞƐ Ğƚ &' ƐŽŶƚ ĚĞƐ ĐĂƌƌĠƐ͕ ƋƵĞ ƉĞƵǆͲƚƵ

ĚŝƌĞ ĚƵ ƚƌŝĂŶŐůĞ & ͍ :ƵƐƚŝĨŝĞ ƚĂ ƌĠƉŽŶƐĞ͘

G C

D 20 ŽŶƐƚƌƵŝƐ ĐĞƐ ƚƌĂƉğǌĞƐ ĂǀĞĐ ůĞƐ ĚŝŵĞŶƐŝŽŶƐ ƌĠĞůůĞƐ͘

5 cm

3 cm

1D 21 >Ă ĐůƀƚƵƌĞ ĚĞ ĨŽƌŵĞ ƌĞĐƚĂŶŐƵůĂŝƌĞ ĞƐƚ ĚŝƐƚĂŶƚĞ 18 ĚĞ ϯ͕ϱ ŵ ĚĞƐ ďŽƌĚƐ ĚĞ ůĂ ƉŝƐĐŝŶĞ͘

Clôture

>͛ĂĐĐğƐ ă ůĂ ƉŝƐĐŝŶĞ Ɛ͛ĞĨĨĞĐƚƵĞ ƉĂƌ ƵŶĞ ƉŽƌƚĞ ĚĞ ϭ ŵ ĚĞ ůĂƌŐĞ͘ CALCULE ůĂ ůŽŶŐƵĞƵƌ ƚŽƚĂůĞ ĚĞ ůĂ ĐůƀƚƵƌĞ ;ƐĂŶƐ ůĂ ƉŽƌƚĞͿ͘ ÉCRIS ƚŽƵƐ ƚĞƐ ĐĂůĐƵůƐ͘

12 m

Piscine

1D 22 DĂƌŝŶĂ ƐŽƵŚĂŝƚĞ ƉĞŝŶĚƌĞ ůĞƐ ŵƵƌƐ ĚĞ ƐĂ ĐŚĂŵďƌĞ͘ >͛ĂŝƌĞ ƚŽƚĂůĞ ĚĞƐ ŵƵƌƐ ĞƐƚ ĚĞ ϯϲ ŵ2͘ 13

hŶ ůŝƚƌĞ ĚĞ ƉĞŝŶƚƵƌĞ ƉĞƌŵĞƚ ĚĞ ĐŽƵǀƌŝƌ ϰ ŵ2͘ hŶ ƉŽƚ ĚĞ ϯ ůŝƚƌĞƐ ĚĞ ƉĞŝŶƚƵƌĞ ĐŽƵƚĞ ϰϱ €͘ CALCULE ůĞ ŵŽŶƚĂŶƚ ă ƉĂǇĞƌ ƉŽƵƌ ƉĞŝŶĚƌĞ ůĞƐ ŵƵƌƐ ĚĞ ůĂ ĐŚĂŵďƌĞ͘ ÉCRIS ƚŽƵƚ ƚŽŶ ƌĂŝƐŽŶŶĞŵĞŶƚ Ğƚ ƚŽƵƐ ƚĞƐ ĐĂůĐƵůƐ͘ DŽŶƚĂŶƚ ă ƉĂǇĞƌ ͗ ͘͘͘ €

1D 23 hŶ ƉƌŽƉƌŝĠƚĂŝƌĞ ƉŽƐƐğĚĞ ƵŶ ƚĞƌƌĂŝŶ ă ďąƚŝƌ ĚŝǀŝƐĠ ĞŶ ĚĞƵǆ ƉĂƌĐĞůůĞƐ͘ 13 /ů ǀĞŶĚ ůĂ ƉĂƌĐĞůůĞ ŶΣϭ ;ĐĂƌƌĠĞͿ ƉŽƵƌ ϳϱ ϲϬϬ €͘

3 cm

30° 120°

DÉTERMINE ůĞ Ɖƌŝǆ ĚĞ ǀĞŶƚĞ ĚĞ ůĂ ƉĂƌĐĞůůĞ ŶΣϮ ;ƌĞĐƚĂŶŐƵůĂŝƌĞͿ Ɛŝ ůĞ ƉƌŽƉƌŝĠƚĂŝƌĞ ƐŽƵŚĂŝƚĞ ůĂ ǀĞŶĚƌĞ ĂƵ ŵġŵĞ Ɖƌŝǆ ĚƵ ŵğƚƌĞ ĐĂƌƌĠ͘ ÉCRIS ƚŽƵƚ ƚŽŶ ƌĂŝƐŽŶŶĞŵĞŶƚ Ğƚ ƚŽƵƐ ƚĞƐ ĐĂůĐƵůƐ͘

142

Parcelle n°1

Parcelle n°2

30 m

50 m

30 m

Chapitre 7 Solides Tableaux de compétences Libre ĂůĐƵů ůŝƩ ĠƌĂů Ğƚ ĠƋƵĂƟ ŽŶƐ 22

DĂŠƚƌŝƐĞƌ ůĞƐ ĐŽŶǀĞŶƟ ŽŶƐ Ě͛ĠĐƌŝƚƵƌĞ ŵĂƚŚĠŵĂƟ ƋƵĞ ĚĞƐ ĞǆƉƌĞƐƐŝŽŶƐ ůŝƩ ĠƌĂůĞƐ͘

Les solides 45

ŽŵƉƌĞŶĚƌĞ Ğƚ ƵƟ ůŝƐĞƌ͕ ĚĂŶƐ ůĞƵƌ ĐŽŶƚĞǆƚĞ͕ ĚĞƐ ƚĞƌŵĞƐ ƵƐƵĞůƐ ƉƌŽƉƌĞƐ ă ůĂ ŐĠŽŵĠƚƌŝĞ ĚĞƐ ƐŽůŝĚĞƐ͘

ZĞĐŽŶŶĂŠƚƌĞ͕ ĐŽŵƉĂƌĞƌ͕ Ěŝī ĠƌĞŶĐŝĞƌ Ğƚ ĐůĂƐƐĞƌ ĚĞƐ ƐŽůŝĚĞƐ ƐƵƌ ďĂƐĞ ĚĞ ůĞƵƌƐ ĠůĠŵĞŶƚƐ ĐĂƌĂĐƚĠƌŝƐƟ ƋƵĞƐ͘

ZĞĐŽŶŶĂŠƚƌĞ Ğƚ ĐŽŵƉĂƌĞƌ Ěŝī ĠƌĞŶƚƐ ƚǇƉĞƐ ĚĞ ƌĞƉƌĠƐĞŶƚĂƟ ŽŶƐ ƉůĂŶĞƐ ĚĞ ƐŽůŝĚĞƐ͘

ŽŶƐƚƌƵŝƌĞ ůĞƐ ĚĠǀĞůŽƉƉĞŵĞŶƚƐ ƉŽƐƐŝďůĞƐ ĚĞ ƐŽůŝĚĞƐ ;ĐƵďĞƐ͕ ƉĂƌĂůůĠůĠƉŝƉğĚĞƐ ƌĞĐƚĂŶŐůĞƐ͕ ƉƌŝƐŵĞƐ ĚƌŽŝƚƐͿ͘

ƐƐŽĐŝĞƌ ƵŶ ƐŽůŝĚĞ ă ƐĂ ƌĞƉƌĠƐĞŶƚĂƟ ŽŶ ĚĂŶƐ ůĞ ƉůĂŶ Ğƚ ƌĠĐŝƉƌŽƋƵĞŵĞŶƚ͘

ŽŶƐƚƌƵŝƌĞ ƵŶ ƉĂƌĂůůĠůĠƉŝƉğĚĞ ƌĞĐƚĂŶŐůĞ ĞŶ ƉĞƌƐƉĞĐƟ ǀĞ ĐĂǀĂůŝğƌĞ͘

ZĠƐŽƵĚƌĞ ĚĞƐ ƉƌŽďůğŵĞƐ Ě͛ĂŝƌĞƐ͕ ĚĞ ǀŽůƵŵĞƐ͕ ĚĞ ĚĠǀĞůŽƉƉĞŵĞŶƚƐ͘

ĂŶƐ ƵŶĞ ƌĞƉƌĠƐĞŶƚĂƟ ŽŶ ĞŶ ƉĞƌƐƉĞĐƟ ǀĞ Ě͛ƵŶ ŽďũĞƚ ĚĞ ů͛ĞƐƉĂĐĞ͕ ƌĞƉĠƌĞƌ ůĞƐ ĠůĠŵĞŶƚƐ ĞŶ ǀƌĂŝĞ ŐƌĂŶĚĞƵƌ͘

Ŷ ƵƟ ůŝƐĂŶƚ ƵŶĞ ƌĞƉƌĠƐĞŶƚĂƟ ŽŶ ĞŶ ƉĞƌƐƉĞĐƟ ǀĞ Ě͛ƵŶ ŽďũĞƚ ĚĞ ů͛ĞƐƉĂĐĞ͕ ĚĞƐƐŝŶĞƌ ĞŶ ǀƌĂŝĞ ŐƌĂŶĚĞƵƌ ĐĞƌƚĂŝŶƐ ĠůĠŵĞŶƚƐ ĚĠĨŽƌŵĠƐ ƉĂƌ ůĂ ƉƌŽũĞĐƟ ŽŶ͘

143

ACTIVITÉS

Chapitre 7 Solides

>ĞƐ Į ŐƵƌĞƐ ƉůĂŶĞƐ 55

ŽŵƉƌĞŶĚƌĞ Ğƚ ƵƟ ůŝƐĞƌ͕ ĚĂŶƐ ůĞƵƌ ĐŽŶƚĞǆƚĞ͕ ĚĞƐ ƚĞƌŵĞƐ ƵƐƵĞůƐ ƉƌŽƉƌĞƐ ă ůĂ ŐĠŽŵĠƚƌŝĞ ĚĞƐ Į ŐƵƌĞƐ ƉůĂŶĞƐ͘

dƌĂĐĞƌ ƵŶĞ ĚƌŽŝƚĞ ƉĞƌƉĞŶĚŝĐƵůĂŝƌĞ;ƉĂƌĂůůğůĞͿ ă ƵŶĞ ĂƵƚƌĞ͘

DĞƐƵƌĞ Ě͛ĂŶŐůĞƐ 72

dƌĂĐĞƌ ƵŶ ĂŶŐůĞ Ě͛ĂŵƉůŝƚƵĚĞ ĚŽŶŶĠĞ͘

Kĸ ĐŝĞů ĠŶŽŵďƌĞƌ 1

ZĠƐŽƵĚƌĞ ĚĞƐ ƉƌŽďůğŵĞƐ ĚĞ ĚĠŶŽŵďƌĞŵĞŶƚ ĚĂŶƐ ĚĞƐ ĐŽŶƚĞǆƚĞƐ ŶƵŵĠƌŝƋƵĞƐ Ğƚ ŐĠŽŵĠƚƌŝƋƵĞƐ͘

^ŽůŝĚĞƐ Ğƚ Į ŐƵƌĞƐ ƉůĂŶĞƐ

ZĞĐŽŶŶĂŠƚƌĞ Ğƚ ĐůĂƐƐĞƌ ůĞƐ ƐŽůŝĚĞƐ ŐĠŽŵĠƚƌŝƋƵĞƐ ͗ ůĞƐ ƉŽůǇğĚƌĞƐ ;ĐƵďĞ͕ ƉĂƌĂůůĠůĠƉŝƉğĚĞ ƌĞĐƚĂŶŐůĞ͕ ƉƌŝƐŵĞƐ ĚƌŽŝƚƐ͕ ƉǇƌĂŵŝĚĞͿ Ğƚ ůĞƐ ĐŽƌƉƐ ƌŽŶĚƐ ;ĐǇůŝŶĚƌĞ͕ ĐƀŶĞ͕ ƐƉŚğƌĞͿ͘

ĠĐƌŝƌĞ ĐĞƐ ƐŽůŝĚĞƐ ŐĠŽŵĠƚƌŝƋƵĞƐ ĞŶ ƵƟ ůŝƐĂŶƚ ůĞ ǀŽĐĂďƵůĂŝƌĞ ĂĚĠƋƵĂƚ ͗ ĨĂĐĞ͕ ĂƌġƚĞ͕ ƐŽŵŵĞƚ͕ ďĂƐĞ͕ ƐƵƌĨĂĐĞ ůĂƚĠƌĂůĞ͘͘͘

ĠƚĞƌŵŝŶĞƌ ůĞƐ ƉŽƐŝƟ ŽŶƐ ƌĞůĂƟ ǀĞƐ ĚĞ ƐŽŵŵĞƚƐ͕ Ě͛ĂƌġƚĞƐ͕ ĚĞ ĨĂĐĞƐ͘

ƐƐŽĐŝĞƌ ƵŶ ƐŽůŝĚĞ ă ƐĞƐ Ěŝī ĠƌĞŶƚĞƐ ƌĞƉƌĠƐĞŶƚĂƟ ŽŶƐ ĚĂŶƐ ůĞ ƉůĂŶ͘

ŽŶƐƚƌƵŝƌĞ ƵŶ ĐƵďĞ͕ ƵŶ ƉĂƌĂůůĠůĠƉŝƉğĚĞ ƌĞĐƚĂŶŐůĞ ĞŶ ƉĞƌƐƉĞĐƟ ǀĞ ĐĂǀĂůŝğƌĞ͘

ZĞĐŽŶŶĂŠƚƌĞ ůĞ ĚĠǀĞůŽƉƉĞŵĞŶƚ Ě͛ƵŶ ĐƵďĞ͕ Ě͛ƵŶ ƉĂƌĂůůĠůĠƉŝƉğĚĞ ƌĞĐƚĂŶŐůĞ͕ Ě͛ƵŶ ƉƌŝƐŵĞ ĚƌŽŝƚ͘

ĂůĐƵůĞƌ ů͛ĂŝƌĞ Ğƚ ůĞ ǀŽůƵŵĞ ĚƵ ĐƵďĞ͕ ĚƵ ƉĂƌĂůůĠůĠƉŝƉğĚĞ ƌĞĐƚĂŶŐůĞ͕ ĚƵ ƉƌŝƐŵĞ ĚƌŽŝƚ Ğƚ ĚƵ ĐǇůŝŶĚƌĞ͘

&ŝŐƵƌĞƐ ŐĠŽŵĠƚƌŝƋƵĞƐ ĠůĠŵĞŶƚĂŝƌĞƐ Ğƚ ĚŝƐƚĂŶĐĞƐ 65

ŝī ĠƌĞŶĐŝĞƌ ƐƵƌĨĂĐĞ ƉůĂŶĞ Ğƚ ƉůĂŶ͘

ŝī ĠƌĞŶĐŝĞƌ ƵŶĞ ĚƌŽŝƚĞ͕ ƵŶĞ ĚĞŵŝͲĚƌŽŝƚĞ Ğƚ ƵŶ ƐĞŐŵĞŶƚ ĚĞ ĚƌŽŝƚĞ͘

ZĞĐŽŶŶĂŠƚƌĞ Ğƚ Ěŝī ĠƌĞŶĐŝĞƌ ĚĞƐ ĚƌŽŝƚĞƐ ƉĂƌĂůůğůĞƐ͕ ĚĞƐ ĚƌŽŝƚĞƐ ƐĠĐĂŶƚĞƐ Ğƚ ĚĞƐ ĚƌŽŝƚĞƐ ƉĞƌƉĞŶĚŝĐƵůĂŝƌĞƐ͘

dƌĂĐĞƌ ƵŶĞ ĚƌŽŝƚĞ ƉĂƌĂůůğůĞ ă ƵŶĞ ĂƵƚƌĞ ĚƌŽŝƚĞ͘

dƌĂĐĞƌ ƵŶĞ ĚƌŽŝƚĞ ƉĞƌƉĞŶĚŝĐƵůĂŝƌĞ ă ƵŶĞ ĂƵƚƌĞ ĚƌŽŝƚĞ͘

ZĞƉŽƌƚĞƌ ƵŶ ĂŶŐůĞ ĚŽŶŶĠ͘

144

ACTIVITÉS

Chapitre 7 Solides

ĐƚŝǀŝƚĠ ϭ ^ŽůŝĚĞƐ ĂƵ ƋƵŽƚŝĚŝĞŶ 1 >Ă ŵĂŵĂŶ ĚĞ DĂƚƚĠŽ ůƵŝ ĚĞŵĂŶĚĞ ĚĞ ƌĂŶŐĞƌ ůĞƐ ĐŽƵƌƐĞƐ ƋƵ͛ĞůůĞ ǀŝĞŶƚ ĚĞ ĨĂŝƌĞ ĚĂŶƐ ƵŶ ƐƵƉĞƌŵĂƌĐŚĠ͘ DĂƚƚĠŽ ƚƌŽƵǀĞ ƋƵĞ ĐĞƌƚĂŝŶƐ ĂƌƚŝĐůĞƐ ƌĞƐƐĞŵďůĞŶƚ ă ĚĞƐ ƐŽůŝĚĞƐ ƋƵ͛ŝů Ă ĠƚƵĚŝĠƐ ĞŶ ϲe ƉƌŝŵĂŝƌĞ͘ 1 2 3 4 5

ĂͿ ƐƐŽĐŝĞ ĐŚĂƋƵĞ ŽďũĞƚ ă ƐĂ ƌĞƉƌĠƐĞŶƚĂƟ ŽŶ ŐĠŽŵĠƚƌŝƋƵĞ͕ ŶŽŵŵĞͲůĂ͘

n° ͘ ͘ ͘ ͘ ͘ ͘

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

n° ͘ ͘ ͘ ͘ ͘ ͘

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

n° ͘ ͘ ͘ ͘ ͘ ͘

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ďͿ ŽŵƉůğƚĞ ůĞƐ ƉŚƌĂƐĞƐ͘ >ĞƐ ƐŽůŝĚĞƐ ĚŽŶƚ ƚŽƵƚĞƐ ůĞƐ ĨĂĐĞƐ ƐŽŶƚ ĚĞƐ ƐƵƌĨĂĐĞƐ ƉůĂŶĞƐ ƐŽŶƚ ĂƉƉĞůĠƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ >ĞƐ ƐŽůŝĚĞƐ ĚŽŶƚ ĂƵ ŵŽŝŶƐ ƵŶĞ ĚĞƐ ĨĂĐĞƐ ĞƐƚ ƵŶĞ ƐƵƌĨĂĐĞ ŶŽŶͲƉůĂŶĞ ƐŽŶƚ ĂƉƉĞůĠƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

145

ACTIVITÉS

Chapitre 7 Solides

ĐͿ ŽŵƉůğƚĞ͕ Ɛŝ ƉŽƐƐŝďůĞ͕ ůĞ ƚĂďůĞĂƵ ĂǀĞĐ ůĞ ŶƵŵĠƌŽ ĚĞƐ ƐŽůŝĚĞƐ ƌĞŶĐŽŶƚƌĠƐ͘ >ĞƐ ƐŽůŝĚĞƐ ͘͘͘

WŽůǇğĚƌĞ

EŽŶͲWŽůǇğĚƌĞ

ƉŽƐƐğĚĞŶƚ ĚĞƵǆ ďĂƐĞƐ ƐƵƉĞƌƉŽƐĂďůĞƐ͘ ƉŽƐƐğĚĞŶƚ ƵŶĞ ƐĞƵůĞ ďĂƐĞ͘ ŶĞ ƉŽƐƐğĚĞŶƚ ƉĂƐ ĚĞ ďĂƐĞ͘ 2 ĞƌƚĂŝŶƐ ƐŽůŝĚĞƐ ĚĞ ůĂ ƉĂŐĞ ƉƌĠĐĠĚĞŶƚĞ ĂƉƉĂƌƚŝĞŶŶĞŶƚ ă ůĂ ŐƌĂŶĚĞ ĨĂŵŝůůĞ ĚĞƐ ƉƌŝƐŵĞƐ ĚƌŽŝƚƐ͘ >ĞƐƋƵĞůƐ ͍ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ŽŵƉůğƚĞ ůĞƐ ƉŚƌĂƐĞƐ ƐƵŝǀĂŶƚĞƐ͘ ĂŶƐ ƵŶ ƉƌŝƐŵĞ ĚƌŽŝƚ͕ ʹ ůĞƐ ďĂƐĞƐ ƐŽŶƚ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ; ʹ ůĞƐ ĂƵƚƌĞƐ ĨĂĐĞƐ ƐŽŶƚ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

͘ KŶ ůĞƐ ĂƉƉĞůůĞ ůĞƐ ĨĂĐĞƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹ ůĞƐ ĂƌġƚĞƐ ƋƵŝ ƌĞůŝĞŶƚ ůĞƐ ĚĞƵǆ ďĂƐĞƐ ŽŶƚ ůĂ ŵġŵĞ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ĞƩ Ğ ůŽŶŐƵĞƵƌ Ɛ͛ĂƉƉĞůůĞ ůĂ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ĚƵ ƉƌŝƐŵĞ ĚƌŽŝƚ͘ /ů Ǉ Ă ĚĞƐ ƉƌŝƐŵĞƐ ĚƌŽŝƚƐ ƉĂƌƟ ĐƵůŝĞƌƐ ƉŽƵƌ ůĞƐƋƵĞůƐ ŽŶ ŶĞ ƐĂŝƚ ƉĂƐ ĚŝƐƟ ŶŐƵĞƌ ůĞƐ ďĂƐĞƐ ĚĞƐ ĂƵƚƌĞƐ ĨĂĐĞƐ͘ YƵĞůƐ ƐŽŶƚ ĐĞƐ ƉƌŝƐŵĞƐ ĚƌŽŝƚƐ ͍

3 sŽŝĐŝ ĚĞƐ ƐŽůŝĚĞƐ͘ WĂƌŵŝ ĐĞƵǆͲĐŝ͕ ĐĞƌƚĂŝŶƐ ŶĞ ƐŽŶƚ ƉĂƐ ĚĞƐ ƉƌŝƐŵĞƐ ĚƌŽŝƚƐ͖ ďĂƌƌĞͲůĞƐ͘ YƵĂŶĚ ůĞ ƐŽůŝĚĞ ĞƐƚ ƵŶ ƉƌŝƐŵĞ ĚƌŽŝƚ͕ ĐŽůŽƌŝĞ ĞŶ ƌŽƵŐĞ ƵŶĞ ďĂƐĞ͕ ĞŶ ǀĞƌƚ ƵŶĞ ĨĂĐĞ ůĂƚĠƌĂůĞ Ğƚ ĞŶ ďůĞƵ ƵŶĞ ŚĂƵƚĞƵƌ͘ ; ƌƌĂŶŐĞͲƚŽŝ ƉŽƵƌ ƋƵĞ ůĞƐ ĐŽƵůĞƵƌƐ ŶĞ ƐĞ ƐƵƉĞƌƉŽƐĞŶƚ ƉĂƐ ͊Ϳ 1

146

p.63 A1

ACTIVITÉS

Chapitre 7 Solides

p.63 Ϯͳϯ

ĂͿ ĂŶƐ ůĞ ƉŽůǇğĚƌĞ ĐŝͲĐŽŶƚƌĞ͕

ůĞ ƌĞĐƚĂŶŐůĞ ƌĞƉƌĠƐĞŶƚĞ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

p.64 B

ůĞ ƉŽŝŶƚ ƌĞƉƌĠƐĞŶƚĞ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ůĞ ƐĞŐŵĞŶƚ ΀&'΁ ƌĞƉƌĠƐĞŶƚĞ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ůĞ ƐĞŐŵĞŶƚ ΀, ΁ ƌĞƉƌĠƐĞŶƚĞ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ďͿ EŽƚĞ ůΖŝŶƚĞƌƐĞĐƟ ŽŶ ͙ ĚĞƐ ĂƌġƚĞƐ ΀ ΁ Ğƚ ΀ &΁ ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ĚĞƐ ĨĂĐĞƐ Ğƚ & ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ĚĞƐ ĂƌġƚĞƐ ΀ ,΁ Ğƚ ΀ ,΁ ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ĚĞƐ ĨĂĐĞƐ , Ğƚ & ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ĐƚŝǀŝƚĠ Ϯ ZĞƉƌĠƐĞŶƚĂƚŝŽŶƐ ĚĞ ƐŽůŝĚĞƐ 1 KŶ Ă ƌĞƉƌĠƐĞŶƚĠ ƵŶ ĐƵďĞ ĚĞ Ϯ͕ϱ Đŵ Ě͛ĂƌġƚĞ ƐŽƵƐ ĚĞƵǆ ƉĞƌƐƉĞĐƚŝǀĞƐ ĚŝĨĨĠƌĞŶƚĞƐ͘ ĂŶƐ ĐŚĂƋƵĞ ƌĞƉƌĠƐĞŶƚĂƟ ŽŶ͕ ͻ ƵƟ ůŝƐĞ ƵŶĞ ĐŽƵůĞƵƌ Ěŝī ĠƌĞŶƚĞ ƉŽƵƌ ƌĞƉĂƐƐĞƌ ĐŚĂƋƵĞ ƐĠƌŝĞ ĚΖĂƌġƚĞƐ ƉĂƌĂůůğůĞƐ͕ ͻ ƌĞƉğƌĞ ů͛;ůĞƐͿ ĂƌġƚĞ;ƐͿ ƌĞƉƌĠƐĞŶƚĠĞ;ƐͿ ĞŶ ǀƌĂŝĞ ŐƌĂŶĚĞƵƌ ƉĂƌ ƵŶ ƐǇŵďŽůĞ Ě͛ĠŐĂůŝƚĠ ; ͻ ƌĞƉğƌĞ ůĞƐ ĂŶŐůĞƐ ĚƌŽŝƚƐ ƉĂƌ ƵŶ ƐǇŵďŽůĞ ĚĞ ƉĞƌƉĞŶĚŝĐƵůĂƌŝƚĠ ; Ϳ͘ WĞƌƐƉĞĐƟ ǀĞ ĐĂǀĂůŝğƌĞ WĞƌƐƉĞĐƟ ǀĞ ĂǀĞĐ ƵŶ ƉŽŝŶƚ ĚĞ ĨƵŝƚĞ

ŽŵƉůğƚĞ ůĞ ƚĂďůĞĂƵ ƉĂƌ ͨ sƌĂŝ ͩ ŽƵ ͨ &ĂƵǆ ͩ͘ ůĞ ƉĂƌĂůůĠůŝƐŵĞ ĞƐƚ ůĂ ůŽŶŐƵĞƵƌ ĞƐƚ ĐŽŶƐĞƌǀĠ ƉŽƵƌ ůĞƐ ĐŽŶƐĞƌǀĠĞ ƉŽƵƌ ůĞƐ ĂƌġƚĞƐ ͘͘͘ ĂƌġƚĞƐ ͙ ǀĞƌƟ ĐĂůĞƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ĚĞ ůĂ ĨĂĐĞ ĂǀĂŶƚ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ĂŶƐ ƵŶĞ

7 Ϳ͕

ůĂ ƉĞƌƉĞŶĚŝĐƵůĂƌŝƚĠ ĚĞƐ ĂƌġƚĞƐ ĞƐƚ ĐŽŶƐĞƌǀĠĞ ĚĂŶƐ ͙ la face avant ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ƉĞƌƐƉĞĐƟ ǀĞ ĐĂǀĂůŝğƌĞ͕

ŚŽƌŝǌŽŶƚĂůĞƐ

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ĚĞ ůĂ ĨĂĐĞ ĂƌƌŝğƌĞ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ůĂ ĨĂĐĞ ĂƌƌŝğƌĞ

ŽďůŝƋƵĞƐ

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ĚĞƐ ĂƵƚƌĞƐ ĨĂĐĞƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ůĞƐ ĂƵƚƌĞƐ ĨĂĐĞƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ĂŶƐ ƵŶĞ ƉĞƌƐƉĞĐƟ ǀĞ ĂǀĞĐ ƵŶ ƉŽŝŶƚ ĚĞ ĨƵŝƚĞ͕

ǀĞƌƟ ĐĂůĞƐ

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ĚĞ ůĂ ĨĂĐĞ ĂǀĂŶƚ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

la face avant

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ŚŽƌŝǌŽŶƚĂůĞƐ

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ĚĞ ůĂ ĨĂĐĞ ĂƌƌŝğƌĞ ͘ ͘ ͘ ͘ ͘ ͘

ůĂ ĨĂĐĞ ĂƌƌŝğƌĞ

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ŽďůŝƋƵĞƐ

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ĚĞƐ ĂƵƚƌĞƐ ĨĂĐĞƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ůĞƐ ĂƵƚƌĞƐ ĨĂĐĞƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

147

ACTIVITÉS

Chapitre 7 Solides

WĞƌƐƉĞĐƟ ǀĞ ĂǀĞĐ ĚĞƵǆ ƉŽŝŶƚƐ ĚĞ ĨƵŝƚĞ

YƵĞůůĞƐ ƐŽŶƚ ůĞƐ ƉƌŽƉƌŝĠƚĠƐ ĐŽŶƐĞƌǀĠĞƐ ĚĂŶƐ ĐĞ ƚǇƉĞ ĚĞ ƉĞƌƐƉĞĐƟ ǀĞ ͍ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

YƵĞůůĞ ĞƐƚ ůĂ ƉĞƌƐƉĞĐƟ ǀĞ ƋƵĞ ƚƵ ĂƐ ůĞ ƉůƵƐ ƵƟ ůŝƐĠĞ ă ů͛ĠĐŽůĞ ƉƌŝŵĂŝƌĞ Ğƚ ƉŽƵƌƋƵŽŝ ͍ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

2 /ŶĚŝƋƵĞ ƐŽƵƐ ĐŚĂƋƵĞ ŝŵĂŐĞ͕ ůĞ ƚǇƉĞ ĚĞ ƉĞƌƐƉĞĐƚŝǀĞ ƵƚŝůŝƐĠ͘

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

3 ǆƉůŝƋƵĞ ƉŽƵƌƋƵŽŝ ĐĞƐ ƚƌŽŝƐ ƌĞƉƌĠƐĞŶƚĂƟ ŽŶƐ Ě͛ƵŶ ĐƵďĞ ĞŶ ƉĞƌƐƉĞĐƟ ǀĞ ĐĂǀĂůŝğƌĞ ƐŽŶƚ ŝŶĐŽƌƌĞĐƚĞƐ͘ H

H D

148

F B

H D

C E

E A

C E

F B

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

p.65

C ϭͳϮͳϯ

ACTIVITÉS

Chapitre 7 Solides

4 >Ğ ĐƵďĞ ĐŝͲĐŽŶƚƌĞ Ă ĠƚĠ ƌĞƉƌĠƐĞŶƚĠ ĞŶ ƉĞƌƐƉĞĐƟ ǀĞ ĐĂǀĂůŝğƌĞ ĞŶ ƵƟ ůŝƐĂŶƚ ůĞƐ ƉĂƌĂŵğƚƌĞƐ ĐŝͲĚĞƐƐŽƵƐ͘ WůĂĐĞͲůĞƐ ƐƵƌ ĐĞ ĐƵďĞ͘

H D

G C

ZĂƉƉŽƌƚ ĚĞ ƌĠĚƵĐƟ ŽŶ ĚĞƐ ĨƵǇĂŶƚĞƐ ͗ ϭͬϮ ͮ ͮ с ϯ Đŵ Ğƚ ͮ &ͮ с ϭ͕ϱ Đŵ ŶŐůĞ ĚĞ ĨƵŝƚĞ ͗ ϯϬΣ |FBTͮ с ϯϬΣ

F A

Ŷ ƵƟ ůŝƐĂŶƚ ůĞ ŵġŵĞ ƌĂƉƉŽƌƚ ĚĞ ƌĠĚƵĐƟ ŽŶ Ğƚ ůĞ ŵġŵĞ ĂŶŐůĞ ĚĞ ĨƵŝƚĞ͕ ĐŽŶƐƚƌƵŝƐ ͘͘͘ ƵŶ ƉĂƌĂůůĠůĠƉŝƉğĚĞ ƌĞĐƚĂŶŐůĞ ƋƵŝ Ă ƉŽƵƌ ƵŶ ĐƵďĞ ĚĞ ϰ Đŵ Ě͛ĂƌġƚĞ͘ ůŽŶŐƵĞƵƌ ϱϬ ŵŵ͕ ƉŽƵƌ ůĂƌŐĞƵƌ ϯϰ ŵŵ Ğƚ ƉŽƵƌ ŚĂƵƚĞƵƌ Ϯϴ ŵŵ͘

5 ĐŚğǀĞ ůĞƐ ƉĂƌĂůůĠůĠƉŝƉğĚĞƐ ƌĞĐƚĂŶŐůĞƐ ĚŽŶƚ ƚƌŽŝƐ ĂƌġƚĞƐ ƐŽŶƚ ƚƌĂĐĠĞƐ ĞŶ ƌĞƉƌĠƐĞŶƚĂŶƚ ƵŶŝƋƵĞŵĞŶƚ ůĞƐ ĂƌġƚĞƐ ǀŝƐŝďůĞƐ͘ ŶƐƵŝƚĞ͕ ƚƌĂĐĞ ůĞƐ ĂƌġƚĞƐ ĐĂĐŚĠĞƐ ĞŶ ƉŽŝŶƟ ůůĠƐ͘

ĐŚğǀĞ ůĞƐ ĐƵďĞƐ ĚŽŶƚ ĚĞƵǆ ĂƌġƚĞƐ ƐŽŶƚ ƚƌĂĐĠĞƐ ĞŶ ƌĞƉƌĠƐĞŶƚĂŶƚ ƵŶŝƋƵĞŵĞŶƚ ůĞƐ ĂƌġƚĞƐ ǀŝƐŝďůĞƐ͘ ŶƐƵŝƚĞ͕ ƚƌĂĐĞ ůĞƐ ĂƌġƚĞƐ ĐĂĐŚĠĞƐ ĞŶ ƉŽŝŶƟ ůůĠƐ͘

6 ^ŝ ƚƵ ƐĂŝƐ ƋƵĞ ůĂ ĨĂĐĞ ǀĞƌƚĞ ĞƐƚ ƵŶĞ ĨĂĐĞ ĞŶƟ ğƌĞŵĞŶƚ ǀŝƐŝďůĞ͕ ƌĞƉĂƐƐĞ ĞŶ ƌŽƵŐĞ ůĞƐ ĂƌġƚĞƐ ǀŝƐŝďůĞƐ Ğƚ ĐŽůŽƌŝĞ ůĞƐ ĨĂĐĞƐ ǀŝƐŝďůĞƐ ĚĂŶƐ ĚĞƐ ĐŽƵůĞƵƌƐ Ěŝī ĠƌĞŶƚĞƐ͘

149

ACTIVITÉS

Chapitre 7 Solides

7 Ƶ ĐŽƵƌƐ ĚĞ ĚĞƐƐŝŶ͕ ƋƵĂƚƌĞ ĠůğǀĞƐ ;DĂƌŝĞ͕ ,ĠůğŶĞ͕ ^ŽƉŚŝĞ Ğƚ &ůŽƌŝĞͿ ŽŶƚ ƌĠĂůŝƐĠ ůĂ ƉĞƌƐƉĞĐƟ ǀĞ ĐĂǀĂůŝğƌĞ Ě͛ƵŶ ƐŽůŝĚĞ ƋƵ͛ĞůůĞƐ ŽŶƚ ŽďƐĞƌǀĠ ă ƉĂƌƟ ƌ ĚĞ ůĞƵƌ ƉŽƐŝƟ ŽŶ ƌĞƐƉĞĐƟ ǀĞ͘ Ŷ ĚĞƐƐŽƵƐ ĚĞƐ ǀƵĞƐ ƉƌŽƉŽƐĠĞƐ͕ ŝŶƐĐƌŝƐ ůĞ ŶŽŵ ĚĞ ƚƌŽŝƐ ĚĞ ĐĞƐ ƋƵĂƚƌĞ ĠůğǀĞƐ͘ ŶƐƵŝƚĞ͕ ƌĞƉƌĠƐĞŶƚĞ ĚĂŶƐ ĐŚĂƋƵĞ ǀƵĞ͕ ůĞƐ ĂƌġƚĞƐ ĐĂĐŚĠĞƐ͘

ne Hélè

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Flor

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Marie

Sophie

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

8 sŽŝĐŝ ƵŶ ĐƵďĞ ƌĞƉƌĠƐĞŶƚĠ ĞŶ ƉĞƌƐƉĞĐƚŝǀĞ ĐĂǀĂůŝğƌĞ͘

ŽŵƉůğƚĞ ůĞƐ ƉŚƌĂƐĞƐ ƐƵŝǀĂŶƚĞƐ ͗

G F

ʹ ĚĂŶƐ ůĂ ƌĠĂůŝƚĠ͕ ůĞƐ ϲ ĨĂĐĞƐ ĚƵ ĐƵďĞ ƐŽŶƚ ĚĞƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ; ʹ ƐƵƌ ůĞ ĚĞƐƐŝŶ͕ ůĂ ĨĂĐĞ & ĞƐƚ ƵŶ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ; ʹ ƐƵƌ ůĞ ĚĞƐƐŝŶ͕ ůĂ ĨĂĐĞ &' ĞƐƚ ƵŶ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘͘

C A

B dƌĂĐĞ ƐƵƌ ůĞ ĐƵďĞ͕ ůĞƐ ƚƌŝĂŶŐůĞƐ ,' Ğƚ ' ͘ /ŶĚŝƋƵĞ͕ ĚĂŶƐ ůĂ ƌĠĂůŝƚĠ͕ ůĂ ŶĂƚƵƌĞ ĚĞ ĐĞƐ ƚƌŝĂŶŐůĞƐ Ğƚ ũƵƐƟ Į Ğ͘

,' ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ 9

' ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ZĞƉƌŽĚƵŝƐ ůĞƐ ƋƵĂĚƌŝůĂƚğƌĞƐ &D, Ğƚ Zhd^ ŝŶƐĐƌŝƚƐ ĚĂŶƐ ůĞƐ ĨĂĐĞƐ &', Ğƚ '& ĚƵ ĐƵďĞ ƌĞƉƌĠƐĞŶƚĠ ĞŶ ƉĞƌƐƉĞĐƚŝǀĞ ĐĂǀĂůŝğƌĞ͘ H M G H

R D U

T C

E F A >Ğ ƋƵĂĚƌŝůĂƚğƌĞ &D, ĞƐƚ ƵŶ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

C B B >Ğ ƋƵĂĚƌŝůĂƚğƌĞ Zhd^ ĞƐƚ ƵŶ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ZĞƉƌŽĚƵŝƐ ůĞƐ ƋƵĂĚƌŝůĂƚğƌĞƐ YKEW Ğƚ /:<> ŝŶƐĐƌŝƚƐ ĚĂŶƐ ůĞƐ ĨĂĐĞƐ &', Ğƚ '& ĚƵ ĐƵďĞ ƌĞƉƌĠƐĞŶƚĠ ĞŶ ƉĞƌƐƉĞĐƟ ǀĞ ĐĂǀĂůŝğƌĞ͘ H P G Q E H G G F N O J F I L K D C E F A >Ğ ƋƵĂĚƌŝůĂƚğƌĞ YKEW ĞƐƚ ƵŶ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ 150

C B B >Ğ ƋƵĂĚƌŝůĂƚğƌĞ /:<> ĞƐƚ ƵŶ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ACTIVITÉS

Chapitre 7 Solides

ĐƚŝǀŝƚĠ ϯ WůĂŶƐ͕ ĨĂĐĞƐ͕ ĚƌŽŝƚĞƐ Ğƚ ĂƌġƚĞƐ 1 ĂͿ >Ğ ƐŽůŝĚĞ ƌĞƉƌĠƐĞŶƚĠ ĐŝͲĐŽŶƚƌĞ ĞƐƚ ƵŶ ĐƵďĞ͘ ^ŝ ůΖŽŶ ƉƌŽůŽŶŐĞ ůĂ ĨĂĐĞ ĚĂŶƐ ƚŽƵƐ ůĞƐ ƐĞŶƐ͕ ŽŶ ŽďƟ ĞŶƚ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

F d

EŽƵƐ ƉŽƵǀŽŶƐ ůĞ ŶŽŵŵĞƌ ƉĂƌ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

^ŝ ůΖŽŶ ƉƌŽůŽŶŐĞ ůΖĂƌġƚĞ ΀ &΁ ĚĂŶƐ ůĞƐ ĚĞƵǆ ƐĞŶƐ͕ ŽŶ ŽďƟ ĞŶƚ

EŽƵƐ ƉŽƵǀŽŶƐ ůĂ ŶŽŵŵĞƌ ƉĂƌ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

p.66 D

ďͿ ĂŶƐ ĐŚĂƋƵĞ ĐĂƐ͕ ƚƌĂĐĞ ůĞƐ ĚƌŽŝƚĞƐ ĚĞŵĂŶĚĠĞƐ ƐƵƌ ůĞ ĐƵďĞ͘ ĠƚĞƌŵŝŶĞ Ɛŝ ĞůůĞƐ ƐĞ ƚƌŽƵǀĞŶƚ͕ ŽƵŝ ŽƵ ŶŽŶ͕ ĚĂŶƐ ƵŶ ŵġŵĞ ƉůĂŶ͘ ŽŶŶĞ ĂǀĞĐ ƉƌĠĐŝƐŝŽŶ ůĞƵƌ ƉŽƐŝƟ ŽŶ ƌĞůĂƟ ǀĞ Ğƚ ƚƌĂĚƵŝƐ ĐĞůůĞͲĐŝ ĞŶ ůĂŶŐĂŐĞ ŵĂƚŚĠŵĂƟ ƋƵĞ͘ Ğƚ & &' Ğƚ & & Ğƚ , Ğƚ B A

E G

p.67

E G

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ &

&' ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ &

& ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

, ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

2 >Ğ ƉƌŝƐŵĞ ĐŝͲĐŽŶƚƌĞ ĞƐƚ ĐŽŶƐƚƌƵŝƚ ă ƉĂƌƚŝƌ ĚĞ ůĂ ũƵǆƚĂƉŽƐŝƚŝŽŶ ĚĞ ĐƵďĞƐ ŝĚĞŶƚŝƋƵĞƐ͘ ĂͿ ŽŵƉůğƚĞ ƉĂƌ sƌĂŝ ŽƵ &ĂƵǆ͘ >Ğ ƉŽŝŶƚ͙

>Ğ ƐĞŐŵĞŶƚ͙

ĂƉƉĂƌƟ ĞŶƚ ĂƵ ƉůĂŶ ͘

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

΀,/΁ ĞƐƚ ƵŶĞ ƉĂƌƟ Ğ ĚƵ ƉůĂŶ >͘

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

' ĂƉƉĂƌƟ ĞŶƚ ĂƵ ƉůĂŶ >͘

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

΀&'΁ ĞƐƚ ƵŶĞ ƉĂƌƟ Ğ ĚƵ ƉůĂŶ ,͘

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

, ĂƉƉĂƌƟ ĞŶƚ ĂƵ ƉůĂŶ :<>͘

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

΀:<΁ ĞƐƚ ƵŶĞ ƉĂƌƟ Ğ ĚĞ ůĂ ĚƌŽŝƚĞ &:͘

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

: ĂƉƉĂƌƟ ĞŶƚ ĂƵ ƉůĂŶ &'͘

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

΀ ΁ ĞƐƚ ƵŶĞ ƉĂƌƟ Ğ ĚĞ ůĂ ĚƌŽŝƚĞ ',͘

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ďͿ ŽŵƉůğƚĞ ƉĂƌ ͕ͬͬ ͕ͬͬ ^ ŽƵ Ő ;ŐĂƵĐŚĞͿ ͘ ͘ ͘ ͘ ͘ ͘ ͘ & >< ͘ ͘ ͘ ͘ ͘ ͘ ͘ ',/: ',/: ͘ ͘ ͘ ͘ ͘ ͘ ͘/:<>

& ͘ ͘ ͘ ͘ ͘ ͘ ͘ /: AE ͘ ͘ ͘ ͘ ͘ ͘ ͘ , & ͘ ͘ ͘ ͘ ͘ ͘ ͘ :<

AD ͘ ͘ ͘ ͘ ͘ ͘ ͘ >< ,> ͘ ͘ ͘ ͘ ͘ ͘ ͘ DI , ͘ ͘ ͘ ͘ ͘ ͘ ͘ &'

&', ͘ ͘ ͘ ͘ ͘ ͘ ͘ ',/: & ͘ ͘ ͘ ͘ ͘ ͘ ͘ ',/: >/, ͘ ͘ ͘ ͘ ͘ ͘ ͘ /:<>

΀ ΁ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ΀ ΁ ΀':΁ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ΀:<΁ ΀ ,΁ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ΀&'΁

΀/>΁ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ΀ >΁ ΀<>΁ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ΀<:΁ ΀ ΁ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ΀/:΁

F E

G I H D

K L 151

ACTIVITÉS

Chapitre 7 Solides

3 >Ğ ƐŽůŝĚĞ ĐŝͲĐŽŶƚƌĞ ĞƐƚ ƵŶ ƉƌŝƐŵĞ ĚƌŽŝƚ ă ďĂƐĞ ƚƌĂƉĠǌŽŢĚĂůĞ͘ ; Ʃ ĞŶƟ ŽŶ͕ ůĞƐ ĚƌŽŝƚĞƐ ĂƩ ĞŶĚƵĞƐ ĐŽŵŵĞ ƐŽůƵƟ ŽŶƐ ĚŽŝǀĞŶƚ ĐŽŶƚĞŶŝƌ ƵŶĞ ĂƌġƚĞ ĚƵ ƉƌŝƐŵĞ͘Ϳ G ŝƚĞ ůĞƐ ĨĂĐĞƐ ƉĞƌƉĞŶĚŝĐƵůĂŝƌĞƐ ă ůĂ ĨĂĐĞ ', ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ŝƚĞ ůĂ ;ůĞƐͿ ĨĂĐĞ;ƐͿ ƉĂƌĂůůğůĞ;ƐͿ ă ůĂ ĨĂĐĞ & ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ C F ŝƚĞ ůĂ ;ůĞƐͿ ĨĂĐĞ;ƐͿ ƉĂƌĂůůğůĞ;ƐͿ ă ůĂ ĚƌŽŝƚĞ ', ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ B ŝƚĞ ůĂ ;ůĞƐͿ ĨĂĐĞ;ƐͿ ƐĠĐĂŶƚĞ;ƐͿ ă ůĂ ĚƌŽŝƚĞ ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ H E ŝƚĞ ůĂ ;ůĞƐͿ ĨĂĐĞ;ƐͿ ŐĂƵĐŚĞ;ƐͿ ă ůĂ ĚƌŽŝƚĞ ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ D A

ĐƚŝǀŝƚĠ ϰ Développements de solides 1 ZĞƚƌŽƵǀĞ ůĞƐ ĚĠǀĞůŽƉƉĞŵĞŶƚƐ ĐŽƌƌĞƐƉŽŶĚĂŶƚ ĂƵǆ ƐŽůŝĚĞƐ ĐŝͲĚĞƐƐŽƵƐ͘ ŽŵƉůğƚĞ ůĞ ƚĂďůĞĂƵ͘ a

f g

^ŽůŝĚĞ

ĠǀĞůŽƉƉĞŵĞŶƚ

2 1 3

7 6

152

ACTIVITÉS

Chapitre 7 Solides

2 WĂƌŵŝ ůĞƐ ĨŝŐƵƌĞƐ ƐƵŝǀĂŶƚĞƐ͕ ƋƵĞůůĞƐ ƐŽŶƚ ĐĞůůĞƐ ƋƵŝ ƌĞƉƌĠƐĞŶƚĞŶƚ ůĞ ĚĠǀĞůŽƉƉĞŵĞŶƚ Ě͛ƵŶ ƉĂƌĂůůĠůĠƉŝƉğĚĞ ƌĞĐƚĂŶŐůĞ ͍ WŽƵƌ ƚ͛ĂŝĚĞƌ͕ ĐŽůŽƌŝĞ ĚĂŶƐ ĐŚĂƋƵĞ ĚĠǀĞůŽƉƉĞŵĞŶƚ ůĞƐ ĠǀĞŶƚƵĞůůĞƐ ĨĂĐĞƐ ƉĂƌĂůůğůĞƐ ĂǀĞĐ ůĂ ŵġŵĞ ĐŽƵůĞƵƌ͘ 1 2

6 3 dĞƌŵŝŶĞ ůĞƐ ĚĠǀĞůŽƉƉĞŵĞŶƚƐ ĚĞƐ ƉĂƌĂůůĠůĠƉŝƉğĚĞƐ ƌĞĐƚĂŶŐůĞƐ ƉƌŽƉŽƐĠƐ͘

ĐƚŝǀŝƚĠ ϱ Développements du cube 1 >Ğ ĚĠǀĞůŽƉƉĞŵĞŶƚ ĚƵ ĐƵďĞ ĞƐƚ ĐŽŵƉŽƐĠ ĚĞ Ɛŝǆ ĐĂƌƌĠƐ͘ YƵĞŶƟ Ŷ Ă ĚĞƐƐŝŶĠ ĞŶ ǀĞƌƚ ůĞƐ ĐŝŶƋ ƉƌĞŵŝğƌĞƐ ĨĂĐĞƐ ĚƵ ĚĠǀĞůŽƉƉĞŵĞŶƚ͘ /ů ŚĠƐŝƚĞ ƉŽƵƌ ƉůĂĐĞƌ ůĂ ĚĞƌŶŝğƌĞ͘ ŝĚĞͲůĞ ĞŶ ĐŽůŽƌŝĂŶƚ ůĂ ƐŝǆŝğŵĞ ĨĂĐĞ ƉĂƌŵŝ ůĞƐ ƉƌŽƉŽƐŝƟ ŽŶƐ ϭ͕ Ϯ ŽƵ ϯ͘ ĂͿ ďͿ ĐͿ 1 3 1

2 2 3

3 2 sŽŝĐŝ ƵŶ ĐƵďĞ Ğƚ ĚĞƵǆ ĚĠǀĞůŽƉƉĞŵĞŶƚƐ ƌĠĚƵŝƚƐ ĚĞ ĐĞůƵŝͲĐŝ͘ ^Ƶƌ ĐŚĂƋƵĞ ĚĠǀĞůŽƉƉĞŵĞŶƚ͕ ĐŽůŽƌŝĞ ůĞƐ ĨĂĐĞƐ ƋƵŝ ůĞ ƐŽŶƚ ƐƵƌ ůĞ ĐƵďĞ͘ WůĂĐĞ ůĞƐ ůĞƩ ƌĞƐ ŵĂŶƋƵĂŶƚĞƐ ƐƵƌ ĐŚĂĐƵŶ Ě͛ĞƵǆ͘ D

C B

H E

G F

153

ACTIVITÉS

Chapitre 7 Solides

3 ZĞƉƌŽĚƵŝƐ ůĞƐ ƚƌĂĐĠƐ ƐƵƌ ůĂ ƉĞƌƐƉĞĐƟ ǀĞ͘ C G H E F

H E G

ZĞƉƌŽĚƵŝƐ ůĞƐ ƚƌĂĐĠƐ ƐƵƌ ůĞ ĚĠǀĞůŽƉƉĞŵĞŶƚ͘ C G

B E

F D

ĐƚŝǀŝƚĠ ϲ sƵĞƐ ĐŽŽƌĚŽŶŶĠĞƐ >ĞƐ ǀƵĞƐ ĐŽŽƌĚŽŶŶĠĞƐ ƌĞƉƌĠƐĞŶƚĞŶƚ ůĞƐ ŽďũĞƚƐ ĞŶ ƐĞ ƉŽƐŝƟ ŽŶŶĂŶƚ ă ƚƌŽŝƐ ĞŶĚƌŽŝƚƐ Ěŝī ĠƌĞŶƚƐ ͗ ĞŶ ĨĂĐĞ ĚĞ ů͛ŽďũĞƚ ;ǀƵĞ ĚĞ ĨĂĐĞͿ͕ ƐƵƌ ůĞ ĐƀƚĠ ŐĂƵĐŚĞ ĚĞ ů͛ŽďũĞƚ ;ǀƵĞ ĚĞ ĐƀƚĠͿ Ğƚ ĂƵͲĚĞƐƐƵƐ ĚĞ ů͛ŽďũĞƚ ;ǀƵĞ ĚĞ ĚĞƐƐƵƐͿ͘ hŶĞ ƉĂƌƟ ĐƵůĂƌŝƚĠ ĚĞ ĐĞƩ Ğ ƌĞƉƌĠƐĞŶƚĂƟ ŽŶ ĞƐƚ ƋƵĞ ůĂ ǀƵĞ ĚĞ ĚĞƐƐƵƐ ƐĞ ĚĞƐƐŝŶĞ ĞŶ ĚĞƐƐŽƵƐ ĚĞ ůĂ ǀƵĞ ĚĞ ĨĂĐĞ Ğƚ ƋƵĞ ůĂ ǀƵĞ ĚĞ ĐƀƚĠ ŐĂƵĐŚĞ ƐĞ ĚĞƐƐŝŶĞ ă ĚƌŽŝƚĞ ĚĞ ůĂ ǀƵĞ ĚĞ ĨĂĐĞ͘ e ed

e fac

Vu ed ec ôté

Vue de face

Vue de côté

7 us

e Vu

ss de

Vue de dessus

ŽůŽƌŝĞ ůĞƐ ƚƌŽŝƐ ǀƵĞƐ ĐŽŽƌĚŽŶŶĠĞƐ͘ Vue de face Vue de côté

Vue de face Vue de côté

Vue de dessus

2 ŽůŽƌŝĞ ůĂ ƉĞƌƐƉĞĐƟ ǀĞ͘

154

Vue de face Vue de côté

Vue de dessus

p.66 C4

ACTIVITÉS

Chapitre 7 Solides

3 /ŶĚŝƋƵĞ ůĞƐ ĐŽƚĞƐ ƐƵƌ ůĂ ƉĞƌƐƉĞĐƟ ǀĞ͘ Vue de face

Vue de côté

Vue de face

Vue de côté 4

8 16

4 3

Vue de dessus

ĐƚŝǀŝƚĠ ϳ WƌŝƐŵĞƐ Ğƚ ĚĠŶŽŵďƌĞŵĞŶƚ 1 ŽŵƉůğƚĞ͘

EŽŵďƌĞ ĚĞ ƐŽŵŵĞƚƐ

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

EŽŵďƌĞ Ě͛ĂƌġƚĞƐ

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

EŽŵďƌĞ ĚĞ ĨĂĐĞƐ

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

2 ĠƚĞƌŵŝŶĞ ůĞƐ ƌĞŶƐĞŝŐŶĞŵĞŶƚƐ ĚĞŵĂŶĚĠƐ ƐĂŶƐ ƌĞƉƌĠƐĞŶƚĞƌ ůĞƐ ƐŽůŝĚĞƐ͘ WƌŝƐŵĞ ă ďĂƐĞ ƉĞŶƚĂŐŽŶĂůĞ ŚĞǆĂŐŽŶĂůĞ ;ϱ ĐƀƚĠƐͿ ;ϲ ĐƀƚĠƐͿ

ŽĐƚŽŐŽŶĂůĞ ;ϴ ĐƀƚĠƐͿ

ă ϭϬϬ ĐƀƚĠƐ

ă Ŷ ĐƀƚĠƐ

EŽŵďƌĞ ĚĞ ƐŽŵŵĞƚƐ EŽŵďƌĞ Ě͛ĂƌġƚĞƐ

p.64 A4

EŽŵďƌĞ ĚĞ ĨĂĐĞƐ 3 hŶ ƉƌŝƐŵĞ ĚƌŽŝƚ Ă ϯϲ ĂƌġƚĞƐ͘ YƵĞů ĞƐƚ ůĞ ŶŽŵďƌĞ ĚĞ ĨĂĐĞƐ Ğƚ ĚĞ ƐŽŵŵĞƚƐ ĚĞ ĐĞ ƉƌŝƐŵĞ ͍ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

155

ACTIVITÉS

Chapitre 7 Solides

ĐƚŝǀŝƚĠ ϴ WƌŽďůğŵĞƐ 1 >Ă ŵĂƋƵĞƚƚĞ ƌĞƉƌĠƐĞŶƚĞ ƵŶ ĞŶƐĞŵďůĞ ĚĞ ďąƚŝŵĞŶƚƐ ĚĞ ĨĞƌŵĞ͘ ŚĂƋƵĞ ďąƚŝŵĞŶƚ ĞƐƚ ĐŽŵƉŽƐĠ ĚĞ ĚŝĨĨĠƌĞŶƚƐ ƐŽůŝĚĞƐ͘ ĂůĐƵůĞ ƉŽƵƌ ĐŚĂĐƵŶ Ě͛ĞƵǆ ƐŽŶ ǀŽůƵŵĞ ƐĂĐŚĂŶƚ ƋƵĞ ůĞƐ ŵĞƐƵƌĞƐ ƐŽŶƚ ĞǆƉƌŝŵĠĞƐ ĞŶ ŵğƚƌĞ͘ Vue de face Vue de côté 2 2 6 6

1,5

3 2

Vue de dessus

Perspec ve 7 6 1

156

p.68

Chapitre 7 Solides

ACTIVITÉS

2 dŚŽŵĂƐ͕ ƉĂƐƐŝŽŶŶĠ ĚĞ ƉŽŝƐƐŽŶƐ͕ Ă ĂŵĠŶĂŐĠ ƵŶ ŶŽƵǀĞů ĂƋƵĂƌŝƵŵ ĞŶ ƌĞƐƉĞĐƚĂŶƚ ůĞƐ ĐŽŶƐĞŝůƐ ĚƵ ǀĞŶĚĞƵƌ͘ /ů Ă ĚŽŶĐ ƉůĂĐĠ ĂƵ ĨŽŶĚ ĚĞ ĐĞůƵŝͲĐŝ ƵŶĞ ĐŽƵĐŚĞ ĚĞ ƐĂďůĞ ĚĞ ϱ Đŵ Ě͛ĠƉĂŝƐƐĞƵƌ Ğƚ͕ ƉŽƵƌ ĠǀŝƚĞƌ ůĞƐ ĚĠďŽƌĚĞŵĞŶƚƐ͕ ŝů ů͛Ă ƌĞŵƉůŝ ũƵƐƋƵ͛ă ϱ Đŵ ĚƵ ďŽƌĚ͘ ^ĂĐŚĂŶƚ ƋƵΖŝů Ă ƵƚŝůŝƐĠ ƵŶ ƐĞĂƵ ĚΖƵŶĞ ĐĂƉĂĐŝƚĠ ĚĞ ϭϬ ůŝƚƌĞƐ͕ ĚĂŶƐ ůĞƋƵĞů ŝů ǀĞƌƐĞ ĐŚĂƋƵĞ ĨŽŝƐ ϴ ůŝƚƌĞƐ ĚΖĞĂƵ͕ ĚĠƚĞƌŵŝŶĞ ůĞ ŶŽŵďƌĞ ĚĞ ƐĞĂƵǆ ƋƵŝ ĨƵƌĞŶƚ ŶĠĐĞƐƐĂŝƌĞƐ ĂƵ ƌĞŵƉůŝƐƐĂŐĞ ĚĞ ů͛ĂƋƵĂƌŝƵŵ͘ ŝŵĞŶƐŝŽŶƐ ĚĞ ůΖĂƋƵĂƌŝƵŵ ͗ > с ϲϬ Đŵപപů с ϰϬ ĐŵപപŚ с ϱϬ Đŵ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ƵƌĂŶƚ ůĂ ŶƵŝƚ͕ dŚŽŵĂƐ ƌġǀĞ ƋƵ͛ŝů ƉŽƐƐğĚĞ ƋƵĂƚƌĞ ƉŽŝƐƐŽŶƐ ͨ ůĂǀĞͲǀŝƚƌĞ ͩ ŝŶƚĞůůŝŐĞŶƚƐ ƋƵŝ ƐĞƌĂŝĞŶƚ ĐĂƉĂďůĞƐ ĚĞ Ɛ͛ŽƌŐĂŶŝƐĞƌ ƉŽƵƌ ŶĞƩ ŽǇĞƌ ĐŚĂƋƵĞ ũŽƵƌ ƵŶĞ ƉĂƌƟ Ğ ĚĞƐ ǀŝƚƌĞƐ͘ ŝŶƐŝ͕ ƋƵŽƟ ĚŝĞŶŶĞŵĞŶƚ͕ ĐŚĂƋƵĞ ƉŽŝƐƐŽŶ ůĂǀĞƌĂŝƚ ůΖĠƋƵŝǀĂůĞŶƚ ĚΖƵŶ ĐĂƌƌĠ ĚĞ ϮϬ Đŵ ĚĞ ĐƀƚĠ͘ ŽŵďŝĞŶ ĚĞ ũŽƵƌƐ ŵĞƩ ƌŽŶƚ ĐĞƵǆͲĐŝ ƉŽƵƌ ŶĞƩ ŽǇĞƌ ƚŽƵƚĞƐ ůĞƐ ǀŝƚƌĞƐ ͍ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

3 hŶĞ ĞŶƚƌĞƉƌŝƐĞ ƐƚŽĐŬĞ ůĞƐ ĐĠƌĠĂůĞƐ ĚĂŶƐ ƵŶ ƐŝůŽ ĚŽŶƚ ǀŽŝĐŝ ůĞƐ ĚŝŵĞŶƐŝŽŶƐ ͗ >ϭ с ϭϬ ŵ͕ >Ϯ с Ϯ ŵ͕ с ϲ ŵ /ů ĞƐƚ ĂůŝŵĞŶƚĠ ƉĂƌ ĚĞƐ ĐĂŵŝŽŶƐ ĚŽŶƚ ůĂ ďĞŶŶĞ Ă ƉŽƵƌ ĚŝŵĞŶƐŝŽŶƐ ͗ ϰ ŵ ĚĞ ůŽŶŐƵĞƵƌ͕ Ϯ͕ϱ ŵ ĚĞ ůĂƌŐĞƵƌ Ğƚ Ϯ ŵ ĚĞ ŚĂƵƚĞƵƌ͘ ĂͿ hŶ ƐĞƵů ĐĂŵŝŽŶ ƉŽƵƌƌĂŝƚͲŝů ƌĞŵƉůŝƌ ůĂ ƉĂƌƟ Ğ ďĂƐƐĞ ;ĐƀŶĞͿ ĚƵ ƐŝůŽ ͍ ďͿ ŽŵďŝĞŶ ĨĂƵĚƌĂͲƚͲŝů ĚĞ ĐĂŵŝŽŶƐ ƉŽƵƌ ƌĞŵƉůŝƌ ĐŽŵƉůğƚĞŵĞŶƚ ĐĞ ƐŝůŽ ͍ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

157

EXERCICES COMPLÉMENTAIRES

Chapitre 7 Solides

ŽŶŶĂŠƚƌĞ 1

WĂƌŵŝ ůĞƐ ƐŽůŝĚĞƐ ĐŝͲĚĞƐƐŽƵƐ͕ ďĂƌƌĞ ĐĞƵǆ ƋƵŝ ŶĞ ƐŽŶƚ ƉĂƐ ĚĞƐ ƉƌŝƐŵĞƐ ĚƌŽŝƚƐ͘ WŽƵƌ ĐĞƵǆ ƋƵĞ ƚƵ ĂƐ ĐŚŽŝƐŝƐ ĐŽŵŵĞ ĠƚĂŶƚ ĚĞƐ ƉƌŝƐŵĞƐ ĚƌŽŝƚƐ͕ ĐŽůŽƌŝĞ ƵŶĞ ďĂƐĞ ĞŶ ǀĞƌƚ͕ ƵŶĞ ŚĂƵƚĞƵƌ ĞŶ ďůĞƵ Ğƚ ƵŶĞ ĨĂĐĞ ůĂƚĠƌĂůĞ ĞŶ ƌŽƵŐĞ͘

ŚĂƋƵĞ ƉƌŝƐŵĞ ĐŝͲĚĞƐƐŽƵƐ ĠƚĂŶƚ ƵŶ ĐƵďĞ͕ ƋƵĞůůĞ ĞƐƚ ůĂ ŶĂƚƵƌĞ ĚĞƐ ĨŝŐƵƌĞƐ ĐŽůŽƌĠĞƐ ͍ H H H S H G G G R E E E E T M F M F U F M N D D D D C C C A B A A A B B

1D 3 18

>Ğ ƐŽůŝĚĞ ƌĞƉƌĠƐĞŶƚĠ ĐŝͲĐŽŶƚƌĞ ĞƐƚ ƵŶ ĐƵďĞ͘ COLORIE ĞŶ ǀĞƌƚ ƵŶĞ ĨŝŐƵƌĞ ŝƐŽŵĠƚƌŝƋƵĞ ;ĚĞ ŵġŵĞƐ ŵĞƐƵƌĞƐͿ ĂƵ ƌĞĐƚĂŶŐůĞ ,&͘ DÉTERMINE ůĂ ŶĂƚƵƌĞ ĚƵ ƚƌŝĂŶŐůĞ ͘ >Ğ ƚƌŝĂŶŐůĞ ĞƐƚ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ et ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

158

F C B

B A

C D

F E

G H

ĂŶƐ ůΖĞƐƉĂĐĞ͕ ůĞƐ ĂĨĨŝƌŵĂƚŝŽŶƐ ƐƵŝǀĂŶƚĞƐ ƐŽŶƚͲĞůůĞƐ ǀƌĂŝĞƐ ;sͿ ŽƵ ĨĂƵƐƐĞƐ ;&Ϳ ͍ ĂͿ ^ŝ Ă ͬͬ ď͕ ĂůŽƌƐ Ă Ğƚ ď Ŷ͛ŽŶƚ ƉĂƐ ĚĞ ƉŽŝŶƚ Ě͛ŝŶƚĞƌƐĞĐƚŝŽŶ͘ ďͿ ^ŝ Ă Ğƚ ď Ŷ͛ŽŶƚ ƉĂƐ ĚĞ ƉŽŝŶƚ Ě͛ŝŶƚĞƌƐĞĐƚŝŽŶ͕ ĂůŽƌƐ Ă ͬͬ ď͘ ĐͿ ^ŝ Ă ^ ď͕ ĂůŽƌƐ Ă ͬͬ ď͘ ĚͿ ^ŝ Ă ͬͬ ď͕ ĂůŽƌƐ Ă ^ ď͘ ĞͿ ^ŝ ĚĞƵǆ ĚƌŽŝƚĞƐ ƐŽŶƚ ƐĠĐĂŶƚĞƐ͕ ĂůŽƌƐ ĞůůĞƐ ƐŽŶƚ ĚĂŶƐ ƵŶ ŵġŵĞ ƉůĂŶ͘ ĨͿ ^ŝ ĚĞƵǆ ĚƌŽŝƚĞƐ ƐŽŶƚ ĚĂŶƐ ƵŶ ŵġŵĞ ƉůĂŶ͕ ĂůŽƌƐ ĞůůĞƐ ƐŽŶƚ ƐĠĐĂŶƚĞƐ͘ ŐͿ ^ŝ ĚĞƵǆ ĚƌŽŝƚĞƐ ƐŽŶƚ ƉĞƌƉĞŶĚŝĐƵůĂŝƌĞƐ͕ ĂůŽƌƐ ĞůůĞƐ ŽŶƚ ƵŶ ƉŽŝŶƚ Ě͛ŝŶƚĞƌƐĞĐƚŝŽŶ͘ ŚͿ ^ŝ ĚĞƵǆ ĚƌŽŝƚĞƐ ŽŶƚ ƵŶ ƉŽŝŶƚ Ě͛ŝŶƚĞƌƐĞĐƚŝŽŶ͕ ĂůŽƌƐ ĞůůĞƐ ƐŽŶƚ ƉĞƌƉĞŶĚŝĐƵůĂŝƌĞƐ͘ ŝͿ ĂŶƐ ƵŶ ŵġŵĞ ƉůĂŶ͕ Ɛŝ Ă ͬͬ ď Ğƚ ď ͬͬ Đ͕ ĂůŽƌƐ Ă ͬͬ Đ͘ ũͿ ĂŶƐ ƵŶ ŵġŵĞ ƉůĂŶ͕ Ɛŝ Ă ^ ď Ğƚ ď ^ Đ͕ ĂůŽƌƐ Ă ^ Đ͘ ŬͿ ĂŶƐ ƵŶ ŵġŵĞ ƉůĂŶ͕ Ɛŝ Ă ^ ď Ğƚ ď ^ Đ͕ ĂůŽƌƐ Ă ͬͬ Đ͘ ^ĂĐŚĂŶƚ ƋƵĞ ĚĂŶƐ ĐŚĂƋƵĞ ĐĂƐ ůĞƐ ĚƌŽŝƚĞƐ ƐŽŶƚ ĚĂŶƐ ƵŶ ŵġŵĞ ƉůĂŶ͕ ĚĠƚĞƌŵŝŶĞ Ɛŝ ůĞƐ ĂĨĨŝƌŵĂƚŝŽŶƐ ƐƵŝǀĂŶƚĞƐ ƐŽŶƚ ǀƌĂŝĞƐ ;sͿ ŽƵ ĨĂƵƐƐĞƐ ;&Ϳ͘ ĂͿ ^ŝ ĚĞƵǆ ĚƌŽŝƚĞƐ ƐŽŶƚ ƉĂƌĂůůğůĞƐ͕ ĂůŽƌƐ ƚŽƵƚĞ ƉĞƌƉĞŶĚŝĐƵůĂŝƌĞ ă ů͛ƵŶĞ ĞƐƚ ƉĞƌƉĞŶĚŝĐƵůĂŝƌĞ ă ů͛ĂƵƚƌĞ͘ ďͿ ^ŝ ĚĞƵǆ ĚƌŽŝƚĞƐ ƐŽŶƚ ƉĞƌƉĞŶĚŝĐƵůĂŝƌĞƐ ă ƵŶĞ ŵġŵĞ ĚƌŽŝƚĞ͕ ĂůŽƌƐ ĞůůĞƐ ƐŽŶƚ ƉĂƌĂůůğůĞƐ ĞŶƚƌĞ ĞůůĞƐ͘ ĐͿ ^ŝ ĚĞƵǆ ĚƌŽŝƚĞƐ ƐŽŶƚ ƐĠĐĂŶƚĞƐ͕ ĂůŽƌƐ ƚŽƵƚĞ ƐĠĐĂŶƚĞ ă ů͛ƵŶĞ ĞƐƚ ƐĠĐĂŶƚĞ ă ů͛ĂƵƚƌĞ͘ ĚͿ ^ŝ ĚĞƵǆ ĚƌŽŝƚĞƐ ƐŽŶƚ ƉĞƌƉĞŶĚŝĐƵůĂŝƌĞƐ͕ ĂůŽƌƐ ƚŽƵƚĞ ƉĂƌĂůůğůĞ ă ů͛ƵŶĞ ĞƐƚ ƉĂƌĂůůğůĞ ă ů͛ĂƵƚƌĞ͘ ĞͿ ^ŝ ĚĞƵǆ ĚƌŽŝƚĞƐ ƐŽŶƚ ƉĂƌĂůůğůĞƐ͕ ĂůŽƌƐ ƚŽƵƚĞ ƐĠĐĂŶƚĞ ă ů͛ƵŶĞ ĞƐƚ ƐĠĐĂŶƚĞ ă ů͛ĂƵƚƌĞ͘ ĨͿ ^ŝ ĚĞƵǆ ĚƌŽŝƚĞƐ ƐŽŶƚ ƐĠĐĂŶƚĞƐ͕ ĂůŽƌƐ ƚŽƵƚĞ ƉĂƌĂůůğůĞ ă ů͛ƵŶĞ ĞƐƚ ƐĠĐĂŶƚĞ ă ů͛ĂƵƚƌĞ͘ ŐͿ ^ŝ ĚĞƵǆ ĚƌŽŝƚĞƐ ƐŽŶƚ ƐĠĐĂŶƚĞƐ͕ ĂůŽƌƐ ƚŽƵƚĞ ƐĠĐĂŶƚĞ ă ů͛ƵŶĞ ĞƐƚ ƉĂƌĂůůğůĞ ă ů͛ĂƵƚƌĞ͘

ƉƉůŝƋƵĞƌ 1

ĞƐƐŝŶĞ ůĞƐ ĂƌġƚĞƐ ĐĂĐŚĠĞƐ ĞŶ ƉŽŝŶƚŝůůĠƐ͘

Chapitre 7 Solides

EXERCICES COMPLÉMENTAIRES

2 ĐŚğǀĞ ůĞƐ ĐƵďĞƐ Ğƚ ůĞƐ ƉĂƌĂůůĠůĠƉŝƉğĚĞƐ ƌĞĐƚĂŶŐůĞƐ ĚŽŶƚ ĐĞƌƚĂŝŶĞƐ ĂƌġƚĞƐ ƐŽŶƚ ĚĞƐƐŝŶĠĞƐ͘

ĞƐƐŝŶĞ ůĞƐ ĂƌġƚĞƐ ĐĂĐŚĠĞƐ ĞŶ ƉŽŝŶƚŝůůĠƐ͘

ZĞŵƉůŝƐ ůĞƐ ƐŽůŝĚĞƐ ĂǀĞĐ ĚĞƐ ĐƵďĞƐ ŝĚĞŶƚŝƋƵĞƐ ă ĐĞůƵŝ ƌĞƉƌĠƐĞŶƚĠ Đŝ ĐŽŶƚƌĞ͘ ^ĂĐŚĂŶƚ ƋƵĞ ůĞ ǀŽůƵŵĞ ĚĞ ĐĞůƵŝͲĐŝ ǀĂƵƚ ϭ ĐŵϹ͕ ĚĠƚĞƌŵŝŶĞ ůĞ ǀŽůƵŵĞ ĚĞ ĐŚĂĐƵŶ ĚĞƐ ƉƌŝƐŵĞƐ ĐŝͲĚĞƐƐŽƵƐ͘

7 4

ZĞƉƌĠƐĞŶƚĞ ĞŶ ƉĞƌƐƉĞĐƚŝǀĞ ĐĂǀĂůŝğƌĞ ƵŶ ĐƵďĞ ĚĞ ϯ Đŵ Ě͛ĂƌġƚĞ ƚĞů ƋƵĞ ͗ ĂͿ ů͛ĂŶŐůĞ ĚĞ ĨƵŝƚĞ ĞƐƚ ĚĞ ϰϱΣ Ğƚ ůĞ ƌĂƉƉŽƌƚ ĚĞ ƌĠĚƵĐƚŝŽŶ ĞƐƚ ĚĞ ϭͬϮ͘ ďͿ ů͛ĂŶŐůĞ ĚĞ ĨƵŝƚĞ ĞƐƚ ĚĞ ϲϬΣ Ğƚ ůĞ ƌĂƉƉŽƌƚ ĚĞ ƌĠĚƵĐƚŝŽŶ ĞƐƚ ĚĞ ϭͬϮ͘ ĐͿ ů͛ĂŶŐůĞ ĚĞ ĨƵŝƚĞ ĞƐƚ ĚĞ ϯϬΣ Ğƚ ůĞ ƌĂƉƉŽƌƚ ĚĞ ƌĠĚƵĐƚŝŽŶ ĞƐƚ ĚĞ Ϯͬϯ͘

ZĞƉƌĠƐĞŶƚĞ ĞŶ ƉĞƌƐƉĞĐƚŝǀĞ ĐĂǀĂůŝğƌĞ ƵŶ ƉĂƌĂůůĠůĠƉŝƉğĚĞ ƌĞĐƚĂŶŐůĞ ĚĞ ϱ Đŵ ĚĞ ůŽŶŐƵĞƵƌ͕ ĚĞ ϯ Đŵ ĚĞ ůĂƌŐĞƵƌ Ğƚ ĚĞ ϰ Đŵ ĚĞ ŚĂƵƚĞƵƌ ƚĞů ƋƵĞ ͗ ĂͿ ů͛ĂŶŐůĞ ĚĞ ĨƵŝƚĞ ĞƐƚ ĚĞ ϰϱΣ Ğƚ ůĞ ƌĂƉƉŽƌƚ ĚĞ ƌĠĚƵĐƚŝŽŶ ĞƐƚ ĚĞ ϭͬϮ͘ ďͿ ů͛ĂŶŐůĞ ĚĞ ĨƵŝƚĞ ĞƐƚ ĚĞ ϲϬΣ Ğƚ ůĞ ƌĂƉƉŽƌƚ ĚĞ ƌĠĚƵĐƚŝŽŶ ĞƐƚ ĚĞ ϭͬϮ͘ ĐͿ ů͛ĂŶŐůĞ ĚĞ ĨƵŝƚĞ ĞƐƚ ĚĞ ϯϬΣ Ğƚ ůĞ ƌĂƉƉŽƌƚ ĚĞ ƌĠĚƵĐƚŝŽŶ ĞƐƚ ĚĞ Ϯͬϯ͘

6 ŽůŽƌŝĞ ůĞƐ ƚƌŽŝƐ ǀƵĞƐ ĐŽŽƌĚŽŶŶĠĞƐ͘

Vue de face

Vue de dessus

Vue de côté

Vue de face

Vue de côté

Vue de dessus

159

EXERCICES COMPLÉMENTAIRES

Chapitre 7 Solides

7 ŽůŽƌŝĞ ůĂ ƉĞƌƐƉĞĐƚŝǀĞ͘

Vue de face Vue de côté

Vue de dessus

8 >͛ĂƌġƚĞ ƌŽƵŐĞ Ă ĠƚĠ ĚĞƐƐŝŶĠĞ ĚĂŶƐ ůĞƐ ƚƌŽŝƐ ǀƵĞƐ͘ dĞƌŵŝŶĞͲůĞƐ͘ Vue de face

Vue de côté

Vue de dessus

LĞ ƐŽůŝĚĞ ĐŝͲĐŽŶƚƌĞ ĞƐƚ ƵŶ ƉƌŝƐŵĞ ĚƌŽŝƚ ĚŽŶƚ ůĂ ďĂƐĞ ĞƐƚ ƵŶ ŚĞǆĂŐŽŶĞ ƌĠŐƵůŝĞƌ͘

C L

G ŽŵƉůğƚĞ ƉĂƌ ͬͬ ͕ ^͕ ͬͬ ŽƵ Ő͘ ΀ ΁ ͙͙ ΀ ΁ ΀,/΁ ΀ ΁ ͙͙ ΀',΁ ΀ /΁ ΀ ΁ ͙͙ ΀ &΁ ΀,/΁ ΀',΁ ͙͙ ΀, ΁ ΀ ΁

J H

͙͙ ͙͙ ͙͙ ͙͙

΀/:΁ ΀ '΁ ΀ '΁ ΀><΁

/, /, /, ',/:<>

͙͙ ͙͙ ͙͙ ͙͙

:/ & <> & &

&>' ͙͙ ,' ͙͙ ><:/,' ͙͙ &>' ͙͙

:/ :< >< & :<

10 sŽŝĐŝ ƵŶĞ ƉǇƌĂŵŝĚĞ ă ďĂƐĞ ĐĂƌƌĠĞ ĚŽŶƚ ŽŶ Ă ĐŽƵƉĠ ůĂ ƉŽŝŶƚĞ ƉĂƌĂůůğůĞŵĞŶƚ ă ůĂ ďĂƐĞ͘

ĂͿ ĠƚĞƌŵŝŶĞ ůĂ ŶĂƚƵƌĞ ƉƌĠĐŝƐĞ ĚƵ ƋƵĂĚƌŝůĂƚğƌĞ , ͘ ďͿ ĠƚĞƌŵŝŶĞ ůĞƐ ĚƌŽŝƚĞƐ ƉĂƌĂůůğůĞƐ ă ůĂ ĚƌŽŝƚĞ ͕ ă ůĂ ĚƌŽŝƚĞ &'͘ ĠƚĞƌŵŝŶĞ ůĞƐ ĚƌŽŝƚĞƐ ŐĂƵĐŚĞƐ ă ůĂ ĚƌŽŝƚĞ ͕ ă ůĂ ĚƌŽŝƚĞ &͘ ĠƚĞƌŵŝŶĞ ůĞƐ ĚƌŽŝƚĞƐ ƉĞƌƉĞŶĚŝĐƵůĂŝƌĞƐ ă ůĂ ĚƌŽŝƚĞ ,'͕ ă ůĂ ĚƌŽŝƚĞ ,͘ ĠƚĞƌŵŝŶĞ ůĞƐ ĚƌŽŝƚĞƐ ƐĠĐĂŶƚĞƐ ă ůĂ ĚƌŽŝƚĞ &͘ ĠƚĞƌŵŝŶĞ ůĂ ĨĂĐĞ ƉĂƌĂůůğůĞ ă ůĂ ĨĂĐĞ ͘ ĠƚĞƌŵŝŶĞ ůĞƐ ĨĂĐĞƐ ƉĞƌƉĞŶĚŝĐƵůĂŝƌĞƐ ă ůĂ ĨĂĐĞ , ͘ ĠƚĞƌŵŝŶĞ ůĞƐ ĨĂĐĞƐ ƐĠĐĂŶƚĞƐ ă ůĂ ĨĂĐĞ & ͘ ĐͿ ŽŵƉůğƚĞ ƉĂƌ ͬͬ ͕ ^͕ ͬͬ ŽƵ Ő͘ ͙͙ ', , ͙͙ ͙͙ ' ͙͙ & ͙͙ , ͙͙

160

D A

C B G

H E

, ͙͙ , , ͙͙ '& , ͙͙ ,'

F ͙͙ &', '& ͙͙ & ͙͙ '&

Chapitre 7 Solides

EXERCICES COMPLÉMENTAIRES

11 ZĞĐŽƉŝĞ͕ ƉƵŝƐ ĐŽŵƉůğƚĞ ůĞƐ ĚĠǀĞůŽƉƉĞŵĞŶƚƐ ĚĞƐ ƉƌŝƐŵĞƐ ĐŝͲĚĞƐƐŽƵƐ͘

ĂͿ WƌŝƐŵĞ ĚƌŽŝƚ ă ďĂƐĞ ƚƌŝĂŶŐƵůĂŝƌĞ

ďͿ WƌŝƐŵĞ ĚƌŽŝƚ ă ďĂƐĞ ƚƌŝĂŶŐƵůĂŝƌĞ ĠƋƵŝůĂƚĠƌĂůĞ

ĐͿ WƌŝƐŵĞ ĚƌŽŝƚ ă ďĂƐĞ ƚƌŝĂŶŐƵůĂŝƌĞ ƌĞĐƚĂŶŐůĞ ĚͿ WƌŝƐŵĞ ĚƌŽŝƚ ă ďĂƐĞ ƚƌŝĂŶŐƵůĂŝƌĞ ĠƋƵŝůĂƚĠƌĂůĞ

12 hŶ ƉƌŝƐŵĞ Ă ϯϲ ĂƌġƚĞƐ͘ YƵĞů ĞƐƚ ůĞ ŶŽŵďƌĞ ĚĞ ĨĂĐĞƐ Ğƚ ĚĞ ƐŽŵŵĞƚƐ ĚĞ ĐĞ ƉƌŝƐŵĞ ͍ 13 hŶ ƉƌŝƐŵĞ Ă ϭϴ ĨĂĐĞƐ͘ YƵĞů ĞƐƚ ůĞ ŶŽŵďƌĞ ĚĞ ƐŽŵŵĞƚƐ Ğƚ Ě͛ĂƌġƚĞƐ ĚĞ ĐĞ ƉƌŝƐŵĞ ͍ 14 >Ă ďĂƐĞ Ě͛ƵŶ ƉƌŝƐŵĞ ĞƐƚ ƵŶ ƉŽůǇŐŽŶĞ ĂǇĂŶƚ ϭϬϬ ĐƀƚĠƐ͘ YƵĞů ĞƐƚ ůĞ ŶŽŵďƌĞ ĚĞ ƐŽŵŵĞƚƐ͕ Ě͛ĂƌġƚĞƐ Ğƚ

ĚĞ ĨĂĐĞƐ ĚĞ ĐĞ ƉƌŝƐŵĞ ͍ 15 >Ă ďĂƐĞ Ě͛ƵŶ ƉƌŝƐŵĞ ĞƐƚ ĚĠƚĞƌŵŝŶĠĞ ƉĂƌ ƵŶ ƉŽůǇŐŽŶĞ ă Ɖ ĐƀƚĠƐ͘ YƵĞů ĞƐƚ ůĞ ŶŽŵďƌĞ ĚĞ ƐŽŵŵĞƚƐ͕

Ě͛ĂƌġƚĞƐ Ğƚ ĚĞ ĨĂĐĞƐ ĚĞ ĐĞ ƉƌŝƐŵĞ ͍ 16 YƵĞů ĞƐƚ ůĞ ŶŽŵďƌĞ ŵŝŶŝŵĂů ĚĞ ĨĂĐĞƐ ƉŽƵƌ ƵŶ ƉƌŝƐŵĞ ĚƌŽŝƚ ͍ ĂŶƐ ĐĞ ĐĂƐ͕ ƉƌĠĐŝƐĞ ůĂ ŶĂƚƵƌĞ ĚĞ

ůĂ ďĂƐĞ͕ ůĞ ŶŽŵďƌĞ Ě͛ĂƌġƚĞƐ Ğƚ ĚĞ ƐŽŵŵĞƚƐ͘

1D 17 hŶ ĐƵďĞ ƚƌŽŶƋƵĠ ĞƐƚ ƵŶ ĐƵďĞ ĚƵƋƵĞů ŽŶ Ă ƌĞƚŝƌĠ ĐŚĂƋƵĞ ͨ ĐŽŝŶ ͩ͘ 1 8 DÉTERMINE ƐƵƌ ĐĞ ĐƵďĞ ƚƌŽŶƋƵĠ ͗

ͻ ůĞ ŶŽŵďƌĞ ĚĞ ĨĂĐĞƐ ŽĐƚŽŐŽŶĂůĞƐ ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͻ ůĞ ŶŽŵďƌĞ ĚĞ ĨĂĐĞƐ ƚƌŝĂŶŐƵůĂŝƌĞƐ ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͻ ůĞ ŶŽŵďƌĞ ĚĞ ƐŽŵŵĞƚƐ ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

cube

cube tronqué

dƌĂŶƐĨĠƌĞƌ 1

sŽŝĐŝ ůĞ ĐƌŽƋƵŝƐ Ě͛ƵŶĞ ĂƌŵŽŝƌĞ Ě͛ĂŶŐůĞ ;ϵϬΣͿ ĨĂďƌŝƋƵĠĞ ƉĂƌ ŵŽŶ ŐƌĂŶĚͲƉğƌĞ͘ ĂůĐƵůĞ ůĞ ǀŽůƵŵĞ ĚĞ ĐĞůůĞͲĐŝ͘ 95 cm

:Ğ ƉůŽŶŐĞ ƵŶĞ ďŝůůĞ ĚĂŶƐ ƵŶ ǀĞƌƌĞ ;ĐǇůŝŶĚƌŝƋƵĞͿ ĚĞ ϴ Đŵ ĚĞ ĚŝĂŵğƚƌĞ͘ ĞůůĞͲĐŝ ĚĞƐĐĞŶĚ ĚĂŶƐ ůĞ ĨŽŶĚ ĚƵ ǀĞƌƌĞ Ğƚ ĞƐƚ ĐŽŵƉůğƚĞŵĞŶƚ ƌĞĐŽƵǀĞƌƚĞ Ě͛ĞĂƵ͘ DĂŝƐ ĞŶ ĨĂŝƐĂŶƚ ĐĞƚƚĞ ĞǆƉĠƌŝĞŶĐĞ͕ ů͛ĞĂƵ ŵŽŶƚĞ ĚĞ ϱ ŵŵ ĚĂŶƐ ůĞ ǀĞƌƌĞ ŵĂŝƐ ŶĞ ĚĠďŽƌĚĞ ƉĂƐ͘ ĠƚĞƌŵŝŶĞ ůĞ ǀŽůƵŵĞ ĚĞ ůĂ ďŝůůĞ͘

2m 5 mm

hŶ ĐǇůŝŶĚƌĞ ĚĞ ϱ Đŵ ĚĞ ƌĂǇŽŶ Ğƚ ĚĞ ϮϬ Đŵ ĚĞ ŚĂƵƚ ĞƐƚ ă ŵŽŝƚŝĠ ƌĞŵƉůŝ Ě͛ĞĂƵ͘ KŶ Ǉ ƉůŽŶŐĞ ƵŶĞ ďŝůůĞ ĚĞ ƉůŽŵď ĚĞ ϰ Đŵ ĚĞ ƌĂǇŽŶ͘ ƋƵĞůůĞ ŚĂƵƚĞƵƌ ĂƌƌŝǀĞƌĂ ů͛ĞĂƵ ĚĂŶƐ ůĞ ĐǇůŝŶĚƌĞ ͍

DŽŶ ǀŽŝƐŝŶ ĚĠĐŝĚĞ ĚĞ ƌĠĂůŝƐĞƌ ƵŶĞ ĚĂůůĞ ĞŶ Situa on A ďĠƚŽŶ ƉŽƵƌ ŐĂƌĞƌ ƐĂ ǀŽŝƚƵƌĞ ă ƉƌŽǆŝŵŝƚĠ ĚĞ ƐĂ ŵĂŝƐŽŶ͕ ŵĂŝƐ ŝů ŚĠƐŝƚĞ ĞŶƚƌĞ ĚĞƵǆ ĞŶĚƌŽŝƚƐ ĚŝĨĨĠƌĞŶƚƐ͘ ĂŶƐ ĐŚĂĐƵŶĞ ĚĞƐ 5m ƐŝƚƵĂƚŝŽŶƐ͕ ĐŽŵďŝĞŶ ĚĞ ŵĠůĂŶŐĞƐ ĚĞǀƌĂͲƚͲŝů ƌĠĂůŝƐĞƌ Ɛŝ ůĂ ĚĂůůĞ ĚĞ ďĠƚŽŶ ĚŽŝƚ ŵĞƐƵƌĞƌ 6m ϭϱ Đŵ Ě͛ĠƉĂŝƐƐĞƵƌ Ğƚ ƋƵĞ͕ ƉŽƵƌ ĨĂďƌŝƋƵĞƌ ůĞ ďĠƚŽŶ͕ ŝů ƵƚŝůŝƐĞ ƵŶĞ ďĠƚŽŶŶŝğƌĞ ĚĞ ϭϰϬ ůŝƚƌĞƐ ĚĞ ĐĂƉĂĐŝƚĠ ͍

Situa on B 4m 3 m 2,5 m

1m 5m

161

EXERCICES COMPLÉMENTAIRES 5

Chapitre 7 Solides

dƵ ƚƌŽƵǀĞƌĂƐ ĐŝͲĚĞƐƐŽƵƐ ƵŶĞ ƉŚŽƚŽ Ğƚ ƵŶ ĐƌŽƋƵŝƐ ĚĞ ůĂ ďĂƐĞ ĚĞ ŵŽŶ ĂƋƵĂƌŝƵŵ ĂǀĞĐ ƐĞƐ ĚŝŵĞŶƐŝŽŶƐ͘ WŽƵƌ ůĞ ƌĞŵƉůŝƌ͕ ũ͛Ăŝ ƵƚŝůŝƐĠ ƵŶ ƐĞĂƵ ĚΖƵŶĞ ĐĂƉĂĐŝƚĠ ĚĞ ϲ ůŝƚƌĞƐ͕ ĚĂŶƐ ůĞƋƵĞů ũĞ ǀĞƌƐĞ ĐŚĂƋƵĞ ĨŽŝƐ ϱ ůŝƚƌĞƐ ĚΖĞĂƵ͘ ŽŵďŝĞŶ ĚĞ ƚƌĂũĞƚƐ ĂŝͲũĞ ĚƸ ĨĂŝƌĞ Ɛŝ ƚƵ ƐĂŝƐ ƋƵĞ ŵŽŶ ĂƋƵĂƌŝƵŵ Ă ƵŶĞ ŚĂƵƚĞƵƌ ƵƚŝůĞ ĚĞ ϯϯ Đŵ ͍ 80 cm 20 cm 35 cm 50 cm

>Ă ƉŝƐĐŝŶĞ ĚƵ ǀĞƐƚŝĂŝƌĞ Ě͛ƵŶ ĐůƵď ƉƌŽĨĞƐƐŝŽŶŶĞů ĚĞ ĨŽŽƚďĂůů ĚŽŝƚ ġƚƌĞ ƌĠŶŽǀĠĞ͘ ĞůůĞͲĐŝ Ă ƉŽƵƌ ĚŝŵĞŶƐŝŽŶƐ ͗ ϭϬ ŵ ĚĞ ůŽŶŐƵĞƵƌ͕ ϲ ŵ ĚĞ ůĂƌŐĞƵƌ Ğƚ ϭ͕ϱ ŵ ĚĞ ƉƌŽĨŽŶĚĞƵƌ͘ KŶ ĨĂŝƚ ĂƉƉĞů ă ĚĞƵǆ ĞŶƚƌĞƉƌĞŶĞƵƌƐ͘ ĞƵǆͲĐŝ ƌĞŵĞƚƚĞŶƚ ĐŚĂĐƵŶ ƵŶ ĚĞǀŝƐ͘ >Ğ ƉƌĞŵŝĞƌ ƉƌŽƉŽƐĞ ƵŶĞ ĐŽƵĐŚĞ Ě͛ŚǇĚƌŽĨƵŐĞ ƐƵƌ ƚŽƵƚĞƐ ůĞƐ ƉĂƌŽŝƐ ůĂƚĠƌĂůĞƐ ă ϮϬ €ͬŵϮ Ğƚ ƵŶ ĐĂƌƌĞůĂŐĞ ĐůĂƐƐŝƋƵĞ ă ϱϬ €ͬŵϮ ƉŽƵƌ ƚŽƵƚĞ ůĂ ƉŝƐĐŝŶĞ͘ >Ğ ƐĞĐŽŶĚ ƉƌŽƉŽƐĞ ƵŶ ĐĂƌƌĞůĂŐĞ ƐƉĠĐŝĂů ƉŽƵƌ ůĞ ĨŽŶĚ ă ϲϱ €ͬŵϮ Ğƚ ƵŶ ĐĂƌƌĞůĂŐĞ ĐůĂƐƐŝƋƵĞ ă ϱϱ €ͬŵϮ ƉŽƵƌ ůĞƐ ĨĂĐĞƐ ůĂƚĠƌĂůĞƐ͘ YƵĞů ĞƐƚ ů͛ĞŶƚƌĞƉƌĞŶĞƵƌ ůĞ ŵŽŝŶƐ ĐŚĞƌ ͍ YƵĞůůĞ ĞƐƚ ůĂ ĚŝĨĨĠƌĞŶĐĞ ĚĞ Ɖƌŝǆ ͍ hŶĞ ĨŽŝƐ ƌĠŶŽǀĠĞ͕ ůĞ ƌĞƐƉŽŶƐĂďůĞ ĚĞƐ ǀĞƐƚŝĂŝƌĞƐ ƌĞŵƉůŝƌĂ ůĂ ƉŝƐĐŝŶĞ ĂǀĂŶƚ ůĞ ƉƌĞŵŝĞƌ ŵĂƚĐŚ ĚĞ ůĂ ƐĂŝƐŽŶ͘ >Ă ƉŽŵƉĞ ƵƚŝůŝƐĠĞ ƉŽƵƌ ƌĞŵƉůŝƌ ůĂ ƉŝƐĐŝŶĞ Ă ƵŶ ĚĠďŝƚ ĚĞ ϭϱ ϬϬϬ ů ă ů͛ŚĞƵƌĞ Ğƚ ŝů ĨĂƵƚ ϴ ŚĞƵƌĞƐ ƉŽƵƌ ŵĞƚƚƌĞ ů͛ĞĂƵ ă ůĂ ďŽŶŶĞ ƚĞŵƉĠƌĂƚƵƌĞ͘ ƋƵĞůůĞ ŚĞƵƌĞ ůĞ ƌĞƐƉŽŶƐĂďůĞ ĚƵ ǀĞƐƚŝĂŝƌĞ ĚŽŝƚͲŝů ĐŽŵŵĞŶĐĞƌ ůĞ ƌĞŵƉůŝƐƐĂŐĞ ƉŽƵƌ ƋƵĞ ůĂ ƉŝƐĐŝŶĞ ƐŽŝƚ ƉƌġƚĞ ă ďŽŶŶĞ ƚĞŵƉĠƌĂƚƵƌĞ ƉŽƵƌ ůĂ ĨŝŶ ĚƵ ŵĂƚĐŚ ƉƌĠǀƵĞ ă ϮϮ Ś ϬϬ ͍

ůĂƌĂ ĐŽůůĞ ĚĞƐ ƉĞƚŝƚƐ ĐƵďĞƐ ĚĞ ϭ Đŵ Ě͛ĂƌġƚĞ ĂĨŝŶ Ě͛ŽďƚĞŶŝƌ ƵŶ ŐƌĂŶĚ ĐƵďĞ ĚĞ ϳ Đŵ Ě͛ĂƌġƚĞ͘ ĂͿ ŽŵďŝĞŶ ĂͲƚͲĞůůĞ ĐŽůůĠ ĚĞ ƉĞƚŝƚƐ ĐƵďĞƐ ͍ ďͿ ǀĞĐ ƵŶĞ ŵğĐŚĞ ĚĞ ϲ ŵŵ ĚĞ ĚŝĂŵğƚƌĞ͕ ĞůůĞ ƉĞƌĐĞ ůĞ ŐƌĂŶĚ ĐƵďĞ ĚƵ ĐĞŶƚƌĞ ĚĞ ůĂ ĨĂĐĞ ĂǀĂŶƚ ĂƵ ĐĞŶƚƌĞ ĚĞ ůĂ ĨĂĐĞ ĂƌƌŝğƌĞ͖ ĐŽŵďŝĞŶ ĂͲƚͲĞůůĞ ƉĞƌĨŽƌĠ ĚĞ ƉĞƚŝƚƐ ĐƵďĞƐ ͍ ĐͿ ŶƐƵŝƚĞ͕ ĞůůĞ ƉĞƌĐĞ ůĞ ŐƌĂŶĚ ĐƵďĞ ĚƵ ĐĞŶƚƌĞ ĚĞ ůĂ ĨĂĐĞ ƐƵƉĠƌŝĞƵƌĞ ĂƵ ĐĞŶƚƌĞ ĚĞ ůĂ ĨĂĐĞ ŝŶĨĠƌŝĞƵƌĞ͖ ĐŽŵďŝĞŶ ĚĞ ƉĞƚŝƚƐ ĐƵďĞƐ ŽŶƚ ĠƚĠ ƉĞƌĨŽƌĠƐ ƵŶĞ ĨŽŝƐ ͍ ĚĞƵǆ ĨŽŝƐ ͍ ĚͿ ŶĨŝŶ͕ ĞůůĞ ƉĞƌĐĞ ůĞ ŐƌĂŶĚ ĐƵďĞ ĚƵ ĐĞŶƚƌĞ ĚĞ ůĂ ĨĂĐĞ ŐĂƵĐŚĞ ĂƵ ĐĞŶƚƌĞ ĚĞ ůĂ ĨĂĐĞ ĚƌŽŝƚĞ͖ ĐŽŵďŝĞŶ ĚĞ ƉĞƚŝƚƐ ĐƵďĞƐ ŽŶƚ ĠƚĠ ƉĞƌĨŽƌĠƐ ƵŶĞ ĨŽŝƐ ͍ ĚĞƵǆ ĨŽŝƐ ͍ ƚƌŽŝƐ ĨŽŝƐ ͍ ĞͿ ůůĞ ƉĞŝŶƚ ůĞ ŐƌĂŶĚ ĐƵďĞ ĞŶ ǀĞƌƚ͘ ŽŵďŝĞŶ ĚĞ ƉĞƚŝƚƐ ĐƵďĞƐ ĂƵƌŽŶƚ ƚƌŽŝƐ ĨĂĐĞƐ ƉĞŝŶƚĞƐ ͍ ĚĞƵǆ ĨĂĐĞƐ ƉĞŝŶƚĞƐ ͍ ƵŶĞ ĨĂĐĞ ƉĞŝŶƚĞ ͍ ƉĂƐ ĚĞ ĨĂĐĞ ƉĞŝŶƚĞ ͍

:ƵůŝĂŶĞ ǀŽƵĚƌĂŝƚ ǀĠƌŝĨŝĞƌ ůĂ ĐŽŶƚĞŶĂŶĐĞ ĚĞ ƐĂ ĐĂŶĞƚƚĞ ĚĞ ͨ &ĂŶƚĂ ͩ ;ϯϯ ĐůͿ͘ WŽƵƌ ĐĞůĂ͕ ĞůůĞ Ă ŵĞƐƵƌĠ ůĞ ĚŝĂŵğƚƌĞ ĚĞ ůĂ ďĂƐĞ ;ϲ͕ϱ ĐŵͿ Ğƚ ůĂ ŚĂƵƚĞƵƌ ;ϭϭ͕ϱ ĐŵͿ͘ WĞƵǆͲƚƵ ů͛ĂŝĚĞƌ ĚĂŶƐ ƐĞƐ ĐĂůĐƵůƐ ͍ 8 cm YƵĞ ƉĞŶƐĞƐͲƚƵ ĚƵ ƌĠƐƵůƚĂƚ ƚƌŽƵǀĠ ͍ ůĂƌĂ ůƵŝ ƉƌŽƉŽƐĞ ƵŶ ǀĞƌƌĞ ŽƌŝŐŝŶĂů ƉŽƵƌ ďŽŝƌĞ ƐĂ ďŽŝƐƐŽŶ ĨĂǀŽƌŝƚĞ͘ ŽŵďŝĞŶ ĚĞ ǀĞƌƌĞƐ ƉŽƵƌƌĂͲƚͲĞůůĞ ƌĞŵƉůŝƌ ă ƌĂƐ ďŽƌĚ ĂǀĞĐ ƵŶĞ ĐĂŶĞƚƚĞ ƉůĞŝŶĞ ͍ 7 cm

1D 9 18

162

>Ğ ĐĂƌƚŽŶ ĐŝͲĐŽŶƚƌĞ ĐŽŶƚŝĞŶƚ ĚĞƵǆ ŶŝǀĞĂƵǆ ĚĞ ƋƵŝŶǌĞ ďŽŠƚĞƐ ĚĞ ĐŽŶƐĞƌǀĞ ĐǇůŝŶĚƌŝƋƵĞƐ͘ ŚĂƋƵĞ ďŽŠƚĞ Ă ƵŶĞ ŚĂƵƚĞƵƌ ĚĞ ϭϭ͕ϱ Đŵ Ğƚ ƵŶ ƌĂǇŽŶ ĚĞ ϱ Đŵ͘ >Ă ĨŽƌŵƵůĞ ƉŽƵƌ ĐĂůĐƵůĞƌ ůĞ ǀŽůƵŵĞ Ě͛ƵŶ ĐǇůŝŶĚƌĞ ĞƐƚ s с p . rϮ . Ś ĂǀĞĐ ƌ ƌĞƉƌĠƐĞŶƚĂŶƚ ƐŽŶ ƌĂǇŽŶ Ğƚ Ś ƐĂ ŚĂƵƚĞƵƌ͘ CALCULE ůĞ ǀŽůƵŵĞ ůĂŝƐƐĠ ůŝďƌĞ ĂƵƚŽƵƌ ĚĞƐ ďŽŠƚĞƐ ĚĞ ĐŽŶƐĞƌǀĞ͘ 30 cm 50 cm ÉCRIS ƚŽƵƐ ƚĞƐ ĐĂůĐƵůƐ͘

23 cm

Chapitre 8 Opérations avec les nombres entiers Tableaux de compétences Libre EŽŵďƌĞƐ ĞŶƟ ĞƌƐ 7

DĂŠƚƌŝƐĞƌ ůĞƐ ĐŽŶǀĞŶƟ ŽŶƐ Ě͛ĠĐƌŝƚƵƌĞ ŵĂƚŚĠŵĂƟ ƋƵĞ ĚĞƐ ŽƉĠƌĂƟ ŽŶƐ ĂǀĞĐ ĚĞƐ ĞŶƟ ĞƌƐ͘

/ĚĞŶƟ Į Ğƌ Ğƚ Ğī ĞĐƚƵĞƌ ĚĞƐ ŽƉĠƌĂƟ ŽŶƐ ĚĂŶƐ ĚĞƐ ƐŝƚƵĂƟ ŽŶƐ ǀĂƌŝĠĞƐ ĂǀĞĐ ĚĞƐ ĞŶƟ ĞƌƐ͘

EŽŵďƌĞƐ ;ĞŶƟ ĞƌƐ Ğƚ ƌĂƟ ŽŶŶĞůƐͿ 15

:ƵƐƟ Į Ğƌ ƵŶĞ ŵĠƚŚŽĚĞ ĚĞ ĐĂůĐƵů ĞŶ ƵƟ ůŝƐĂŶƚ ůĞƐ ƉƌŽƉƌŝĠƚĠƐ ĚĞƐ ŽƉĠƌĂƟ ŽŶƐ͘

ZĞƐƉĞĐƚĞƌ ůĞƐ ƉƌŝŽƌŝƚĠƐ ĚĞƐ ŽƉĠƌĂƟ ŽŶƐ ƉŽƵƌ Ğī ĞĐƚƵĞƌ ĚĞƐ ŽƉĠƌĂƟ ŽŶƐ ĚĂŶƐ ĚĞƐ ƐŝƚƵĂƟ ŽŶƐ ǀĂƌŝĠĞƐ͘

ī ĞĐƚƵĞƌ ƵŶ ĐĂůĐƵů ĐŽŵƉŽƌƚĂŶƚ ƉůƵƐŝĞƵƌƐ ĠƚĂƉĞƐ ă ů͛ĂŝĚĞ Ě͛ƵŶĞ ĐĂůĐƵůĂƚƌŝĐĞ͘

ĂůĐƵů ůŝƩ ĠƌĂů Ğƚ ĠƋƵĂƟ ŽŶƐ 28

ĂůĐƵůĞƌ ĚĞƐ ǀĂůĞƵƌƐ ŶƵŵĠƌŝƋƵĞƐ Ě͛ĞǆƉƌĞƐƐŝŽŶƐ ůŝƩ ĠƌĂůĞƐ͘

ƐƐŽĐŝĞƌ ƵŶ ƉŽŝŶƚ Ğƚ ƐŽŶ ĂďƐĐŝƐƐĞ ƐƵƌ ƵŶ ĂǆĞ͘

ƐƐŽĐŝĞƌ ƵŶ ƉŽŝŶƚ Ğƚ ƐĞƐ ĐŽŽƌĚŽŶŶĠĞƐ ƐƵƌ ƵŶ ƋƵĂĚƌŝůůĂŐĞ͘

163

ACTIVITÉS

Chapitre 8 Opérations avec les nombres entiers

Kĸ ĐŝĞů Repérer et classer 13

ĠƚĞƌŵŝŶĞƌ ůĂ ǀĂůĞƵƌ ĂďƐŽůƵĞ Ě͛ƵŶ ŶŽŵďƌĞ ĞŶƟ Ğƌ͘

WůĂĐĞƌ ƵŶ ĐŽƵƉůĞ ĚĞ ŶŽŵďƌĞƐ ĚĂŶƐ ƵŶ ƌĞƉğƌĞ ĐĂƌƚĠƐŝĞŶ͘

ī ĞĐƚƵĞƌ ĚĞƐ ŽƉĠƌĂƟ ŽŶƐ 27

ĂůĐƵůĞƌ ĚĞƐ ƉƵŝƐƐĂŶĐĞƐ ă ĞǆƉŽƐĂŶƚƐ ŶĂƚƵƌĞůƐ͘

ĂůĐƵůĞƌ ůĂ ƐŽŵŵĞ͕ ůĂ Ěŝī ĠƌĞŶĐĞ Ğƚ ůĞ ƉƌŽĚƵŝƚ ĚĞ ĚĞƵǆ ŶŽŵďƌĞƐ ĞŶƟ ĞƌƐ͘

ĂůĐƵůĞƌ ƵŶĞ ĞǆƉƌĞƐƐŝŽŶ ĐŽŵƉƌĞŶĂŶƚ ĂƵ ƉůƵƐ ƚƌŽŝƐ ŽƉĠƌĂƟ ŽŶƐ Ěŝī ĠƌĞŶƚĞƐ͘

ĐƌŝƌĞ ƵŶĞ ĞǆƉƌĞƐƐŝŽŶ ƋƵŝ ĐŽƌƌĞƐƉŽŶĚ ă ƵŶĞ ƐƵĐĐĞƐƐŝŽŶ Ě͛ŽƉĠƌĂƟ ŽŶƐ͘

hƟ ůŝƐĞƌ ůĂ ĐŽŵŵƵƚĂƟ ǀŝƚĠ Ğƚ ů͛ĂƐƐŽĐŝĂƟ ǀŝƚĠ ĚĞ ů͛ĂĚĚŝƟ ŽŶ Ğƚ ĚĞ ůĂ ŵƵůƟ ƉůŝĐĂƟ ŽŶ͘

ǆƉƌĞƐƐŝŽŶƐ ůŝƩ ĠƌĂůĞƐ 48

164

ĂůĐƵůĞƌ ůĂ ǀĂůĞƵƌ Ě͛ƵŶĞ ĞǆƉƌĞƐƐŝŽŶ ůŝƩ ĠƌĂůĞ ĞŶ ĚŽŶŶĂŶƚ ĂƵǆ ǀĂƌŝĂďůĞƐ ĚĞƐ ǀĂůĞƵƌƐ ĞŶƟ ğƌĞƐ͘

ACTIVITÉS

Chapitre 8 Opérations avec les nombres entiers

ĐƚŝǀŝƚĠ ϭ Produit de deux nombres entiers 1 ĂͿ ŝŶƋ ĐŽƉĂŝŶƐ ũŽƵĞŶƚ ĂƵ ũĞƵ ĚĞ Ň ĠĐŚĞƩ ĞƐ͘ ^ĞůŽŶ ƋƵĞ ů͛ŝŵƉĂĐƚ Ă ůŝĞƵ ă ů͛ŝŶƚĠƌŝĞƵƌ ŽƵ ă ů͛ĞǆƚĠƌŝĞƵƌ ĚĞ ůĂ ĐŝďůĞ͕ ŝůƐ ƌĞĕŽŝǀĞŶƚ ƵŶ ũĞƚŽŶ ďůĞƵ ŽƵ ƵŶ ũĞƚŽŶ ƌŽƵŐĞ͘ ^Ƶƌ ĐŚĂƋƵĞ ũĞƚŽŶ ďůĞƵ ĞƐƚ ŝŶƐĐƌŝƚ ůĞ ŶŽŵďƌĞ нϯ Ğƚ ƐƵƌ ĐŚĂƋƵĞ ũĞƚŽŶ ƌŽƵŐĞ ůĞ ŶŽŵďƌĞ ʹϮ͘ /ůƐ ŽŶƚ ĚƌŽŝƚ ĐŚĂĐƵŶ ă ĐŝŶƋ ĞƐƐĂŝƐ͘ sŽŝĐŝ ůĞƐ ƌĠƐƵůƚĂƚƐ͘ DĂƚŚŝĞƵ͕ ƚƌğƐ ĂĚƌŽŝƚ͕ Ă ŽďƚĞŶƵ ĐŝŶƋ ũĞƚŽŶƐ ďůĞƵƐ Ğƚ ZŽŵĂŝŶ͕ ƚƌğƐ ŵĂůĐŚĂŶĐĞƵǆ͕ Ă ŽďƚĞŶƵ ĐŝŶƋ ũĞƚŽŶƐ ƌŽƵŐĞƐ͘ ĐƌŝƐ ůĞ ĐĂůĐƵů ƋƵŝ ƉĞƌŵĞƚ ĚĞ ĚĠƚĞƌŵŝŶĞƌ ůĞ ƐĐŽƌĞ ĚĞ ĐŚĂĐƵŶ Ğƚ Ğī ĞĐƚƵĞͲůĞ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

^ĂĐŚĂŶƚ ƋƵĞ WĂƐĐĂů Ă ŽďƚĞŶƵ ƵŶ ƐĐŽƌĞ ŶƵů͕ ĐŽŵďŝĞŶ ĂͲƚͲŝů ŽďƚĞŶƵ ĚĞ ũĞƚŽŶƐ ĚĞ ĐŚĂƋƵĞ ĐŽƵůĞƵƌ ͍ :ƵƐƟ Į Ğ ƉĂƌ ƵŶ ĐĂůĐƵů͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

WŝĞƌƌĞ Ă ŽďƚĞŶƵ нϱ ĐŽŵŵĞ ƐĐŽƌĞ͘ ŽŵďŝĞŶ ĂͲƚͲŝů ŽďƚĞŶƵ ĚĞ ũĞƚŽŶƐ ĚĞ ĐŚĂƋƵĞ ĐŽƵůĞƵƌ ͍ :ƵƐƟ Į Ğ ƉĂƌ ƵŶ ĐĂůĐƵů͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

'ŝůůĞƐ Ă ŽďƚĞŶƵ ʹϱ ĐŽŵŵĞ ƐĐŽƌĞ͘ ŽŵďŝĞŶ ĂͲƚͲŝů ŽďƚĞŶƵ ĚĞ ũĞƚŽŶƐ ĚĞ ĐŚĂƋƵĞ ĐŽƵůĞƵƌ ͍ :ƵƐƟ Į Ğ ƉĂƌ ƵŶ ĐĂůĐƵů͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ďͿ Ŷ ĂƉƉůŝƋƵĂŶƚ ůĞƐ ƌğŐůĞƐ ĚĠĐŽƵǀĞƌƚĞƐ ĞŶ ĂͿ͕ ĐĂůĐƵůĞ͕ Ɛŝ ƉŽƐƐŝďůĞ͕ ůĞƐ ƉƌŽĚƵŝƚƐ ƐƵŝǀĂŶƚƐ͘ 7 . ;ʹϮͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

8 . ;нϯͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;ʹϵͿ . ϱ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;ʹϯͿ . ;ʹϮͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;ʹϮͿ . ϱ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;нϯͿ . ϭϬ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Ϯ . ;ʹϲͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;ʹϱͿ . ;ʹϰͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ĐͿ ĂůĐƵůĞ ĞŶ ĂƉƉůŝƋƵĂŶƚ ůĞƐ ƉƌŝŽƌŝƚĠƐ ĚĞƐ ŽƉĠƌĂƟ ŽŶƐ͘ ;ʹϱ н ϱͿ . ;ʹϰͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ĂůĐƵůĞ ĞŶ ƵƟ ůŝƐĂŶƚ ůĂ ĚŝƐƚƌŝďƵƟ ǀŝƚĠ Ğƚ ĚĠĚƵŝƐ ůĞ ƐŝŐŶĞ ĚƵ ƉƌŽĚƵŝƚ ĚĞ ĚĞƵǆ ŶŽŵďƌĞƐ ĞŶƟ ĞƌƐ ŶĠŐĂƟ ĨƐ͘ ;ʹϱ н ϱͿ . ;ʹϰͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ĚͿ ŽŵƉůğƚĞ ůĞƐ ƚĂďůĞƐ ĚĞ ŵƵůƟ ƉůŝĐĂƟ ŽŶ ĞŶ ƌĞƐƉĞĐƚĂŶƚ ůĂ ĚĠŵĂƌĐŚĞ ƐƵŝǀĂŶƚĞ ͗ ƚŽƵƚ Ě͛ĂďŽƌĚ͕ ĞŶ ďůĞƵ ͗ ůĞƐ ƉƌŽĚƵŝƚƐ ĚĞ ĚĞƵǆ ŶŽŵďƌĞƐ ƉŽƐŝƟ ĨƐ͕ ĞŶƐƵŝƚĞ͕ ĞŶ ǀĞƌƚ ͗ ůĞƐ ƉƌŽĚƵŝƚƐ ĚĞ ĚĞƵǆ ŶŽŵďƌĞƐ ĚĞ ƐŝŐŶĞƐ ĐŽŶƚƌĂŝƌĞƐ Ğƚ ĞŶĮ Ŷ͕ ĞŶ ƌŽƵŐĞ ͗ ůĞƐ ƉƌŽĚƵŝƚƐ ĚĞ ĚĞƵǆ ŶŽŵďƌĞƐ ŶĠŐĂƟ ĨƐ͘ ϯ . ϱ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϯ . ϯ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϯ . ;ʹϰͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϯ . ;ʹϮͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Ϯ . ϱ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Ϯ . ϯ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Ϯ . ;ʹϰͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Ϯ . ;ʹϮͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϭ . ϱ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϭ . ϯ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϭ . ;ʹϰͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϭ . ;ʹϮͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Ϭ . ϱ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Ϭ . ϯ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Ϭ . ;ʹϰͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Ϭ . ;ʹϮͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;ʹϭͿ . ϱ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;ʹϭͿ . ϯ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;ʹϭͿ . ;ʹϰͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;ʹϭͿ . ;ʹϮͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;ʹϮͿ . ϱ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;ʹϮͿ . ϯ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;ʹϮͿ . ;ʹϰͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;ʹϮͿ . ;ʹϮͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;ʹϯͿ . ϱ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;ʹϯͿ . ϯ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;ʹϯͿ . ;ʹϰͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;ʹϯͿ . ;ʹϮͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ 165

ACTIVITÉS

Chapitre 8 Opérations avec les nombres entiers

e) WŽƵƌ ĐŚĂƋƵĞ ĚƌŽŝƚĞ ĚĞƐƐŝŶĠĞ ͗ b ĐŽŵƉůğƚĞ ůĞ ƚĂďůĞĂƵ ĂŝŶƐŝ ƋƵĞ ůΖĠŐĂůŝƚĠ ĂůŐĠďƌŝƋƵĞ ƌĞůŝĂŶƚ ůĞƐ ĐŽƵƉůĞƐ ͖ ĞǆƉƌŝŵĞ ƉŽƵƌ ĐŚĂƋƵĞ ĐŽƵƉůĞ ĚƵ ƚĂďůĞĂƵ ůĂ ǀĂůĞƵƌ ĚĞ Ǉ ƉĂƌ ƵŶ ƉƌŽĚƵŝƚ͘ x ƌŽŝƚĞ Ă

ʹϯ

ʹϮ

ʹϭ

Ǉ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

x ƌŽŝƚĞ ď

ʹϯ

ʹϮ

ʹϭ

Ǉ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

p.70 A1

2 ĂͿ ^ĂŶƐ ĐĂůĐƵůĞƌ͕ ĚĠƚĞƌŵŝŶĞ ůĞ ƐŝŐŶĞ ĚĞƐ ƉƌŽĚƵŝƚƐ ƐƵŝǀĂŶƚƐ͘ ;ʹϰͿ . ;ʹϱͿ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ;ʹϯͿ . ;нϭͿ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ;ʹϭϮͿ . ;ʹϱͿ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ 7 . ;ʹϯͿ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ;нϲͿ . ;ʹϳͿ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ;нϴͿ . ;нϮͿ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ;ʹϭϬͿ . ;ʹϭϬͿ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ʹϱ . 7 ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ďͿ ĂůĐƵůĞ ůĞƐ ƉƌŽĚƵŝƚƐ ƐƵŝǀĂŶƚƐ͘

;ʹϳͿ . ;нϯͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϲ . ;ʹϰͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϭϰ . ;ʹϮͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϮ . ;ʹϴͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;ʹϴͿ . ;ʹϰͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϱ . ϯ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϯ . ϭϱ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϰ . ;ʹϭͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;нϱͿ . ;нϲͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

7 . ;ʹϴͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϵ . ϵ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϳ . ϭ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;нϵͿ . ;ʹϮͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϰ . ;ʹϯͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϵ . ;ʹϵͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϮ . ;ʹϮͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ĐͿ ŽŵƉůğƚĞ ůĞƐ ƉǇƌĂŵŝĚĞƐ ƐĂĐŚĂŶƚ ƋƵĞ ĐŚĂƋƵĞ ďƌŝƋƵĞ ĞƐƚ ůĞ ƉƌŽĚƵŝƚ ĚĞƐ ďƌŝƋƵĞƐ ƐƵƌ ůĞƐƋƵĞůůĞƐ ĞůůĞ ƌĞƉŽƐĞ͘

ϲ ʹϰ Ϯ

ʹϭ

ʹϮ

ʹϭ

ĚͿ ŽŵƉůğƚĞ ůĞƐ ƉƌŽĚƵŝƚƐ ĞŶ ĠĐƌŝǀĂŶƚ ƵŶ ŵŝŶŝŵƵŵ ĚĞ ƉĂƌĞŶƚŚğƐĞƐ͘

166

ϭϮ с ʹϮ . ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Ϯϱ с ϱ . ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϳ с ϳ . ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϲ с ϯ . ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϭϱ с ϯ . ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϭϲ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ . ;ʹϴͿ

ϰϱ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ . ;ʹϵͿ

Ϯϴ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ . 7

ʹϭϮ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ . ϰ

ʹϴ с ʹϮ . ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϭϴ с ʹϮ . ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϯϲ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ . ;ʹϲͿ

ACTIVITÉS

Chapitre 8 Opérations avec les nombres entiers

ĐƚŝǀŝƚĠ Ϯ Propriétés de la multiplication 1 ĂͿ ZĞůŝĞ ĐŚĂƋƵĞ ĐĂůĐƵů ă ůĂ ƉƌŽƉƌŝĠƚĠ ƋƵ͛ŝů ŝůůƵƐƚƌĞ͘ ϱ . ;ʹϯͿ . Ϯ с ϱ . Ϯ . ;ʹϯͿ • ϭ . ;ʹϱͿ с ʹ ϱ •

• >Ă ŵƵůƟ ƉůŝĐĂƟ ŽŶ ĞƐƚ ƵŶĞ ŽƉĠƌĂƟ ŽŶ ĂƐƐŽĐŝĂƟ ǀĞ͘ • >Ă ŵƵůƟ ƉůŝĐĂƟ ŽŶ ĂĚŵĞƚ Ϭ ĐŽŵŵĞ ĠůĠŵĞŶƚ ĂďƐŽƌďĂŶƚ͘

;ʹϯͿ . Ϭ с Ϭ •

• >Ă ŵƵůƟ ƉůŝĐĂƟ ŽŶ ĂĚŵĞƚ ϭ ĐŽŵŵĞ ĠůĠŵĞŶƚ ŶĞƵƚƌĞ͘

ϰ . Ϯϱ . ;ʹϯͿ с ;ϰ . ϮϱͿ . ;ʹϯͿ •

• >Ă ŵƵůƟ ƉůŝĐĂƟ ŽŶ ĞƐƚ ƵŶĞ ŽƉĠƌĂƟ ŽŶ ĐŽŵŵƵƚĂƟ ǀĞ͘

ďͿ ĂůĐƵůĞ͘ 7 . ϭ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϲ . ϲ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Ϭ . ϴ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϭ . Ϭ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϭ . ;ʹϱͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϰ . Ϭ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϱ . ;ʹϱͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;ʹϭͿ . ;ʹϭͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;ʹϭͿ . ϯ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϭ . ;ʹϭͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Ϭ . ;ʹϭͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϭ . ϭ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

c) WŽƵƌ ĐŚĂƋƵĞ ĠƚĂƉĞ ĚƵ ĐĂůĐƵů͕ Ɛŝ ƵŶĞ ƉƌŽƉƌŝĠƚĠ ĚĞ ůĂ ŵƵůƟ ƉůŝĐĂƟ ŽŶ Ă ĠƚĠ ƵƟ ůŝƐĠĞ͕ ŶŽŵŵĞͲůĂ͘ ;ʹϰͿ . ;ʹϲͿ . Ϯϱ . ϭ

p.70 A2

с ;ʹϰͿ . ;ʹϲͿ . Ϯϱ

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

с ;ʹϰͿ . Ϯϱ . ;ʹϲͿ

с ;;ʹϰͿ . ϮϱͿ . ;ʹϲͿ

с ;ʹϭϬϬͿ . ;ʹϲͿ

с ϲϬϬ

ĚͿ ĂůĐƵůĞ ĞŶ ŶŽƚĂŶƚ ůĞƐ ƉƌŝŶĐŝƉĂůĞƐ ĠƚĂƉĞƐ ĚĞ ƚŽŶ ƌĂŝƐŽŶŶĞŵĞŶƚ͘ ϯϱ . ;ʹϯͿ . ;ʹϮͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ Ϯ . ϯ . ;ʹϱͿ . ϳ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ;ʹϯͿ . ;ʹϮͿ . ;ʹϱͿ . ;ʹϮͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ;ʹϭϱͿ . ;ʹϮͿ . ϰ . ;ʹϯͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ʹϰ . ;ʹϱͿ . ϯ . ϰ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ʹϮ . ;ʹϱͿ . ;ʹϯͿ . ;ʹϮϱͿ . ;ʹϰͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ 2 a) ĠƚĞƌŵŝŶĞ͕ ƐĂŶƐ ůĞƐ ĐĂůĐƵůĞƌ͕ ůĞ ƐŝŐŶĞ ĚĞƐ ƉƌŽĚƵŝƚƐ ƐƵŝǀĂŶƚƐ͘

p.71 A3

Ϯ . ϱ . ϯ . Ϯϱ . ϰ

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϮ . ;ʹϱͿ . ;ʹϯͿ . Ϯϱ . ϰ

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϮ . ϱ . ϯ . Ϯϱ . ϰ

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϮ . ;ʹϱͿ . ;ʹϯͿ . ;ʹϮϱͿ . ϰ

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϮ . ;ʹϱͿ . ;ʹϯͿ . ;ʹϮϱͿ . ;ʹϰͿ

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϮ . ;ʹϱͿ . ϯ . Ϯϱ . ϰ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ďͿ ĂůĐƵůĞ ĞŶ ĚĠƚĞƌŵŝŶĂŶƚ Ě͛ĂďŽƌĚ ůĞ ƐŝŐŶĞ ĚƵ ƉƌŽĚƵŝƚ͘ ʹϱ . 7 . ;ʹϮͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϮ . ;ʹϰͿ . ;ʹϭϬͿ . ϳ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

8 . ;ʹϭͿ . ;ʹϮͿ . ;ʹϯͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϱ . ;ʹϯͿ . ;ʹϭͿ . ;ʹϮͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϮ . ϱ . ϰ . ;ʹϯͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϭ . 7 . ;ʹϰͿ . ;ʹϴͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Ϯ . ϱ . ;ʹϴͿ . ϭ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϭ . ;ʹϭͿ . ;ʹϮͿ . ;ʹϭͿ . ;ʹϮͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϰ . ;ʹϱͿ . ;ʹϯͿ . ;ʹϮͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϱ . ;ʹϮͿ . Ϭ . ;ʹϭϬͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ 167

ACTIVITÉS

Chapitre 8 Opérations avec les nombres entiers

3 ĂͿ WŽƵƌ ĐŚĂƋƵĞ ƉƌŽĚƵŝƚ͕ ĚŽŶŶĞ ůĂ ƌĠƉŽŶƐĞ Ğƚ ƵŶĞ ĠĐƌŝƚƵƌĞ ƐŝŵƉůŝĮ ĠĞ ĚĞ ĐĞůƵŝͲĐŝ͘ ;ʹϯͿ . ;ʹϯͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;нϲͿ . ;нϲͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;нϮͿ . ;нϮͿ . ;нϮͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;ʹϱͿ . ;ʹϱͿ . ;ʹϱͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;ʹϰͿ . ;ʹϰͿ . ;ʹϰͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;нϭϬͿ . ;нϭϬͿ . ;нϭϬͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;ʹϮͿ . ;ʹϮͿ . ;ʹϮͿ . ;ʹϮͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;ʹϭͿ . ;ʹϭͿ . ;ʹϭͿ . ;ʹϭͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;нϯͿ . ;нϯͿ . ;нϯͿ . ;нϯͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;нϰͿ . ;нϰͿ . ;нϰͿ . ;нϰͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ďͿ ĐƌŝƐ ĐŚĂƋƵĞ ƉƵŝƐƐĂŶĐĞ ƐŽƵƐ ĨŽƌŵĞ Ě͛ƵŶ ƉƌŽĚƵŝƚ ƉƵŝƐ͕ ĐĂůĐƵůĞͲůĞ͘ ;ʹϮͿϯ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;ʹϯͿϰ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;ʹϭϬͿϯ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;ʹϱͿϯ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;ʹϰͿϮ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;ʹϮͿϰ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;ʹϭϬͿϲ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ;ʹϭͿ7 с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ĐͿ ĂůĐƵůĞ ůĞ ƉůƵƐ ƌĂƉŝĚĞŵĞŶƚ ƉŽƐƐŝďůĞ͘

;ʹϮͿϱ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;нϲͿϯ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Ϯϰ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;ʹϳͿϮ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;ʹϯͿϯ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϰϮ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;ʹϮͿϰ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;ʹϮͿ7 с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;ʹϱͿϮ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;ʹϰͿϯ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Ϯϱ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;ʹϭͿϲ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ĐƚŝǀŝƚĠ ϯ Opérations élémentaires avec les nombres entiers 1 ĂͿ ZĞĐŽŶŶĂŝƐ ů͛ŽƉĠƌĂƟ ŽŶ Ğƚ ŶŽƚĞ ůĂ ƌĠƉŽŶƐĞ ĚĂŶƐ ůĂ ĐŽůŽŶŶĞ ĂĚĠƋƵĂƚĞ͘ ĂůĐƵů

Somme

WƌŽĚƵŝƚ WƵŝƐƐĂŶĐĞ

ĂůĐƵů

;ʹϱͿ н ;ʹϮͿ

ʹϮ н ϱ

;нϮͿ . ;ʹϱͿ

;ʹϱͿ . ;ʹϮͿ

ʹϱ н Ϯ

;ʹϮͿϱ

;ʹϱͿϮ

ʹϱ ʹ Ϯ

Somme

WƌŽĚƵŝƚ WƵŝƐƐĂŶĐĞ

ďͿ WƌĠǀŽŝƐ ůĞ ƐŝŐŶĞ ĚĞƐ ƌĠƐƵůƚĂƚƐ ĚĞƐ ĐĂůĐƵůƐ ĞŶ ĠĐƌŝǀĂŶƚ ͨ ƉŽƐŝƟ Ĩ ͩ ŽƵ ͨ ŶĠŐĂƟ Ĩ ͩ Ğƚ ũƵƐƟ Į Ğ ƉĂƌ ƵŶĞ ƌğŐůĞ͘ ϭϰ н ;ʹϱϯͿ ĞƐƚപ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ car ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;ʹϭϰͿ . ;ʹϱϯͿ ĞƐƚപ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ car ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

168

Chapitre 8 Opérations avec les nombres entiers

ACTIVITÉS

;ʹϭϰͿ н ϱϯ ĞƐƚപ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ car ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϭϰ н ;ʹϱϯͿ ĞƐƚപ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ car ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;ʹϭϰͿϯ ĞƐƚപ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ car ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϱϯ . ϭϰ ĞƐƚപ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ car ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;ʹϱϯͿϰ ĞƐƚപ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ car ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

2 ĂůĐƵůĞ͘ ʹϴ н Ϯ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

8 . ;ʹϮͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϯ ʹ ϱ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϯ . ϱ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϴ . Ϯ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;ʹϴͿϮ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϯϯ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϯ . ;ʹϱͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϮ н ϴ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϮ ʹ ϴ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϯ н ϱ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;ʹϱͿϯ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϰ ʹ ϴ ʹ ϵ н ϳ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϳ н ϱ н ϳ ʹ ϴ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;ʹϯͿ . ;ʹϳͿ . Ϯ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϯ . ;ʹϱͿ . ϰ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

8 . ;ʹϭϬͿ . ;ʹϱͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Ϯ . ;ʹϯͿ . ;ʹϱͿ . ϯ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϴ ʹ ϭϬ ʹ ϱ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϭϳ ʹ ;ʹϯͿ ʹ ϮϬ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϰ . ;ʹϮͿ . ;ʹϯͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϯ . ;ʹϱͿ . Ϯ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϴ н ϯ ʹ ϱ ʹ ϯ н ϳ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϯ ʹ ϱ н Ϯ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϭ . ;ʹϮͿ . ;ʹϭͿ . ;ʹϯͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϱ ʹ ϱ ʹ ϱ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϮ н ϱ н Ϯ ʹ ϴ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϮ . ϱ . Ϯ . ;ʹϴͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϲ н Ϭ н ϭ ʹ ϵ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϲ . Ϭ . ϭ . ;ʹϵͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϱ . ;ʹϭͿ . ;ʹϮͿ . ϭϬ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϱ ʹ ϭ ʹ Ϯ н ϭϬ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

169

ACTIVITĂ&#x2030;S

Chapitre 8 OpĂŠrations avec les nombres entiers

Ä?Ć&#x161;Ĺ?Ç&#x20AC;Ĺ?Ć&#x161;Ä Ď° PrioritĂŠs des opĂŠrations 1 DÄ&#x201A;Ć&#x161;Ĺ&#x161;Ĺ?Ä&#x17E;Ćľ Ç&#x20AC;Ĺ?Ä&#x17E;ĹśĆ&#x161; Ä&#x161;Ä&#x17E; Ć&#x152;Ä&#x17E;Ä?Ä&#x17E;Ç&#x20AC;Ĺ˝Ĺ?Ć&#x152; ĹŻÄ&#x17E;Ć? Ć&#x152;Ä Ć?ĆľĹŻĆ&#x161;Ä&#x201A;Ć&#x161;Ć? Ä&#x161;Ä&#x17E; Ć?Ĺ˝Ĺś Ä?Ĺ˝ĹśĆ&#x161;Ć&#x152;Ć&#x20AC;ĹŻÄ&#x17E; Ć&#x2030;Ĺ˝Ć&#x152;Ć&#x161;Ä&#x201A;ĹśĆ&#x161; Ć?ĆľĆ&#x152; ĹŻÄ&#x17E;Ć? Ć&#x2030;Ć&#x152;Ĺ?Ĺ˝Ć&#x152;Ĺ?Ć&#x161;Ä Ć? Ä&#x161;Ä&#x17E;Ć? Ĺ˝Ć&#x2030;Ä Ć&#x152;Ä&#x201A;Ć&#x; Ĺ˝ĹśĆ?Í&#x2DC; /ĹŻ Ä&#x17E;Ć?Ć&#x161; Ć&#x161;Ć&#x152;Ä&#x;Ć? Ä&#x161;Ä Ä&#x2022;Ćľ Ä?Ä&#x201A;Ć&#x152; Ć&#x161;Ĺ˝ĆľĆ? Ć?Ä&#x17E;Ć? Ä?Ä&#x201A;ĹŻÄ?ĆľĹŻĆ? Ć?Ĺ˝ĹśĆ&#x161; Ĺ?ĹśÄ?Ĺ˝Ć&#x152;Ć&#x152;Ä&#x17E;Ä?Ć&#x161;Ć?Í&#x2DC; ^Ĺ˝Ĺś Ć&#x2030;Ć&#x152;Ĺ˝Ä¨Ä&#x17E;Ć?Ć?Ä&#x17E;ĆľĆ&#x152; Ä&#x201A; Ä&#x17E;ĹśĆ&#x161;Ĺ˝ĆľĆ&#x152;Ä Ä&#x17E;Ĺś Ć&#x152;Ĺ˝ĆľĹ?Ä&#x17E; ĹŻÄ&#x17E;Ć? Ä&#x17E;Ć&#x152;Ć&#x152;Ä&#x17E;ĆľĆ&#x152;Ć? Ä&#x17E;Ć&#x161; Ä&#x201A; ĹśĹ˝Ć&#x161;Ä Ä?Ä&#x17E; Ä?Ĺ˝ĹľĹľÄ&#x17E;ĹśĆ&#x161;Ä&#x201A;Ĺ?Ć&#x152;Ä&#x17E; Ć?ĆľĆ&#x152; Ć?Ä&#x201A; Ä¨Ä&#x17E;ĆľĹ?ĹŻĹŻÄ&#x17E; Í&#x2014; Revois les prioritĂŠs des Ĺ˝Ć&#x2030;Ä Ć&#x152;Ä&#x201A;Ć&#x; Ĺ˝ĹśĆ? Ä&#x201A;Ç&#x20AC;Ä&#x201A;ĹśĆ&#x161; Ä&#x161;Ä&#x17E; Ä?Ĺ˝Ć&#x152;Ć&#x152;Ĺ?Ĺ?Ä&#x17E;Ć&#x152; ĹŻÄ&#x17E;Ć? Ä?Ä&#x201A;ĹŻÄ?ĆľĹŻĆ? Í&#x160; DÄ&#x201A;Ć&#x161;Ĺ&#x161;Ĺ?Ä&#x17E;Ćľ Ä&#x201A; Ć?Ĺ˝ĆľĹŻĹ?Ĺ?ĹśÄ Ä&#x17E;Ĺś Ç&#x20AC;Ä&#x17E;Ć&#x152;Ć&#x161; ĹŻÄ&#x17E;Ć? Ĺ˝Ć&#x2030;Ä Ć&#x152;Ä&#x201A;Ć&#x; Ĺ˝ĹśĆ? Ć&#x2039;ĆľÍ&#x203A;Ĺ?ĹŻĆ? Ä?Ĺ˝ĹśĆ?Ĺ?Ä&#x161;Ä Ć&#x152;Ä&#x201A;Ĺ?Ä&#x17E;ĹśĆ&#x161; Ä?Ĺ˝ĹľĹľÄ&#x17E; Ć&#x2030;Ć&#x152;Ĺ?Ĺ˝Ć&#x152;Ĺ?Ć&#x161;Ä&#x201A;Ĺ?Ć&#x152;Ä&#x17E;Ć?Í&#x2022; ĹľÄ&#x201A;Ĺ?Ć? Ĺ?ĹŻ Ä&#x201A; Ä?Ĺ˝ĹľĹľĹ?Ć? Ä&#x161;Ä&#x17E;Ć? Ä&#x17E;Ć&#x152;Ć&#x152;Ä&#x17E;ĆľĆ&#x152;Ć?Í&#x2DC; Ĺ?Ä&#x161;Ä&#x17E;Í˛ĹŻÄ&#x17E; Ä&#x161;Ä&#x201A;ĹśĆ? Ć?Ä&#x201A; Ä?Ĺ˝Ć&#x152;Ć&#x152;Ä&#x17E;Ä?Ć&#x; Ĺ˝ĹśÍ&#x2DC; ĐžĎŽ Đ˝ ĎŻ . Ďą Ń 1 . 5

Í´ĎŽ Đ˝ ĎŻ . Ďą Ń Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC;

ÍžĎŻ Í´ ĎłÍż . ĎŽ Đ˝ Ď° b. 6

Ĺ¨

ÍžĎŻ Í´ ĎłÍż . ĎŽ Đ˝ Ď° Ń Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Ń Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Ń Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC;

ĎŽ Í´ Ďą . ÍžĎŽ Đ˝ ĎŻÍżĎŽ . ( )

= . 11

Ĺ¨ . 11

Ĺ¨

ĎŻ Đ˝ Ď° . ÍžĎľ ĐžĎŽĎŻÍż Í´ ĎŻĎŽ . ( Ĺ? Ĺ?

ĎŽ Í´ Ďą . ÍžĎŽ Đ˝ ĎŻÍżĎŽ Ń Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC;

ĎŻ Đ˝ Ď° . ÍžĎľ Í´ ĎŽĎŻÍż Í´ ĎŻĎŽ Ń Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC;

= . Ĺ?

= 7 . 1 Ĺ?

Ĺ?

Ĺ¨

p.71 B

Ń Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; 2 Ä&#x201A;Íż >Ä&#x17E;Ć? Ä&#x161;Ä&#x17E;ĆľÇ&#x2020; Ä?Ä&#x201A;ĹŻÄ?ĆľĹŻĆ? Ä?Ĺ?Í˛Ä&#x161;Ä&#x17E;Ć?Ć?Ĺ˝ĆľĆ? Ĺ˝ĹśĆ&#x161; Ä Ć&#x161;Ä Ć&#x152;Ä Ć?Ĺ˝ĹŻĆľĆ? Ä&#x161;Ä&#x17E; Ä&#x161;Ä&#x17E;ĆľÇ&#x2020; ĹľÄ&#x201A;ĹśĹ?Ä&#x;Ć&#x152;Ä&#x17E;Ć? Ä&#x161;Ĺ?ÄŤ Ä Ć&#x152;Ä&#x17E;ĹśĆ&#x161;Ä&#x17E;Ć?Í&#x2DC; Ä&#x201A;ĹśĆ? Ä?Ĺ&#x161;Ä&#x201A;Ć&#x2039;ĆľÄ&#x17E; Ä?Ä&#x201A;ĹŻÄ?ĆľĹŻÍ&#x2022; Ć?Ĺ˝ĆľĹŻĹ?Ĺ?ĹśÄ&#x17E; ĹŻÎ&#x2013;Ĺ˝Ć&#x2030;Ä Ć&#x152;Ä&#x201A;Ć&#x; Ĺ˝Ĺś Ć&#x2039;ĆľĹ? Ä&#x201A; Ä Ć&#x161;Ä Ä&#x17E;ÄŤ Ä&#x17E;Ä?Ć&#x161;ĆľÄ Ä&#x17E; Ä&#x17E;Ĺś Ć&#x2030;Ć&#x152;Ä&#x17E;ĹľĹ?Ä&#x17E;Ć&#x152; ĹŻĹ?Ä&#x17E;ĆľÍ&#x2DC; Ď° Í´ ĎŽ . ÍžÍ´ĎąÍż Ń Ĺ? Ĺ?

Í´Ď° Đ˝ ĎŽ . ÍžÍ´ĎąÍż Ń Ĺ? Ĺ? Ĺ? Ĺ? Ĺ?

Ď° Í´ ĎŽ . ÍžÍ´ĎąÍż Ń

Í´Ď° Đ˝ ĎŽ . ÍžÍ´ĎąÍż Ń Ĺ? Ĺ? Ĺ?

Ä?Íż WĹŻÄ&#x201A;Ä?Ä&#x17E; ĹŻÄ&#x17E;Ć? Ć&#x2030;Ä&#x201A;Ć&#x152;Ä&#x17E;ĹśĆ&#x161;Ĺ&#x161;Ä&#x;Ć?Ä&#x17E;Ć? Ć&#x2039;ĆľĹ? Ĺ˝ĹśĆ&#x161; Ä Ć&#x161;Ä Ĺ˝ĆľÄ?ĹŻĹ?Ä Ä&#x17E;Ć? Ä&#x161;Ä&#x201A;ĹśĆ? ĹŻÄ&#x17E;Ć? Ä&#x161;Ä Ç&#x20AC;Ä&#x17E;ĹŻĹ˝Ć&#x2030;Ć&#x2030;Ä&#x17E;ĹľÄ&#x17E;ĹśĆ&#x161;Ć? Ä&#x161;Ä&#x17E;Ć? Ä?Ä&#x201A;ĹŻÄ?ĆľĹŻĆ?Í&#x2DC; Í´ĎŻ Đ˝ ĎŽ . ÍžÍ´ĎąÍż Ń Í´ĎŻ Đ˝ Í´ĎĎŹ Ń Í´ĎĎŻ

Ďą . ÍžÍ´ĎŻ . ĎŽ Đ˝ ĎľÍż Ń Ďą . Í´Ď˛ Đ˝ Ďľ Ń Ďą . ĎŻ Ń ĎĎą

Ďą . ÍžÍ´Ďł Đ˝ ĎŻÍż Ń Ďą . Í´Ď° Ń Í´ĎŽĎŹ

Ď° . ÍžÍ´ĎŻ . Ďą Đ˝ Ď˛Íż Ń Ď° . Í´ĎĎą Đ˝ Ď˛ Ń Ď° . Í´Ďľ Ń Í´ĎŻĎ˛

ÍžÍ´Ďą Đ˝ ĎŽÍżĎ¸ . ĎŽ Ń Í´ĎŻ Ď¸ . ĎŽ Ń Ďľ . ĎŽ Ń ĎĎ´

Ď° Í´ ÍžĎą Í´ ĎłÍżĎ¸ Ń Ď° Í´ Í´ĎŽ Ď¸ Ń Ď° Í´ Ď° Ń ĎŹ

Ä?Íż Ä&#x201A;ĹŻÄ?ĆľĹŻÄ&#x17E;Í&#x2DC;

170

ÍžĎą Í´ ĎľÍż . ÍžĎŻ Í´ ĎłÍż Ń Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC;

Ďą Í´ Ďľ . ÍžĎŻ Í´ ĎłÍż Ń Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC;

Ďą Í´ Ďľ . ÍžÍ´ĎŻÍż Í´ Ďł Ń Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC;

Ďą . ÍžÍ´ĎľÍż Đ˝ ĎŻ . ÍžÍ´ĎłÍż Ń Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC;

ÍžĎą Í´ ĎľÍżĎš Í´ Ďł Ń Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC;

Ďą Í´ Ďľ . ĎŻ . ÍžÍ´ĎłÍż Ń Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC; Í&#x2DC;

p.72 B

ACTIVITÉS

Chapitre 8 Opérations avec les nombres entiers

ĚͿ WĂƌŵŝ ůĞƐ ƚƌŽŝƐ ƉƌŽƉŽƐŝƟ ŽŶƐ͕ ĞŶƚŽƵƌĞ ĐĞůůĞƐ ƋƵŝ ƐŽŶƚ ĞǆĂĐƚĞƐ͘

ϱ н ϰ . ;ʹϮͿ с

ϱ н ϴ

ϱ ʹ ϴ

ϱ н ;ʹϴͿ

ϰ ʹ ϱ . ;ʹϳͿ с

ϰ ʹ ;ʹϯϱͿ

ϰ н ϯϱ

ϰ ʹ ϯϱ

Ϯ ʹ ϯ . ϰϮ с

ʹϭ . ϰϮ

Ϯ ʹ ϯ . ϭϲ

Ϯ ʹ ϰϴ

;ϭ н ϮͿϯ ʹ ϯϮ с

ϯϯ ʹ ϯϮ

Ϯϳ ʹ ϵ

ϭϯ н Ϯϯ ʹ ϯϮ

CĂůĐƵůĞ ĞŶ ĂƉƉůŝƋƵĂŶƚ ůĞƐ ƉƌŝŽƌŝƚĠƐ ĚĞƐ ŽƉĠƌĂƟ ŽŶƐ Ğƚ ǀĠƌŝĮ Ğ ĂǀĞĐ ƚĂ ĐĂůĐƵůĂƚƌŝĐĞ͘ ϱ н ;ʹϮͿ . ϳ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ Ϯ . ;ʹϲͿ н ;ʹϱͿ . ;ʹϯͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϰ н ;ʹϮͿ . ϱ н ϳ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ʹϮ . ϱ н ;ʹϰͿ . ϳ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϰ ʹ ϱ . ;ʹϳͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ʹϴ . ;ʹϮͿ ʹ ϱ . ϯ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ;ϰ ʹ ϱͿ . ;Ϯ ʹ ϲͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϰ ʹ ϱ . ;Ϯ ʹ ϲͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϱ ʹ ϯ . ϮϮ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ʹϰ н ϱ . ;ʹϯͿϮ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ Ϯ . ;ʹϱͿϮ ʹ ϰ . ;ʹϯͿϯ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϯ ʹ ϯ . ;ʹϮͿϯ н ϱ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϯ . ;ʹϮͿϯ ʹ ;ʹϱͿϮ . Ϯ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϰ . ;ʹϱ н ϯͿϯ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ;ϰ н ϱͿϮ . ;ʹϯ н ϱͿϯ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ϰ н ϱ . ;ϯ ʹ ϱͿϮ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

4 ^ŽƵůŝŐŶĞ ůĞƐ ŽƉĠƌĂƟ ŽŶƐ ƉƌŝŽƌŝƚĂŝƌĞƐ ƐƵĐĐĞƐƐŝǀĞƐ ĚĂŶƐ ĚĞƐ ĐŽƵůĞƵƌƐ Ěŝī ĠƌĞŶƚĞƐ͖ ĞŶƐƵŝƚĞ͕ ƌĞůŝĞ ĐŚĂƋƵĞ ĐĂůĐƵů ă ƐŽŶ ƌĠƐƵůƚĂƚ͘ ϯ ʹ ϮϮ •

• ϭ

;ϰ ʹ ϲͿ . ;ϱ ʹ ϳͿ •

;ϯ ʹ ϮͿϮ •

• ϭϮ

;ϰ ʹ ϲͿ . ϱ ʹ ϳ •

• ϰ

ϯ . ϮϮ •

• ϯϲ

ϰ ʹ ;ϲ . ϱ ʹ ϳͿ •

• ʹϭϳ

;ϯ . ϮͿϮ •

• ʹϭ

ϰ ʹ ϲ . ;ϱ ʹ ϳͿ •

• ʹϯϯ

ϯϮ ʹ ϮϮ •

• ϭϴ

ϰ ʹ ϲ . ϱ ʹ ϳ •

• ʹϱϵ

ϯϮ . Ϯ •

• ϱ

ϰ . ;ʹϲͿ н ϱ . ;ʹϳͿ •

• ʹϭϵ

• ϭϲ

171

ACTIVITÉS

Chapitre 8 Opérations avec les nombres entiers

ĐƚŝǀŝƚĠ ϱ sĂůĞƵƌƐ ŶƵŵĠƌŝƋƵĞƐ 1 ŽŵƉůğƚĞ ůĞƐ ƚĂďůĞĂƵǆ ĚĞ ĐŽŽƌĚŽŶŶĠĞƐ ĚĞƐ ƉŽŝŶƚƐ ĂĮ Ŷ ƋƵ͛ĞůůĞƐ ǀĠƌŝĮ ĞŶƚ ĐŚĂƋƵĞ ĠŐĂůŝƚĠ ƉƌŽƉŽƐĠĞ͘ Ǉ с Ϯǆ н ϰ

Ǉ с Ϯǆ ʹ ϰ

Ǉ с ʹϮǆ н ϰ

–3

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

–3

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

–3

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

–3

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

–2

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

–2

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

–2

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

–2

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

–1

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

–1

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

–1

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

–1

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ĂŶƐ ůĞ ƌĞƉğƌĞ ĐĂƌƚĠƐŝĞŶ ĐŝͲĐŽŶƚƌĞ͕ ƉůĂĐĞ ƵŶ ŵĂǆŝŵƵŵ ĚĞ ĐŽƵƉůĞƐ ;ǆ ͖ ǇͿ ĚĞ ĐŚĂƋƵĞ ƚĂďůĞĂƵ͘

Ǉ с ʹϮǆ ʹ ϰ

ZĞƉƌĠƐĞŶƚĞ͕ ƌĞƐƉĞĐƟ ǀĞŵĞŶƚ ĞŶ ǀĞƌƚ͕ ĞŶ ƌŽƵŐĞ͕ ĞŶ ďůĞƵ Ğƚ ĞŶ ŶŽŝƌ ƚŽƵƐ ůĞƐ ƉŽŝŶƚƐ ĚŽŶƚ ůĞƐ ĐŽŽƌĚŽŶŶĠĞƐ ǀĠƌŝĮ ĞŶƚ ĐŚĂƋƵĞ ĠŐĂůŝƚĠ͘ ^ŝ ůĞƐ ƉŽŝŶƚƐ ƐŽŶƚ ĐŽƌƌĞĐƚĞŵĞŶƚ ƌĞƉƌĠƐĞŶƚĠƐ͕ ƚƵ ŽďƟ ĞŶƐ ƋƵĂƚƌĞ ĚƌŽŝƚĞƐ ͖ ŶŽŵŵĞͲůĞƐ ƌĞƐƉĞĐƟ ǀĞŵĞŶƚ Ă͕ ď͕ Đ Ğƚ Ě͘ ŶƐƵŝƚĞ͕ ŶŽŵŵĞ ͗ ůĞ ƉŽŝŶƚ Ě͛ŝŶƚĞƌƐĞĐƟ ŽŶ ĚĞƐ ĚƌŽŝƚĞƐ Ă Ğƚ Đ͕ ĐĞůƵŝ ĚĞƐ ĚƌŽŝƚĞƐ ď Ğƚ Đ͕ ĐĞůƵŝ ĚĞƐ ĚƌŽŝƚĞƐ ď Ğƚ Ě͕ ĐĞůƵŝ ĚĞƐ ĚƌŽŝƚĞƐ Ă Ğƚ Ě͘

1 0

YƵĞůůĞ ĞƐƚ ůĂ ŶĂƚƵƌĞ ĚƵ ƋƵĂĚƌŝůĂƚğƌĞ ͍ :ƵƐƟ Į Ğ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

2 ĂͿ ĂůĐƵůĞ ůĂ ǀĂůĞƵƌ ŶƵŵĠƌŝƋƵĞ ĚĞƐ ĞǆƉƌĞƐƐŝŽŶƐ ƉƌŽƉŽƐĠĞƐ ƉŽƵƌ Ă с ϯ͕ ď с ʹϱ Ğƚ Đ с Ϯ͘ Ă н Đ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Ϯ . ď с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Ă ʹ ď с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϮĂ ʹ ĂϮ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϯďϮ ʹ ďĐ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ cϯ н Ϯ . ;Đ ʹ ďͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ďͿ ĂůĐƵůĞ ůĂ ǀĂůĞƵƌ ŶƵŵĠƌŝƋƵĞ ĚĞƐ ĞǆƉƌĞƐƐŝŽŶƐ ƉƌŽƉŽƐĠĞƐ ƉŽƵƌ Ă с ʹϭ͕ ď с ϰ Ğƚ Đ с ʹϯ͘ Ă н Đ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϮĂ ʹ ĂϮ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ACTIVITÉS

Chapitre 8 Opérations avec les nombres entiers

ĐͿ ĂůĐƵůĞ ůĂ ǀĂůĞƵƌ ŶƵŵĠƌŝƋƵĞ ĚĞ ů͛ĞǆƉƌĞƐƐŝŽŶ ǆϮ ʹ Ϯǆ ʹ ϯ ƉŽƵƌ ůĞƐ ǀĂůĞƵƌƐ ĚĞ ǆ ƉƌŽƉŽƐĠĞƐ͘ ǆ с ʹϰ

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ǆ с ʹϯ

ǆ с ʹϮ

ǆ с ʹϭ

ǆ с Ϭ

ǆ с ϭ

ǆ с Ϯ

ǆ с ϯ

YƵĞůůĞ ĞƐƚ ůĂ ǀĂůĞƵƌ ŶƵŵĠƌŝƋƵĞ ůĂ ƉůƵƐ ƐŝŵƉůĞ ă ĐĂůĐƵůĞƌ ͍ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ĐƚŝǀŝƚĠ ϲ Problèmes 1 WƌŽďůğŵĞƐ ŵĂƚŚĠŵĂƟ ƋƵĞƐ ĂͿ ĞƐ ŶŽŵďƌĞƐ ƐŽŶƚ ĠĐƌŝƚƐ ƐƵƌ ĚĞƐ ƉĞƟ ƚƐ ďĂůůŽŶƐ͘ Ŷ ŶĞ ůĞƐ ƵƟ ůŝƐĂŶƚ ƋƵ͛ƵŶĞ ƐĞƵůĞ ĨŽŝƐ͕ ŐƌŽƵƉĞ ůĞƐ ďĂůůŽŶƐ ƉĂƌ ƉĂŝƌĞ ƉŽƵƌ ŽďƚĞŶŝƌ ͗ ƵŶ ƉƌŽĚƵŝƚ ĠŐĂů ă ʹϭϴ

ʹ Ϯ

ƵŶĞ ƐŽŵŵĞ ĠŐĂůĞ ă нϳ ʹ ϱ

ƵŶ ƉƌŽĚƵŝƚ ĠŐĂů ă нϮϬ

ƵŶĞ ƐŽŵŵĞ ĠŐĂůĞ ă ʹϱ

ʹ ϵ +3

+2 +10

ʹ ϲ +4

+12

/ů ƌĞƐƚĞ ƵŶ ƐĞƵů ďĂůůŽŶ ŶŽŶ ƵƟ ůŝƐĠ͕ ůĞƋƵĞů ͍

ďͿ >Ğ ƉƌŽĚƵŝƚ ĚĞ ĚĞƵǆ ŶŽŵďƌĞƐ ĞŶƟ ĞƌƐ ĞƐƚ ʹϮϴ Ğƚ ůĞƵƌ ƐŽŵŵĞ ʹϯ͘ YƵĞůƐ ƐŽŶƚ ĐĞƐ ŶŽŵďƌĞƐ ͍ ǆƉůŝƋƵĞ ƚĂ ĚĠŵĂƌĐŚĞ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

173

ACTIVITÉS

Chapitre 8 Opérations avec les nombres entiers

ĐͿ sŽŝĐŝ ƋƵĂƚƌĞ ŶŽŵďƌĞƐ ĞŶƟ ĞƌƐ ͗ ʹϮ͕ ʹϯ͕ ϰ Ğƚ ϱ͘ hƟ ůŝƐĞ ƵŶĞ ĨŽŝƐ ƚƌŽŝƐ ĚĞ ĐĞƐ ŶŽŵďƌĞƐ ƉŽƵƌ ĠĐƌŝƌĞ ƵŶ ĐĂůĐƵů ĐŽŵƉƌĞŶĂŶƚ ĠǀĞŶƚƵĞůůĞŵĞŶƚ ƉůƵƐŝĞƵƌƐ ŽƉĠƌĂƟ ŽŶƐ ĚŽŶƚ ůĞ ƌĠƐƵůƚĂƚ ƐĞƌĂ ʹϭ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ZĞĐŽŵŵĞŶĐĞ ůĞ ŵġŵĞ ƚƌĂǀĂŝů ƉŽƵƌ ŽďƚĞŶŝƌ ƐƵĐĐĞƐƐŝǀĞŵĞŶƚ ůĞƐ ƌĠƐƵůƚĂƚƐ ʹϮϱ͕ ʹϭϰ͕ Ϯϯ Ğƚ ϭϯ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

2 WƌŽďůğŵĞƐ ĐŽŶĐƌĞƚƐ Ŷ ĞůŐŝƋƵĞ͕ ŽŶ ŵĞƐƵƌĞ ůĂ ƚĞŵƉĠƌĂƚƵƌĞ ĞŶ ĚĞŐƌĠƐ ĞůƐŝƵƐ͘ ĂŶƐ ůĞƐ ƉĂǇƐ ĂŶŐůŽͲƐĂǆŽŶƐ͕ ŽŶ ůĂ ŵĞƐƵƌĞ ĞŶ ĚĞŐƌĠƐ &ĂŚƌĞŶŚĞŝƚ͘ >ŽƌƐƋƵ͛ŽŶ ĐŽŶŶĂŠƚ ůĂ ƚĞŵƉĠƌĂƚƵƌĞ ĞŶ ĚĞŐƌĠƐ ĞůƐŝƵƐ ;ǆͿ͕ ŝů ĞƐƚ ƉŽƐƐŝďůĞ ĚĞ ĚĠƚĞƌŵŝŶĞƌ ůĂ ƚĞŵƉĠƌĂƚƵƌĞ ĐŽƌƌĞƐƉŽŶĚĂŶƚĞ ĞŶ ĚĞŐƌĠƐ &ĂŚƌĞŶŚĞŝƚ ;ǇͿ ŐƌąĐĞ ă ůĂ ĨŽƌŵƵůĞ ͗ Ǉ с ϭ͕ϴ . ǆ н ϯϮ ĂͿ hƟ ůŝƐĞ ĐĞƩ Ğ ĨŽƌŵƵůĞ ƉŽƵƌ ĚĠƚĞƌŵŝŶĞƌ ůĞƐ ǀĂůĞƵƌƐ ĚĞ Ǉ ĚĂŶƐ ůĂ ϭre ƉĂƌƟ Ğ ĚƵ ƚĂďůĞĂƵ ĐŝͲĚĞƐƐŽƵƐ͘ ǆ ;Σ Ϳ

ϭϬ

ʹϭϬ

ʹϭϱ

ϮϬ

Ǉ ;Σ&Ϳ

ϯϮ

Ϯϯ

ʹϰ

ʹϮϮ

ďͿ ZĞƉŽƌƚĞ ůĞƐ ĐŽƵƉůĞƐ ;ǆ ͖ ǇͿ ĚĞ ůĂ ϭre ƉĂƌƟ Ğ ĚƵ ƚĂďůĞĂƵ ĚĂŶƐ ůĞ ƌĞƉğƌĞ ĐĂƌƚĠƐŝĞŶ ĐŝͲĚĞƐƐŽƵƐ͖ ƌĞůŝĞ ůĞƐ ƉŽŝŶƚƐ ŽďƚĞŶƵƐ ĂĮ Ŷ Ě͛ŽďƚĞŶŝƌ ůĞ ŐƌĂƉŚŝƋƵĞ ƋƵŝ ĞǆƉƌŝŵĞ ůĂ ƚĞŵƉĠƌĂƚƵƌĞ ĞŶ ĚĞŐƌĠƐ &ĂŚƌĞŶŚĞŝƚ ĞŶ ĨŽŶĐƟ ŽŶ ĚĞ ůĂ ƚĞŵƉĠƌĂƚƵƌĞ ĞŶ ĚĞŐƌĠƐ ĞůƐŝƵƐ͘ y

ĐͿ hƟ ůŝƐĞ ůĞ ŐƌĂƉŚŝƋƵĞ ƉŽƵƌ ĐŽŵƉůĠƚĞƌ ůĞƐ ǀĂůĞƵƌƐ ĚĞ ǆ ĚĂŶƐ ůĂ ƐĞĐŽŶĚĞ ƉĂƌƟ Ğ ĚƵ ƚĂďůĞĂƵ͘ 174

ACTIVITÉS

Chapitre 8 Opérations avec les nombres entiers

ĐƚŝǀŝƚĠ ϳ Lien entre coordonnées et droites 1 sŽŝĐŝ ƚƌŽŝƐ ĚƌŽŝƚĞƐ ĚĞƐƐŝŶĠĞƐ ĚĂŶƐ ƵŶ ƌĞƉğƌĞ ĐĂƌƚĠƐŝĞŶ͘

y c

ŽŵƉůğƚĞ ůĞƐ ƚĂďůĞĂƵǆ ĐŝͲĚĞƐƐŽƵƐ͘

Droite a

ƌŽŝƚĞ ď

Droite c

ϭ Ϭ

ʹϭ

ʹϮ

0 1

ʹϯ

ʹϮ

ʹϯ

ʹϲ

ʹϮ

ǆƉƌŝŵĞ ƉĂƌ ƵŶĞ ƉŚƌĂƐĞ Ğƚ ƉĂƌ ƵŶĞ ĠŐĂůŝƚĠ ůĂ ĐĂƌĂĐƚĠƌŝƐƟ ƋƵĞ ĐŽŵŵƵŶĞ ĚĞƐ ĐŽŽƌĚŽŶŶĠĞƐ ĚĞ ƚŽƵƐ ůĞƐ ƉŽŝŶƚƐ ĚĞ ĐŚĂƋƵĞ ĚƌŽŝƚĞ͘ WŚƌĂƐĞ Droite a

ŐĂůŝƚĠ

ƌŽŝƚĞ ď

Droite c

2 >ĞƐ ƚĂďůĞĂƵǆ ĚĞ ŶŽŵďƌĞƐ ĐŝͲĚĞƐƐŽƵƐ ƌĞƉƌĠƐĞŶƚĞŶƚ ůĞƐ ĐŽŽƌĚŽŶŶĠĞƐ ĚĞ ƉŽŝŶƚƐ ĚĞ ƋƵĂƚƌĞ ĚƌŽŝƚĞƐ͘ ƉƌğƐ ĂǀŽŝƌ ƚƌŽƵǀĠ ůĂ ĐĂƌĂĐƚĠƌŝƐƟ ƋƵĞ ĐŽŵŵƵŶĞ ĚĞƐ ĐŽŽƌĚŽŶŶĠĞƐ ĚĞ ĐĞƐ ƉŽŝŶƚƐ͕ ĂƐƐŽĐŝĞ ĐŚĂƋƵĞ ƚĂďůĞĂƵ ă ƐŽŶ ĠŐĂůŝƚĠ ĂůŐĠďƌŝƋƵĞ͘ x y

ʹϭ ʹϯ

Ϭ Ϭ

ϭ ϯ

Ϯ ϲ

•

• Ǉ с ʹϬ͕ϱǆ

x y

ʹϰ ϭ

ʹϯ Ϭ

ϭ ʹϰ

Ϯ ʹϱ

•

• Ǉ с ϯǆ

x y

ʹϲ ϯ

ʹϮ ϭ

Ϭ Ϭ

ϰ ʹϮ

•

• ǆ н Ǉ с ʹϯ

x y

ʹϱ ʹϮ

ʹϭ Ϯ

Ϭ ϯ

ϱ 8

•

• Ǉ с ǆ н ϯ

175

ACTIVITÉS

Chapitre 8 Opérations avec les nombres entiers

3 sŽŝĐŝ ƚƌŽŝƐ ĚƌŽŝƚĞƐ ĚĞƐƐŝŶĠĞƐ ĚĂŶƐ ƵŶ ƌĞƉğƌĞ ĐĂƌƚĠƐŝĞŶ͘ EŽƚĞ ůĞƐ ĐŽŽƌĚŽŶŶĠĞƐ ĚĞƐ ƚƌŽŝƐ ƉŽŝŶƚƐ ƌĞƉĠƌĠƐ ƐƵƌ ĐŚĂĐƵŶĞ Ě͛ĞŶƚƌĞ ĞůůĞƐ͘

A E

c B D

Droite a ര;͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͖ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ )

ര;͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͖ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ )

1 x

0 1

ƌŽŝƚĞ ď ര;͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͖ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ )

ര;͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͖ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ )

&ര;͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͖ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ )

Droite c ര;͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͖ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ )

'ര;͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͖ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ )

,ര;͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͖ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ )

ĐƌŝƐ ƵŶĞ ĠŐĂůŝƚĠ ĂůŐĠďƌŝƋƵĞ ƚƌĂĚƵŝƐĂŶƚ ůĂ ĐĂƌĂĐƚĠƌŝƐƟ ƋƵĞ ĐŽŵŵƵŶĞ ĚĞƐ ĐŽŽƌĚŽŶŶĠĞƐ ĚĞ ƚŽƵƐ ůĞƐ ƉŽŝŶƚƐ ĚĞ ĐŚĂƋƵĞ ĚƌŽŝƚĞ͘ Droite a ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ƌŽŝƚĞ ď ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Droite c ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

4 ƉĂƌƟ ƌ ĚĞ ůΖĠŐĂůŝƚĠ ĂůŐĠďƌŝƋƵĞ ŽƵ ĚƵ ŐƌĂƉŚŝƋƵĞ͕ ƌĞƚƌŽƵǀĞ Ğƚ ĐŽƌƌŝŐĞ ůĂ ;ůĞƐͿ ĞƌƌĞƵƌ;ƐͿ ĚĂŶƐ ůĞƐ ƐĞĐŽŶĚĞƐ ůŝŐŶĞƐ ĚĞƐ ƚĂďůĞĂƵǆ ĚĞ ǀĂůĞƵƌƐ͘ Ǉ с ǆ ʹ Ϯ

ʹϰ

ʹϮ

ʹϲ

ʹϮ

ʹϭ

ǆ н Ǉ с ϭ

ʹϱ

ʹϯ

ʹϰ

ʹϭ

ʹϮ

ʹϲ

Ǉ с ʹϯǆ

ʹϱ

ʹϮ

ʹϭ

ϭϱ

ʹϯ

ʹϲ

ʹϮ

ʹϭ

ʹϰ

ʹϭ

1 0

176

Chapitre 8 Opérations avec les nombres entiers

EXERCICES COMPLÉMENTAIRES

Connaître 1

ŽŵƉůğƚĞ ůĞƐ ƉŚƌĂƐĞƐ͘ ĂͿ ^ŝ ůĞ ƉƌŽĚƵŝƚ ĚĞ ĚĞƵǆ ŶŽŵďƌĞƐ ĞŶƚŝĞƌƐ ĞƐƚ ŶĠŐĂƚŝĨ͕ ĂůŽƌƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ďͿ ^ŝ ůĂ ƐŽŵŵĞ ĚĞ ĚĞƵǆ ŶŽŵďƌĞƐ ĞŶƚŝĞƌƐ ĞƐƚ ŶƵůůĞ͕ ĂůŽƌƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ĐͿ ^ŝ ůĞ ƉƌŽĚƵŝƚ ĚĞ ĚĞƵǆ ŶŽŵďƌĞƐ ĞŶƚŝĞƌƐ ĞƐƚ ŶƵů͕ ĂůŽƌƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ĚͿ ^ŝ ůĂ ƐŽŵŵĞ ĚĞ ĚĞƵǆ ŶŽŵďƌĞƐ ĞŶƚŝĞƌƐ ĞƐƚ ƉŽƐŝƚŝǀĞ͕ ĂůŽƌƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ĞͿ ^ŝ ůĞ ƉƌŽĚƵŝƚ ĚĞ ƉůƵƐŝĞƵƌƐ ŶŽŵďƌĞƐ ĞŶƚŝĞƌƐ ĞƐƚ ŶĠŐĂƚŝĨ͕ ĂůŽƌƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

>ĞƐ ƉƌŽƉŽƐŝƚŝŽŶƐ ƐƵŝǀĂŶƚĞƐ ƐŽŶƚͲĞůůĞƐ ǀƌĂŝĞƐ ŽƵ ĨĂƵƐƐĞƐ ͍ ^ŝ ůĂ ƉƌŽƉŽƐŝƚŝŽŶ ĞƐƚ ĨĂƵƐƐĞ͕ ĐŽƌƌŝŐĞͲ ůĂ ĞŶ ĐŚĂŶŐĞĂŶƚ ƵŶ ŵŝŶŝŵƵŵ ĚĞ ŵŽƚƐ͘ ĂͿ >Ğ ƉƌŽĚƵŝƚ ĚĞ ĚĞƵǆ ŶŽŵďƌĞƐ ŶĠŐĂƚŝĨƐ ĞƐƚ ƚŽƵũŽƵƌƐ ƉŽƐŝƚŝĨ͘ ďͿ ^ŝ ůĞ ƉƌŽĚƵŝƚ ĚĞ ĚĞƵǆ ŶŽŵďƌĞƐ ĞƐƚ ƉŽƐŝƚŝĨ͕ ĂůŽƌƐ ůĞƐ ĚĞƵǆ ŶŽŵďƌĞƐ ƐŽŶƚ ŶĠŐĂƚŝĨƐ͘ ĐͿ ^ŝ ůĞ ƉƌŽĚƵŝƚ ĚĞ ĚĞƵǆ ŶŽŵďƌĞƐ ĞƐƚ ŶƵů͕ ĂůŽƌƐ ůĞƐ ĚĞƵǆ ŶŽŵďƌĞƐ ƐŽŶƚ ŽƉƉŽƐĠƐ͘ ĚͿ ^ŝ ůĞ ŶŽŵďƌĞ ĚĞ ĨĂĐƚĞƵƌƐ ƉŽƐŝƚŝĨƐ ĞƐƚ ƉĂŝƌ͕ ĂůŽƌƐ ůĞ ƉƌŽĚƵŝƚ ĞƐƚ ƉŽƐŝƚŝĨ͘ ĞͿ ^ŝ ůĞ ŶŽŵďƌĞ ĚĞ ĨĂĐƚĞƵƌƐ ŶĠŐĂƚŝĨƐ ĞƐƚ ŝŵƉĂŝƌ͕ ĂůŽƌƐ ůĞ ƉƌŽĚƵŝƚ ĞƐƚ ŶĠŐĂƚŝĨ͘ ĨͿ >Ğ ƉƌŽĚƵŝƚ ĚĞ ĚĞƵǆ ŶŽŵďƌĞƐ ŽƉƉŽƐĠƐ ĞƐƚ ƚŽƵũŽƵƌƐ ŶĠŐĂƚŝĨ͘

ZĞůŝĞ ĐŚĂƋƵĞ ĐĂůĐƵů ă ůĂ ƉƌŽƉƌŝĠƚĠ ƋƵ͛ŝů ŝůůƵƐƚƌĞ͘ ϲ . ;ʹϰͿ . ϯ с ϲ . ϯ . ;ʹϰͿ ϭ . ;ʹϵͿ с ʹϵ ;ʹϳͿ . Ϭ с Ϭ ϰ . Ϯϱ . ;ʹϱͿ с ;ϰ . ϮϱͿ . ;ʹϱͿ

• • • •

>Ă ŵƵůƚŝƉůŝĐĂƚŝŽŶ ĞƐƚ ƵŶĞ ŽƉĠƌĂƚŝŽŶ ĂƐƐŽĐŝĂƚŝǀĞ >Ă ŵƵůƚŝƉůŝĐĂƚŝŽŶ ĂĚŵĞƚ Ϭ ĐŽŵŵĞ ĠůĠŵĞŶƚ ĂďƐŽƌďĂŶƚ͘ >Ă ŵƵůƚŝƉůŝĐĂƚŝŽŶ ĂĚŵĞƚ ϭ ĐŽŵŵĞ ĠůĠŵĞŶƚ ŶĞƵƚƌĞ͘ >Ă ŵƵůƚŝƉůŝĐĂƚŝŽŶ ĞƐƚ ƵŶĞ ŽƉĠƌĂƚŝŽŶ ĐŽŵŵƵƚĂƚŝǀĞ͘

WŽƵƌ ĐŚĂƋƵĞ ĠƚĂƉĞ ĚƵ ĐĂůĐƵů͕ Ɛŝ ƵŶĞ ƉƌŽƉƌŝĠƚĠ ĚĞ ůĂ ŵƵůƚŝƉůŝĐĂƚŝŽŶ Ă ĠƚĠ ƵƚŝůŝƐĠĞ͕ ŶŽŵŵĞͲůĂ͘ ;ʹϴͿ . ;ʹϳͿ . ϭϮϱ . ϭ с ;ʹϴͿ . ;ʹϳͿ . ;ϭϮϱ . ϭͿ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ с ;ʹϴͿ . ;ʹϳͿ . ϭϮϱ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ с ;ʹϴͿ . ϭϮϱ . ;ʹϳͿ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ с ;;ʹϴͿ . ϭϮϱͿ . ;ʹϳͿ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ с ;ʹϭϬϬϬͿ . ;ʹϳͿ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ с ϳϬϬϬ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ŽŵƉůğƚĞ ůĞƐ ƉŚƌĂƐĞƐ ƐƵŝǀĂŶƚĞƐ ĂǀĞĐ ůĞƐ ŵŽƚƐ ͗ ƐŽŵŵĞ͕ ƉƌŽĚƵŝƚ͕ ĚŝĨĨĠƌĞŶĐĞ͕ ƚĞƌŵĞƐ͕ ĨĂĐƚĞƵƌƐ͕ ĞǆƉŽƐĂŶƚ͕ ďĂƐĞ ŽƵ ƉƵŝƐƐĂŶĐĞ͘ >͛ĞǆƉƌĞƐƐŝŽŶ ʹϲ н ϰ ĞƐƚ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ĚŽŶƚ ʹϲ Ğƚ ϰ ƐŽŶƚ ůĞƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ >͛ĞǆƉƌĞƐƐŝŽŶ ʹϲ . ϰ ĞƐƚ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ĚŽŶƚ ʹϲ Ğƚ ϰ ƐŽŶƚ ůĞƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ >͛ĞǆƉƌĞƐƐŝŽŶ ϲ ʹ ϰ ĞƐƚ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ĚŽŶƚ ϲ Ğƚ ϰ ƐŽŶƚ ůĞƐ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ >͛ĞǆƉƌĞƐƐŝŽŶ ;ʹϲͿϰ est ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ĚŽŶƚ ʹϲ ĞƐƚ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ Ğƚ ϰ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ƉƉůŝƋƵĞƌ 1

ĂůĐƵůĞ ƌĂƉŝĚĞŵĞŶƚ ůĞƐ ƐŽŵŵĞƐ ƐƵŝǀĂŶƚĞƐ͘ a) ʹϲ н Ϯ н ϵ ʹ ϴ с ʹϵ ʹ ϰ н ϱ с ϳ ʹ ϵ ʹ Ϯ н ϱ с ʹϴ н ϳ ʹ ϯ н ϴ с ϭϯ ʹ ϴ ʹ ϱ н ϲ с

ďͿ ʹϳ н ϭϰ ʹ Ϯϰ с ϭϮ ʹ ϭϱ ʹ ϭϯ с ʹϮϯ н ϯϱ н ϭϳ с ϭϲ ʹ Ϯϳ ʹ Ϯϳ ʹ ϭϲ с ʹϵ ʹ ϭϭ н ϲ н ϱ с

c) ʹϯ н ϱ ʹ ϴ ʹ ϳ н ϲ с ϭϲ ʹ ϭϰ н ϰ ʹ Ϯ с ϯϴ н ϭϱ ʹ ϭϲ ʹ ϴ с ʹϰϱ н ϭϱ ʹ ϰϱ н ϭϬ с ʹϭϮ н ϴϴ н ϭϱ ʹ ϴϱ с

ĂůĐƵůĞ ƌĂƉŝĚĞŵĞŶƚ ůĞƐ ƉƌŽĚƵŝƚƐ ƐƵŝǀĂŶƚƐ͘ a) ϰ . ;ʹϮͿ с ;ʹϱͿ . ;ʹϳͿ с ;ʹϲͿ . ϱ с ʹϴ . ;ʹϮͿ с ϱ . ;ʹϱͿ с

ďͿ ʹϰ . ϱ с ʹϮ . ;ʹϮͿ с Ϯ . ;ʹϲͿ с ;ʹϮͿ . ;ʹϮͿ с ʹϴ . ϴ с

c) Ϯ . ;ʹϯͿ . ;ʹϱͿ . ϰ с ĚͿ ʹϰ . ;ʹϰͿ . ϰ с ʹϱ . ;ʹϲͿ . ;ʹϮͿ . ϰ с ʹϮ . Ϯ . ϯ . ;ʹϯͿ с ʹϯ . ;ʹϲͿ . ;ʹϮͿ . ϰ с ʹϱ . ϰ . ;ʹϰͿ . ;ʹϱͿ с ϵ . ;ʹϮϱͿ . ;ʹϰͿ . Ϯ с ʹϮ . ;ʹϯͿ . Ϯ . ϯ . ;ʹϯͿ с ʹϲ . ϭϮϱ . 8 . ;ʹϮͿ . ;ʹϯͿ с ϭϬ . ;ʹϭϬͿ . Ϯ . ;ʹϮͿ . ϱ с

177

EXERCICES COMPLÉMENTAIRES 3

ĂůĐƵůĞ ĂƉƌğƐ ĂǀŽŝƌ ƌĞĐŽŶŶƵ ů͛ŽƉĠƌĂƚŝŽŶ͘ a) ϱ ʹ ϵ с

ďͿ ϴ ʹ ϭϮ с

;ʹϱͿϮ с

ʹϭϬ ʹ ϯ с

ʹϴ . ;ʹϭϮͿ с

;ʹϮͿϯ с

;ʹϮͿϱ с

ʹϭϬ н ϯ с

ʹϱ . ;ʹϵͿ с

ʹϭϮ . ϴ с

;ʹϯͿϮ с

ʹϱ н Ϯ с

ʹϭϬ . ;ʹϯͿ с

ʹϵ н ϱ с

ϭϮ ʹ ϴ с

ʹϮ . ;ʹϯͿ с

ʹϱ ʹ Ϯ с

ϭϬ . ;ʹϯͿ с

ĨͿ ʹϭϱ н ϰ с

ŐͿ ʹϱ ʹ ϲ н ϵ н Ϯ с ʹϱ . ;ʹϲͿ . ϵ . Ϯ с

ʹϭ ʹ ϱ н ϲ н ϵ ʹ Ϯ с

ʹϭϮϱ . 8 . ϭϮϱ . ;ʹϴͿ с

ʹϰ н ϭϱ с

ϭϮ ʹ ϴ н ϱ ʹ Ϯ с

ʹϭ . ;ʹϱͿ . ϲ . ϵ . ;ʹϮͿ с

ϭϬϬ ʹ ϰ н Ϯ ʹ ϱ с

ϰ . ;ʹϭϱͿ с

ϭϮ . ;ʹϴͿ . ϱ . ;ʹϮͿ с

ʹϱ н ϲ ʹ ϲ н ϱ с

ϭϬϬ . ;ʹϰͿ . Ϯ . ;ʹϱͿ с

ʹϰ ʹ ϭϱ с

ʹϭϮ ʹ ϴ ʹ ϱ ʹ Ϯ с

ʹϱ . ϲ . ;ʹϲͿ . ϱ с

ʹϭϬϬ ʹ ϰ н Ϯ ʹ ϱ с

ĂůĐƵůĞ ůĞƐ ƉƵŝƐƐĂŶĐĞƐ Ğƚ ǀĠƌŝĨŝĞ ă ůĂ ĐĂůĐƵůĂƚƌŝĐĞ͘ ďͿ ;ʹϮͿϰ с

ĨͿ ;ʹϭͿϮ с

ϲϮ с

ϭϬϮ с

;ʹϭϬͿϮ с

ϵϮ с

;ʹϳͿϮ с

;ʹϱͿϯ с

;ʹϴͿϮ с

;ʹϭϬͿϱ с

ϰϯ с

;ʹϭͿϯ с

ʹϲ н Ϯ . ;ʹϰͿ с ϴ ʹ Ϯ . ;ʹϱͿ с ϳ ʹ Ϯ . ϯϮ с ;ϴ ʹ ϯͿϮ ʹ Ϯϯ с ϲ ʹ ϵ . ;ϰ ʹ ϴͿ с ϱ ʹ ;ϯ ʹ ϳͿϮ с

ʹϲ н ϴ ϴ ʹ ;ʹϭϬͿ ϱ . ϯϮ ϱϮ ʹ Ϯϯ ϲ н ϵ . ϰ ϱ н ϭϲ

ʹϲ ʹ ϴ ϴ н ϭϬ ϳ ʹ Ϯ . ϵ Ϯϱ ʹ ϴ ϲ ʹ ϵ . ϰ ϱ ʹ ;ʹϰͿϮ

ʹϲ н ;ʹϴͿ ϴ ʹ ϭϬ ϳ ʹ ϭϴ 8Ϯ ʹ ϯϮ ʹ Ϯϯ ϲ ʹ ϵ . ;ʹϰͿ ϱ ʹ ϭϲ

ĂůĐƵůĞ ĞŶ ƵƚŝůŝƐĂŶƚ ůĞƐ ƉƌŝŽƌŝƚĠƐ ĚĞƐ ŽƉĠƌĂƚŝŽŶƐ͘ ďͿ ʹϯ . ϰ н ϱ . ;ʹϮͿ с

c) ;ϱ ʹ ϵͿ . ;ϯ ʹ ϳͿ с

ĚͿ ʹϮ н ϴ . ϱ ʹ ϳс

ϰ ʹ ϯ . ϴ н ϵ с

Ϯ . ;ʹϲͿ ʹ ϱ . ϰ с

ϱ ʹ ϵ . ;ϯ ʹ ϳͿ с

;ʹϮ н ϴͿ . ;ϱ ʹ ϳͿ с

ʹϭϮ ʹ ϯ . ϰ с

ʹϱ . ϰ ʹ ϯ . ;ʹϰͿ с

ϱ ʹ ϵ . ϯ ʹ ϳ с

ʹ Ϯ . ϴ н ϱ . ;ʹϳͿ с

ʹϱ ʹ Ϯ . ϴ ʹ ϵ с

ʹϱ н ;ʹϴͿ . ;ʹϮͿ с

ϱ . ;ʹϵͿ н ϯ . ;ʹϳͿ с

ʹϮ . 8 . ϱ . ;ʹϳͿ с

ϭϱ н ϯ . ϲ ʹ ϰ . ϵ с

ʹϳ . ;ʹϮͿ н ϱ . ϯ с

ϱ ʹ ϵ н ϯ ʹ ϳ с

ʹϮ н ϴ . ;ϱ ʹ ϳͿ с

ĨͿ Ϯ . ;ʹϲͿϮ н ϯ . ;ʹϭͿϯ ʹ Ϯϰ с

ŐͿ Ϯ . ;ϯ н ϮͿϯ с

ϭ ʹ ϰ . ;ʹϮͿ н ;ʹϯͿϮ с

ʹϱ н Ϯ . ;ʹϰͿϯ ʹ ϱϯ с

;ϯ ʹ ϱͿϯ . ;ʹϮ н ϳͿϮ с

ϱ . ;ʹϮͿϯ н Ϯ . ;ʹϱͿϮ с

;ʹϱ н ϯͿ . ;ϱϮ ʹ ϯϯͿ с

ϱ н ;ϴ ʹ ϰͿϯ с

ʹϲ н Ϯ . ;ʹϯͿϯ с

ϭ н ϰ . ;ʹϮ н ϮϮͿ с

Ϯ ʹ ϱ . ;Ϯ ʹ ϴͿϮ с

ʹϮ н ;ʹϰͿϮ . ;ʹϯͿ ʹ ϴ с

;ʹϳͿϮ ʹ ϱ . ;Ϯϯ ʹ ϯϯͿ с

;Ϯ ʹ ϱͿϯ . ;Ϯ ʹ ϴͿϮ с

ŽŵƉůğƚĞ ƉĂƌ ф͕ х ŽƵ с͘ ϰ . ϯ ͘ ͘ ͘ ͘ ͘ ;ʹϰͿ . ;ʹϯͿ ʹϳ н ϭϱ ͘ ͘ ͘ ͘ ͘ ϲ ʹ ϭϴ ʹϮ . ϱϬ ͘ ͘ ͘ ͘ ͘ ʹϱϬ ʹ Ϯ

178

e) ;ʹϯͿϰ с

;ʹϯͿϯ с

e) ϭ н ϰ Ϯ ʹ Ϯ . ϯϮ с

ĚͿ ;ʹϮͿϱ с

;ʹϱͿϮ с

a) ϱ ʹ Ϯ . ϴ с

c) ;ʹϰͿϯ с

WĂƌŵŝ ůĞƐ ƚƌŽŝƐ ƉƌŽƉŽƐŝƚŝŽŶƐ͕ ďĂƌƌĞ ĐĞůůĞ ƋƵŝ ĞƐƚ ĨĂƵƐƐĞ͘ a) ďͿ c) ĚͿ e) ĨͿ

ŚͿ ʹϭϮ . ;ʹϴͿ . ;ʹϱͿ . ;ʹϮͿ с i) ʹϭϮϱ н ϴ н ϭϮϱ ʹ ϴ с

ʹϰ . ;ʹϭϱͿ с

a) Ϯϯ с

e) ;ʹϭϬͿϯ с

ĚͿ ʹϱ . ;ʹϮͿ с

ʹϮ н ϯ с

ʹϱ ʹ ϵ с

c) ;ʹϮͿ . ϯ с

ʹϴ ʹ ϭϮ с

ϱ . ;ʹϵͿ с

Chapitre 8 Opérations avec les nombres entiers

Ϭ ʹ ϭϬ ͘ ͘ ͘ ͘ ͘ Ϭ . ;ʹϭϬͿ Ϯ . ;ʹϭϬͿ ͘ ͘ ͘ ͘ ͘ ϭϬ ʹ Ϯ ϱϬ . ;ʹϭͿ ͘ ͘ ͘ ͘ ͘ ʹϱϬ ʹ ϭ Ϯ . ;ʹϰͿ ͘ ͘ ͘ ͘ ͘ ʹ Ϯ . ϰ ʹϰ . ;ʹϱͿ ͘ ͘ ͘ ͘ ͘ ʹϰ ʹ ϱ ϭϬ ʹ ϭ ͘ ͘ ͘ ͘ ͘ ʹϭ . ;ʹϵͿ

ZĞůŝĞ ĐŚĂƋƵĞ ĐĂůĐƵů ă ƐŽŶ ƌĠƐƵůƚĂƚ͘ a) ʹϱ . ϰ ʹ ϯ . Ϯ • • ʹϱ . ;ϰ ʹ ϯͿ . Ϯ • • ʹϱ ʹ ϰ . ;ʹϯͿ ʹ Ϯ • • ;ʹϱ ʹ ϰͿ . ;ʹϯͿ ʹ Ϯ • • ʹϱ . ;ʹϰͿ ʹ ϯ . Ϯ • •

ʹϭϬ ʹϮϲ Ϯϱ ϱ ϭϰ

ďͿ

ʹϰ . ϱ . ;ʹϮͿ ͘ ͘ ͘ ͘ ͘ ʹϰ . ;ʹϱͿ . ;ʹϮͿ ʹϰ ʹ ϱ н Ϯ ͘ ͘ ͘ ͘ ͘ ʹϰ ʹ ϱ ʹ Ϯ Ϯ . ;ϰ ʹ ϱͿ ͘ ͘ ͘ ͘ ͘ ʹϮ . ;ϰ ʹ ϱͿ

ʹϱ . ;ϰ ʹ ϯͿϮ ʹϱ . ϰ ʹ ϯϮ ʹϱ . ϰϮ ʹ ϯϮ ;ʹϱ н ϰͿϯ . Ϯ ʹϱ н ϰ . ϯϮ

• • • • •

ʹϮϵ ʹϴϵ ʹϱ ϯϭ ʹϮ

Chapitre 8 Opérations avec les nombres entiers

EXERCICES COMPLÉMENTAIRES

ĂŶƐ ĐŚĂƋƵĞ ĠŐĂůŝƚĠ͕ ƌĞŵƉůĂĐĞ ůĞƐ ƉŽŝŶƚŝůůĠƐ ƉĂƌ ůĞ ƐŝŐŶĞ ŽƉĠƌĂƚŽŝƌĞ ƋƵŝ ĐŽŶǀŝĞŶƚ͘ ;ʹϯͿ ͘ ͘ ͘ ͘ ͘ ;ʹϮͿ с ʹϱ ;ʹϯͿ ͘ ͘ ͘ ͘ ͘ ;ʹϮͿ с ϲ ;ʹϯͿ ͘ ͘ ͘ ͘ ͘ ;ʹϮͿ с ʹϭ ;ʹϮͿ ͘ ͘ ͘ ͘ ͘ ;ʹϮͿ с ϰ ;ʹϮͿ ͘ ͘ ͘ ͘ ͘ ;ʹϮͿ с ʹϰ ;ʹϱͿ ͘ ͘ ͘ ͘ ͘ ;нϰͿ с ;ʹϭϮͿ ͘ ͘ ͘ ͘ ͘ ;нϴͿ

10 ŽŵƉůğƚĞ ůĞ ƚĂďůĞĂƵ͘

a Ϯ ϱ ʹϯ

ď ϯ ʹϯ ʹϮ

Ă н ď

Ă ʹ ď

a.ď

aϮ

ϮĂ

ʹϯď

ďϯ

ʹϭϱ ʹϭϰ

11 ^ĂĐŚĂŶƚ ƋƵĞ Ă с ʹϮ͕ ď с ʹϱ Ğƚ Đ с ʹϯ͕ ƉůĂĐĞ ůĞƐ ƉĂƌĞŶƚŚğƐĞƐ ŝŶĚŝƐƉĞŶƐĂďůĞƐ ĚĂŶƐ ůĞƐ ĐĂůĐƵůƐ

ĐŝͲĚĞƐƐŽƵƐ͘ a) Ă н ď н Đ с ʹϮ н ʹϱ н ʹϯ a . ď . Đ с ʹϮ . ʹϱ . ʹϯ a . ď ʹ Đ с ʹϮ . ʹϱ ʹ ʹϯ Ă н ď . Đ с ʹϮ н ʹϱ . ʹϯ ʹϮĂ н ϰĐ с ʹϮ . ʹϮ н ϰ . ʹϯ

ďͿ ʹϯ . ;Ă н ďͿ с ʹϯ . ;ʹϮ н ʹϱͿ Ϯď н ĂϮ с Ϯ . ʹϱ н ʹϮ Ϯ aϯ ʹ ϯďϮ с ʹϮ ϯ ʹ ϯ . ʹϱ Ϯ cϮ н ϮĂď с ʹϯ Ϯ н Ϯ . ʹϮ . ʹϱ (aϮ н ďͿ . Đ с ; ʹϮ Ϯ н ʹϱ Ϳ . ʹϯ

12 WŽƵƌ ĐĂůĐƵůĞƌ ůĞƐ ǀĂůĞƵƌƐ ŶƵŵĠƌŝƋƵĞƐ ĚĞƐ ĞǆƉƌĞƐƐŝŽŶƐ ĐŝͲĚĞƐƐŽƵƐ͕ ŽŶ Ă ƌĞŵƉůĂĐĠ Ă ƉĂƌ ʹϮ͕

ď ƉĂƌ ϯ Ğƚ Đ ƉĂƌ ʹϰ͘ WŽƵƌ ĐŚĂƋƵĞ ĞǆƉƌĞƐƐŝŽŶ͕ ĞŶƚŽƵƌĞ ůĂ ƉƌŽƉŽƐŝƚŝŽŶ ĚĞ ƌĞŵƉůĂĐĞŵĞŶƚ ƋƵŝ ĞƐƚ ĐŽƌƌĞĐƚĞ͘ a) ďͿ c) ĚͿ e)

Ăď н Đ ϱĐ н ĂϮ ĂďϮ ϮĂ н Đ a . ;ď н ĐͿ

ʹϮ н ϯ ʹ ϰ ϱ ʹ ϰ н ϮϮ ʹϮ н ϯϮ Ϯ ʹ Ϯ ʹ ϰ ʹϮ . ϯ н ;ʹϰͿ

ʹϮ . ϯ н ;ʹϰͿ ϱ . ;ʹϰͿ ʹ ϮϮ ʹϮ . ϯϮ Ϯ . ;ʹϮͿ н ;ʹϰͿ ʹϮ . ;ϯ н ϰͿ

ʹϮ . ϯ . ;ʹϰͿ ϱ . ;ʹϰͿ н ;ʹϮͿϮ ;ʹϮ . ϯͿϮ Ϯ . ;ʹϮͿ . ;ʹϰͿ ʹϮ . ;ϯ ʹ ϰͿ

13 ĂůĐƵůĞ ůĞƐ ǀĂůĞƵƌƐ ŶƵŵĠƌŝƋƵĞƐ ĚĞƐ ĞǆƉƌĞƐƐŝŽŶƐ ƐƵŝǀĂŶƚĞƐ Ɛŝ ƚƵ ƐĂŝƐ ƋƵĞ ͗

Ă с ʹϮ a) Ă н ď с a . Đ с ϳĐ с ʹϰĂ с ʹϯĚ с

ď с ϯ

Đ с ʹϱ

Ě с ϰ

e) ϯď ʹ ďϮ с ĨͿ cϮ н ϯĐ н ϭ с ďͿ ϯĂ н Ϯď с c) ϲ . ;Đ н ĚͿ с ĚͿ aϮ с ϯ Ϯ c с ϮĂ ʹ Ăď с ďϮ ʹ ϰď н ϯ с ϱĂ н ϯĐ с 7 . ;ď ʹ ĐͿ с ϯ ϯ ϯď с c н ϮĂĐ с aϮ ʹ Ă ʹ Ϯ с ʹϮď ʹ ϯĚ с ʹϯ . ;Đ ʹ ĂͿ с ϲĂϮ с Ěϯ н ϯ . ;ď ʹ ĐͿ с ϮĚϮ ʹ Ě ʹ ϲ с ʹϮĐ н ϲď с a . ;ď н ĚͿ с Ϯ Ϯ ʹϱĐ с ϯĂ ʹ Ϯ . ;Đ н ĚͿ с ϰĂϮн ϮĂ ʹ ϱ с ϱĂ н ϮĐ с Ě . ;Ă ʹ ĐͿ с

14 ŽŵƉůğƚĞ ůĞƐ ƉǇƌĂŵŝĚĞƐ ĞŶ ƌĞƐƉĞĐƚĂŶƚ ůĞƐ ƉƌŝŶĐŝƉĞƐ ĚĞ ĐŽŶƐƚƌƵĐƚŝŽŶ ĚĞ ĐĞůůĞƐͲĐŝ͘

Ă н ď ď

a . ď

ʹϭϬ Ϯ

ʹϮϬ ʹϴ

ʹϯ

ʹϵ

ϭϴ

ʹϭ ʹϮ ʹϱ

ʹϭϬ ʹϮ

ʹϭ

ʹϯ

179

EXERCICES COMPLÉMENTAIRES

Chapitre 8 Opérations avec les nombres entiers

15 >ĞƐ ƚĂďůĞĂƵǆ ĚĞ ŶŽŵďƌĞƐ ĐŝͲĚĞƐƐŽƵƐ ƌĞƉƌĠƐĞŶƚĞŶƚ ůĞƐ ĐŽŽƌĚŽŶŶĠĞƐ ĚĞ ƉŽŝŶƚƐ ĚĞ ƋƵĂƚƌĞ

ĚƌŽŝƚĞƐ͘ ƐƐŽĐŝĞ ĐŚĂƋƵĞ ƚĂďůĞĂƵ ă ů͛ĠŐĂůŝƚĠ ĂůŐĠďƌŝƋƵĞ ƋƵŝ ĞǆƉƌŝŵĞ ůĂ ƌĞůĂƚŝŽŶ ĞŶƚƌĞ ǆ Ğƚ Ǉ͘ ǆ Ǉ

ʹϱ ϯ

ʹϮ Ϭ

ϭ ʹϯ

Ϯ ʹϰ

•

• Ǉ с ʹϮǆ

ǆ Ǉ

ʹϯ ʹϳ

ʹϭ ʹϯ

ϭ ϭ

ϯ ϱ

•

• Ǉ с ǆ ʹ Ϯ

ǆ Ǉ

ʹϰ 8

ʹϭ Ϯ

Ϭ Ϭ

Ϯ ʹϰ

•

• ǆ н Ǉ с ʹϮ

ǆ Ǉ

ʹϮ ʹϰ

ʹϭ ʹϯ

Ϭ ʹϮ

ϯ ϭ

•

• Ǉ с Ϯǆ ʹ ϭ

Transférer 1

KŶ Ă ŵƵůƚŝƉůŝĠ ƚƌŽŝƐ ƉĂƌ ƚƌŽŝƐ ĚĞ ƚŽƵƚĞƐ ůĞƐ ĨĂĕŽŶƐ ƉŽƐƐŝďůĞƐ ůĞƐ ŶŽŵďƌĞƐ ƐƵŝǀĂŶƚƐ ͗ ϱ͕ ʹϰ͕ ʹϯ Ğƚ Ϯ͘ WĂƌŵŝ ůĞƐ ƉƌŽĚƵŝƚƐ ƐƵŝǀĂŶƚƐ͕ ƋƵĞů ĞƐƚ ĐĞůƵŝ ƋƵĞ ů͛ŽŶ Ŷ͛Ă ƉĂƐ ŽďƚĞŶƵ ͗ ϲϬ ͕ ʹϯϲ ͕ ʹϰϬ ͕ Ϯϰ ͕ ʹϯϬ ͍

ĐƌŝƐ ůĞƐ ƚƌŽŝƐ ƚĞƌŵĞƐ ƐƵŝǀĂŶƚƐ ĚĞ ĐŚĂĐƵŶĞ ĚĞƐ ƐƵŝƚĞƐ ĐŝͲĚĞƐƐŽƵƐ ĞŶ ƌĞƐƉĞĐƚĂŶƚ ůĞƵƌ ƌĠŐƵůĂƌŝƚĠ͘ a) ϳ ͕ ϰ ͕ ϭ ͕ ͘ ͘ ͘ ͘ ͘ ͘ ͕ ͘ ͘ ͘ ͘ ͘ ͘ ͕ ͘ ͘ ͘ ͘ ͘ ͘ ďͿ ϯϮ ͕ ʹϭϲ ͕ ϴ ͕ ͘ ͘ ͘ ͘ ͘ ͘ ͕ ͘ ͘ ͘ ͘ ͘ ͘ ͕ ͘ ͘ ͘ ͘ ͘ ͘

c) ϯ ͕ ϵ ͕ Ϯϳ ͕ ͘ ͘ ͘ ͘ ͘ ͘ ͕ ͘ ͘ ͘ ͘ ͘ ͘ ͕ ͘ ͘ ͘ ͘ ͘ ͘ ĚͿ ʹϮ ͕ ϰ ͕ ʹϴ ͕ ͘ ͘ ͘ ͘ ͘ ͘ ͕ ͘ ͘ ͘ ͘ ͘ ͘ ͕ ͘ ͘ ͘ ͘ ͘ ͘

ǀĞĐ ůĞƐ ŶŽŵďƌĞƐ ƉƌŽƉŽƐĠƐ͕ ƌĞƚƌŽƵǀĞ ůĞƐ ƌĠƐƵůƚĂƚƐ ĚĞŵĂŶĚĠƐ ĞŶ ƐĂĐŚĂŶƚ ƋƵĞ ͗ ʹ ƚƵ ŶĞ ƉĞƵǆ ƵƚŝůŝƐĞƌ ĐŚĂƋƵĞ ŶŽŵďƌĞ ƋƵ͛ƵŶĞ ƐĞƵůĞ ĨŽŝƐ͖ ʹ ƚƵ ĚŽŝƐ ƵƚŝůŝƐĞƌ ƚŽƵƐ ůĞƐ ŶŽŵďƌĞƐ͖ ʹ ƚŽƵƚĞƐ ůĞƐ ŽƉĠƌĂƚŝŽŶƐ ƐŽŶƚ ƉĞƌŵŝƐĞƐ ĂŝŶƐŝ ƋƵĞ ů͛ƵƚŝůŝƐĂƚŝŽŶ ĚĞ ƉĂƌĞŶƚŚğƐĞƐ͘ ĂͿ ǀĞĐ ůĞƐ ŶŽŵďƌĞƐ ʹϯ ͕ ʹϱ ͕ Ϯϱ ͕ ʹϭϬϬ Ğƚ ϳ͕ ƚƵ ĚŽŝƐ ŽďƚĞŶŝƌ ʹϲϱϬ͘ ďͿ ǀĞĐ ůĞƐ ŶŽŵďƌĞƐ ʹϭϮ ͕ Ϯϱ ͕ ϭϬ ͕ ʹϴ Ğƚ ʹϳϱ͕ ƚƵ ĚŽŝƐ ŽďƚĞŶŝƌ ϳϯϬ͘

WůĂĐĞ ĚĂŶƐ ůĞƐ ĐĂƌƌĠƐ ůĞƐ ŶŽŵďƌĞƐ ĞŶƚŝĞƌƐ ĚĞ ʹϭ ă ʹϵ ƉŽƵƌ ů͛ĞǆĞƌĐŝĐĞ Ă Ğƚ ĚĞ ʹϰ ă ϱ ;ƐĂƵĨ ϬͿ ƉŽƵƌ ů͛ĞǆĞƌĐŝĐĞ ď͕ ƐĂŶƐ ůĞƐ ƌĠƉĠƚĞƌ͕ ĚĞ ƚĞůůĞ ƐŽƌƚĞ ƋƵĞ ůĞ ƉƌŽĚƵŝƚ ĚĞ ĚĞƵǆ ŶŽŵďƌĞƐ ƐŝƚƵĠƐ ĚĂŶƐ ĚĞƵǆ ĐĂƌƌĠƐ ĐƀƚĞ ă ĐƀƚĞ ƐŽŝƚ ĠŐĂů ĂƵ ŶŽŵďƌĞ ĠĐƌŝƚ ĚĂŶƐ ůĞ ƚƌŝĂŶŐůĞ ƋƵŝ ůĞƐ ƚŽƵĐŚĞ͘ 27

–20

ďͿ

a) 18

180

–4

–6

–12

–5

Chapitre 9 Calcul littéral Tableaux de compétences Libre EŽŵďƌĞƐ ;ĞŶƟ ĞƌƐ Ğƚ ƌĂƟ ŽŶŶĞůƐͿ 18

ZĞƐƉĞĐƚĞƌ ůĞƐ ƉƌŝŽƌŝƚĠƐ ĚĞƐ ŽƉĠƌĂƟ ŽŶƐ ƉŽƵƌ Ğī ĞĐƚƵĞƌ ĚĞƐ ŽƉĠƌĂƟ ŽŶƐ ĚĂŶƐ ĚĞƐ ƐŝƚƵĂƟ ŽŶƐ ǀĂƌŝĠĞƐ͘

ĂůĐƵů ůŝƩ ĠƌĂů Ğƚ ĠƋƵĂƟ ŽŶƐ 21

ƐƐŽĐŝĞƌ ƵŶĞ ĞǆƉƌĞƐƐŝŽŶ ůŝƩ ĠƌĂůĞ ă ƵŶĞ ĨĂŵŝůůĞ ĚĞ ŶŽŵďƌĞƐ͘

DĂŠƚƌŝƐĞƌ ůĞƐ ĐŽŶǀĞŶƟ ŽŶƐ Ě͛ĠĐƌŝƚƵƌĞ ŵĂƚŚĠŵĂƟ ƋƵĞ ĚĞƐ ĞǆƉƌĞƐƐŝŽŶƐ ůŝƩ ĠƌĂůĞƐ͘

:ƵƐƟ Į Ğƌ ů͛ĠŐĂůŝƚĠ ĚĞ ĚĞƵǆ ĞǆƉƌĞƐƐŝŽŶƐ ůŝƩ ĠƌĂůĞƐ ĞŶ ƵƟ ůŝƐĂŶƚ ĚĞƐ ƉƌŽƉƌŝĠƚĠƐ ĚĞƐ ŽƉĠƌĂƟ ŽŶƐ͘ ZĞĐŽŶŶĂŠƚƌĞ ůĂ ŶĂƚƵƌĞ Ě͛ƵŶĞ ĞǆƉƌĞƐƐŝŽŶ ůŝƩ ĠƌĂůĞ ;ƐŽŵŵĞ ĚĞ ƚĞƌŵĞƐ͕ ƉƌŽĚƵŝƚ ĚĞ ĨĂĐƚĞƵƌƐ͕ ͙Ϳ͘

24 25

:ƵƐƟ Į Ğƌ ƵŶĞ ĚŝƐƚƌŝďƵƟ ǀŝƚĠ ƉĂƌ ƵŶ ĚĞƐƐŝŶ ŽƵ ƵŶ ĞǆĞŵƉůĞ ŐĠŽŵĠƚƌŝƋƵĞ͘

WĂƐƐĞƌ Ě͛ƵŶ ůĂŶŐĂŐĞ ĐŽƵƌĂŶƚ ĂƵ ůĂŶŐĂŐĞ ĂůŐĠďƌŝƋƵĞ Ğƚ ƌĠĐŝƉƌŽƋƵĞŵĞŶƚ͘

ĠŶŽŵďƌĞƌ ƉĂƌ ƵŶ ĐĂůĐƵů Ğƚ ůĞ ĐĂƐ ĠĐŚĠĂŶƚ ƉĂƌ ƵŶĞ ĨŽƌŵƵůĞ͘

ĂůĐƵůĞƌ ĚĞƐ ǀĂůĞƵƌƐ ŶƵŵĠƌŝƋƵĞƐ Ě͛ĞǆƉƌĞƐƐŝŽŶƐ ůŝƩ ĠƌĂůĞƐ ;ƉĂƌ ĞǆĞŵƉůĞ ĚĂŶƐ ĚĞƐ ĨŽƌŵƵůĞƐ Ě͛ĂŝƌĞƐ ŽƵ ĚĞ ǀŽůƵŵĞƐͿ͘ WĂƐƐĞƌ Ě͛ƵŶĞ ĨŽƌŵĞ ůŝƩ ĠƌĂůĞ ă ƵŶĞ ĂƵƚƌĞ ĞŶ ƵƟ ůŝƐĂŶƚ ůĂ ĚŝƐƚƌŝďƵƟ ǀŝƚĠ ƐŝŵƉůĞ ŽƵ ůĂ ŵŝƐĞ ĞŶ ĠǀŝĚĞŶĐĞ͘ dƌĂŶƐĨŽƌŵĞƌ ĚĞƐ ĞǆƉƌĞƐƐŝŽŶƐ ůŝƩ ĠƌĂůĞƐ ĞŶ ƌĞƐƉĞĐƚĂŶƚ ůĂ ƌĞůĂƟ ŽŶ Ě͛ĠŐĂůŝƚĠ Ğƚ ĞŶ ĂǇĂŶƚ ĞŶ ǀƵĞ ƵŶĞ ĨŽƌŵĞ ƉůƵƐ ĐŽŵŵŽĚĞ͘

29 30 31

ZĠƐŽƵĚƌĞ ƵŶĞ ĠƋƵĂƟ ŽŶ ĚĞ ůĂ ĨŽƌŵĞ Ă н ǆ с ď ŽƵ Ăǆ с ď ŽƵ Ăǆ н ď с Đ͘

ůĂďŽƌĞƌ ƵŶĞ ĨŽƌŵƵůĞ ƋƵŝ ƚƌĂĚƵŝƚ ůĂ ƌĠŐƵůĂƌŝƚĠ ĚĂŶƐ ĚĞƐ ƐƵŝƚĞƐ ĚĞ ŵŽƟ ĨƐ ;ŽƵ ĚĞ ŶŽŵďƌĞƐͿ͘ ŽŶƐƚƌƵŝƌĞ ĚĞƐ ĞǆƉƌĞƐƐŝŽŶƐ ůŝƩ ĠƌĂůĞƐ Žƶ ůĂ ůĞƩ ƌĞ Ă ůĞ ƐƚĂƚƵƚ Ě͛ŝŶĚĠƚĞƌŵŝŶĠĞ͕ ĚĞ ǀĂƌŝĂďůĞ ŽƵ Ě͛ŝŶĐŽŶŶƵĞ͘ ZĠƐŽƵĚƌĞ ƵŶ ƉƌŽďůğŵĞ ƐŝŵƉůĞ ŵŽĚĠůŝƐĠ ƉĂƌ ƵŶĞ ĠƋƵĂƟ ŽŶ ĚĞ ůĂ ĨŽƌŵĞ Ă н ǆ с ď ŽƵ Ăǆ с ď ŽƵ Ăǆ н ď с Đ͘

33 34 35

dƌĂĚƵŝƌĞ ƵŶĞ ĞǆƉƌĞƐƐŝŽŶ ůŝƩ ĠƌĂůĞ ŽƵ ĞǆƉůŽŝƚĞƌ ƵŶ ƉƌŽŐƌĂŵŵĞ ĚĞ ĐĂůĐƵů͘ 181

ACTIVITÉS

Chapitre 9 Calcul littéral

Les solides 51

>ĞƐ Į ŐƵƌĞƐ ƉůĂŶĞƐ 59

dƌĂĐĞƌ ĚĞƐ Į ŐƵƌĞƐ ƐŝŵƉůĞƐ ĂǀĞĐ ĚĞƐ ŝŶƐƚƌƵŵĞŶƚƐ͘

Kĸ ĐŝĞů Dénombrer 1

ZĠƐŽƵĚƌĞ ĚĞƐ ƉƌŽďůğŵĞƐ ĚĞ ĚĠŶŽŵďƌĞŵĞŶƚ ĚĂŶƐ ĚĞƐ ĐŽŶƚĞǆƚĞƐ ŶƵŵĠƌŝƋƵĞƐ Ğƚ ŐĠŽŵĠƚƌŝƋƵĞƐ͘

^ƚƌƵĐƚƵƌĞƌ ůĞƐ ŶŽŵďƌĞƐ ŶĂƚƵƌĞůƐ ă ů͛ĂŝĚĞ ĚĞ ůĂ ƌĞůĂƟ ŽŶ ĚĞ ĚŝǀŝƐŝďŝůŝƚĠ 21

hƟ ůŝƐĞƌ ůĞƐ ĐĂƌĂĐƚğƌĞƐ ĚĞ ĚŝǀŝƐŝďŝůŝƚĠ ƉĂƌ Ϯ͕ ϱ͕ ϰ͕ ϴ͕ Ϯϱ͕ ϭϮϱ͕ ϯ Ğƚ ϵ͘

ī ĞĐƚƵĞƌ ĚĞƐ ŽƉĠƌĂƟ ŽŶƐ 29

ĂůĐƵůĞƌ ůĂ ƐŽŵŵĞ͕ ůĂ Ěŝī ĠƌĞŶĐĞ Ğƚ ůĞ ƉƌŽĚƵŝƚ ĚĞ ĚĞƵǆ ŶŽŵďƌĞƐ ĞŶƟ ĞƌƐ͘

ĂůĐƵůĞƌ ƵŶĞ ĞǆƉƌĞƐƐŝŽŶ ĐŽŵƉƌĞŶĂŶƚ ĂƵ ƉůƵƐ ƚƌŽŝƐ ŽƉĠƌĂƟ ŽŶƐ Ěŝī ĠƌĞŶƚĞƐ͘

ĐƌŝƌĞ ƵŶĞ ĞǆƉƌĞƐƐŝŽŶ ƋƵŝ ĐŽƌƌĞƐƉŽŶĚ ă ƵŶĞ ƐƵĐĐĞƐƐŝŽŶ ĚΖŽƉĠƌĂƟ ŽŶƐ͘

hƟ ůŝƐĞƌ ůĂ ĚŝƐƚƌŝďƵƟ ǀŝƚĠ ;ƐŝŵƉůĞͿ ĚĞ ůĂ ŵƵůƟ ƉůŝĐĂƟ ŽŶ ƉĂƌ ƌĂƉƉŽƌƚ ă ů͛ĂĚĚŝƟ ŽŶ Ğƚ ă ůĂ ƐŽƵƐƚƌĂĐƟ ŽŶ͘

Résoudre des problèmes et représenter des données 40

ZĠƐŽƵĚƌĞ ĚĞƐ ƉƌŽďůğŵĞƐ ĐŽŶĚƵŝƐĂŶƚ ă ƵŶĞ ĠƋƵĂƟ ŽŶ ĚƵ ƚǇƉĞ ǆ н Ă с ď ŽƵ Ă . ǆ с ď ŽƵ Ă . ǆ н ď с Đ͘

ī ĞĐƚƵĞƌ ĚĞƐ ŽƉĠƌĂƟ ŽŶƐ 41 42

ĐƌŝƌĞ ĚĞƐ ĞǆƉƌĞƐƐŝŽŶƐ ůŝƩ ĠƌĂůĞƐ ƉŽƵƌ ĞǆƉƌŝŵĞƌ ůĞ ƉĠƌŝŵğƚƌĞ͕ ů͛ĂŝƌĞ͕ ůĞ ǀŽůƵŵĞ͘͘͘ Ğƚ ƉŽƵƌ ŐĠŶĠƌĂůŝƐĞƌ ƵŶ ĐĂůĐƵů͘ ĂŶƐ ƵŶĞ ĨŽƌŵƵůĞ͕ ƌĞŵƉůĂĐĞƌ ĚĞƐ ǀĂƌŝĂďůĞƐ ƉĂƌ ĚĞƐ ŶŽŵďƌĞƐ ĚŽŶŶĠƐ ĂĮ Ŷ ĚĞ ĚĠƚĞƌŵŝŶĞƌ ůĂ ǀĂůĞƵƌ ĚĞ ů͛ŝŶĐŽŶŶƵĞ͘ ĐƌŝƌĞ ĚĞƐ ĞǆƉƌĞƐƐŝŽŶƐ ůŝƩ ĠƌĂůĞƐ ƉŽƵƌ ƚƌĂĚƵŝƌĞ ůĞƐ ĠŶŽŶĐĠƐ ĚĞƐ ƉƌŽƉƌŝĠƚĠƐ ĚĞƐ ŽƉĠƌĂƟ ŽŶƐ Ğƚ ƌĠĐŝƉƌŽƋƵĞŵĞŶƚ͘

dƌĂŶƐĨŽƌŵĞƌ ƵŶĞ ĞǆƉƌĞƐƐŝŽŶ ůŝƩ ĠƌĂůĞ ĞŶ ĂƉƉůŝƋƵĂŶƚ ůĞƐ ƉƌŽƉƌŝĠƚĠƐ ĚĞƐ ŽƉĠƌĂƟ ŽŶƐ͘

ZĠĚƵŝƌĞ ƵŶĞ ĞǆƉƌĞƐƐŝŽŶ ĞŶ ĂĚĚŝƟ ŽŶŶĂŶƚ ůĞƐ ƚĞƌŵĞƐ ƐĞŵďůĂďůĞƐ͘

hƟ ůŝƐĞƌ ůĂ ĚŝƐƚƌŝďƵƟ ǀŝƚĠ ƉŽƵƌ ƚƌĂŶƐĨŽƌŵĞƌ ƵŶ ƉƌŽĚƵŝƚ ĞŶ ƵŶĞ ƐŽŵŵĞ ŽƵ ƵŶĞ Ěŝī ĠƌĞŶĐĞ͘

hƟ ůŝƐĞƌ ůĂ ŵŝƐĞ ĞŶ ĠǀŝĚĞŶĐĞ ƉŽƵƌ ƚƌĂŶƐĨŽƌŵĞƌ ƵŶĞ ƐŽŵŵĞ ŽƵ ƵŶĞ Ěŝī ĠƌĞŶĐĞ ĞŶ ƵŶ ƉƌŽĚƵŝƚ͘ ĂůĐƵůĞƌ ůĂ ǀĂůĞƵƌ ŶƵŵĠƌŝƋƵĞ Ě͛ƵŶĞ ĞǆƉƌĞƐƐŝŽŶ ůŝƩ ĠƌĂůĞ ĞŶ ĚŽŶŶĂŶƚ ĂƵǆ ǀĂƌŝĂďůĞƐ ĚĞƐ ǀĂůĞƵƌƐ ĞŶƟ ğƌĞƐ͘

^ŽůŝĚĞƐ Ğƚ Į ŐƵƌĞƐ ƉůĂŶĞƐ 55

ĂůĐƵůĞƌ ů͛ĂŝƌĞ Ğƚ ůĞ ǀŽůƵŵĞ ĚƵ ĐƵďĞ͕ ĚƵ ƉĂƌĂůůĠůĠƉŝƉğĚĞ ƌĞĐƚĂŶŐůĞ͕ ĚƵ ƉƌŝƐŵĞ ĚƌŽŝƚ Ğƚ ĚƵ ĐǇůŝŶĚƌĞ͘

dƌĂĐĞƌ Ğƚ ƌĞƉƌŽĚƵŝƌĞ ůĞƐ ƚƌŝĂŶŐůĞƐ Ğƚ ůĞƐ ƋƵĂĚƌŝůĂƚğƌĞƐ ƉĂƌƟ ĐƵůŝĞƌƐ͘

ĂůĐƵůĞƌ ĚĞƐ ƉĠƌŝŵğƚƌĞƐ Ğƚ ĚĞƐ ĂŝƌĞƐ͘

182

ACTIVITÉS

Chapitre 9 Calcul littéral

ĐƚŝǀŝƚĠ ϭ ǆƉƌĞƐƐŝŽŶ ůŝƚƚĠƌĂůĞ Ğƚ ĐŽĚĂŐĞ 1 hŶ ŐƌŽƵƉĞ Ě͛ĠůğǀĞƐ ũŽƵĞ ă ƵŶ ũĞƵ ĚĞ ͨ ƋƵĞƐƚŝŽŶƐͬƌĠƉŽŶƐĞƐ ͩ ƐƵƌ ĚŝĨĨĠƌĞŶƚƐ ƚŚğŵĞƐ͘ ĐŚĂƋƵĞ ƚŚğŵĞ ĞƐƚ ĂƚƚƌŝďƵĠ ƵŶĞ ĐŽƵůĞƵƌ Ğƚ ƵŶ ũĞƚŽŶ ĚĞ ŐĂŝŶ ĚĞ ůĂ ŵġŵĞ ĐŽƵůĞƵƌ͘ 'ĠŽŐƌĂƉŚŝĞ ^ĐŝĞŶĐĞƐ DĂƚŚĠŵĂƚŝƋƵĞ ŝŶĠŵĂ DƵƐŝƋƵĞ ĂͿ sŽŝĐŝ ůĞ ƚĂƉŝƐ ĚĞ ŐĂŝŶƐ ĚĞ EŝĐŽůĂƐ ĞŶ ĨŝŶ ĚĞ ƉĂƌƚŝĞ͘ ;ϭͿ WŽƵƌ ĨĂĐŝůŝƚĞƌ ůĞ ĐĂůĐƵů ĚĞƐ ƉŽŝŶƚƐ͕ ĐŚŽŝƐŝƐ͕ ƉŽƵƌ ĐŚĂƋƵĞ ƌƵďƌŝƋƵĞ͕ ƵŶĞ ǀĂƌŝĂďůĞ ƌĞƉƌĠƐĞŶƚĠĞ ƉĂƌ ƵŶĞ ůĞƚƚƌĞ ŵŝŶƵƐĐƵůĞ͘ Rubrique

Musique

Géographie

^ĐŝĞŶĐĞƐ

Mathématique

ŝŶĠŵĂ

:ĞƚŽŶ sĂƌŝĂďůĞ ;ϮͿ ŽĚĞ ůĞ ƚĂƉŝƐ ĚĞ ŐĂŝŶƐ ĚĞ EŝĐŽůĂƐ ͗ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ;ϯͿ DŽĚŝĨŝĞ ĠǀĞŶƚƵĞůůĞŵĞŶƚ ůĞ ĐŽĚĂŐĞ ƋƵĞ ƚƵ ǀŝĞŶƐ Ě͛ĠĐƌŝƌĞ ĞŶ ƚĞŶĂŶƚ ĐŽŵƉƚĞ ĚƵ ĨĂŝƚ ƋƵĞ ůĞ ƐǇŵďŽůĞ ĚĞ ůĂ ŵƵůƚŝƉůŝĐĂƚŝŽŶ Ŷ͛ĞƐƚ ƉĂƐ ŽďůŝŐĂƚŽŝƌĞ ĞŶƚƌĞ ƵŶ ĨĂĐƚĞƵƌ ŶƵŵĠƌŝƋƵĞ Ğƚ ƵŶ ĨĂĐƚĞƵƌ ůŝƚƚĠƌĂů͘ Ğ ŵġŵĞ͕ ůĞ coefficient ͨ ϭ ͩ ŶĞ ƐĞ ŶŽƚĞ ŐĠŶĠƌĂůĞŵĞŶƚ ƉĂƐ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ďͿ ŽĚĞ ůĞ ƚĂƉŝƐ ĚĞ ĐŚĂĐƵŶ ĚĞƐ ĂƵƚƌĞƐ ũŽƵĞƵƌƐ͘ Léa

DĂŢůǇƐ

ŵĞů

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ĐͿ Ŷ ĚĠďƵƚ ĚĞ ƉĂƌƚŝĞ͕ ƵŶ ƚŝƌĂŐĞ ĂƵ ƐŽƌƚ ĂǀĂŝƚ ĂƚƚƌŝďƵĠ ƵŶ ŶŽŵďƌĞ ĚĞ ƉŽŝŶƚƐ ă ĐŚĂƋƵĞ ĐĂƚĠŐŽƌŝĞ ͗ ϰ ƉŽŝŶƚƐ ƉŽƵƌ ůĂ ƌƵďƌŝƋƵĞ ͨരŵƵƐŝƋƵĞര͕ͩ ϯ ƉŽƵƌ ͨരŐĠŽŐƌĂƉŚŝĞര͕ͩ Ϯ ƉŽƵƌ ͨരƐĐŝĞŶĐĞƐര͕ͩ ϱ ƉŽƵƌ ͨരŵĂƚŚĠŵĂƚŝƋƵĞരͩ Ğƚ ϭ ƉŽƵƌ ͨരĐŝŶĠŵĂരͩ͘ ŽŵƉůğƚĞ ůĞ ƚĂďůĞĂƵ ĂǀĞĐ ůĞƐ ǀĂƌŝĂďůĞƐ ĐŚŽŝƐŝĞƐ Ğƚ ůĞƐ ƉŽŝŶƚƐ ĂƚƚƌŝďƵĠƐ ă ĐŚĂĐƵŶĞ Ě͛ĞůůĞƐ͘ sĂƌŝĂďůĞ sĂůĞƵƌ ŽŵƉƚĂďŝůŝƐĞ ůĞƐ ŐĂŝŶƐ ĚĞ ĐŚĂĐƵŶ ĚĞƐ ũŽƵĞƵƌƐ͘ EŝĐŽůĂƐ ͗

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

>ĠĂ ͗

DĂŢůǇƐ ͗

ŵĞů ͗

183

ACTIVITÉS

Chapitre 9 Calcul littéral

Ŷ ĐŽƵƌƐ ĚĞ ƉĂƌƚŝĞ͕ DĂŢůǇƐ Ă ƚŝƌĠ ƵŶĞ ĐĂƌƚĞ ͨ ŽŶƵƐ ͩ ƋƵŝ ƉĞƌŵĞƚ ă Ŷ͛ŝŵƉŽƌƚĞ ƋƵĞů ũŽƵĞƵƌ ƋƵŝ Ă ĂƵ ŵŽŝŶƐ ƋƵĂƚƌĞ ũĞƚŽŶƐ ŝĚĞŶƚŝƋƵĞƐ Ě͛ĞŵƉŽĐŚĞƌ ϭϬ ƉŽŝŶƚƐ ƐƵƉƉůĠŵĞŶƚĂŝƌĞƐ͘ ŽĚĞ ůĞ ƚĂƉŝƐ ĚƵ ;ĚĞƐͿ ũŽƵĞƵƌ;ƐͿ ƋƵŝ ĞŶ ďĠŶĠĨŝĐŝĞ;ŶƚͿ Ğƚ ĂũƵƐƚĞ ƐŽŶ ;ůĞƵƌƐͿ ŐĂŝŶ;ƐͿ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

p.73 A

YƵŝ ĞƐƚ ůĞ ;ůĂͿ ŐĂŐŶĂŶƚ;ĞͿ ͍ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ĐƚŝǀŝƚĠ Ϯ ZĠĚƵĐƚŝŽŶ ĚĞ ƐŽŵŵĞƐ ĂůŐĠďƌŝƋƵĞƐ 1 ĐƌŝƐ ƵŶĞ ĞǆƉƌĞƐƐŝŽŶ ůŝƚƚĠƌĂůĞ ƌĠĚƵŝƚĞ ĚƵ ƉĠƌŝŵğƚƌĞ ĚĞƐ ĨŝŐƵƌĞƐ ĐŝͲĚĞƐƐŽƵƐ͘ ZĞĐƚĂŶŐůĞ

Carré ........

W с ........

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

WĂƌĂůůĠůŽŐƌĂŵŵĞ d

........

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

........

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

........

W с

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

........

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

dƌŝĂŶŐůĞ ŝƐŽĐğůĞ W с

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

W с

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

........

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

b ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

dƌŝĂŶŐůĞ ĠƋƵŝůĂƚĠƌĂů W с

........

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

dƌŝĂŶŐůĞ ƐĐĂůğŶĞ

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

WŽůǇŐŽŶĞ 2b ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

........

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

>ŽƐĂŶŐĞ W с

........

W с

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

........

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

W с

a a

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

b ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

WŽůǇŐŽŶĞƐ ƋƵĞůĐŽŶƋƵĞƐ

a ...................................

..................

2 b

a 2b a

..................

...................................

b W с

184

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

W с

p.73 B

ACTIVITÉS

Chapitre 9 Calcul littéral

2 >ĞƐ ĞǆƉƌĞƐƐŝŽŶƐ ůŝƚƚĠƌĂůĞƐ ĐŝͲĚĞƐƐŽƵƐ ĚĠƐŝŐŶĞŶƚ ůĞƐ ƉĠƌŝŵğƚƌĞƐ ĚĞƐ ĨŝŐƵƌĞƐ ĐŝƚĠĞƐ͘ Ŷ ƐĂĐŚĂŶƚ ƋƵĞ ĐŚĂƋƵĞ ƚĞƌŵĞ ƌĞƉƌĠƐĞŶƚĞ ůĂ ůŽŶŐƵĞƵƌ Ě͛ƵŶ ĐƀƚĠ͕ ƌĞůŝĞ ĐŚĂƋƵĞ ĨŝŐƵƌĞ ă ů͛ĞǆƉƌĞƐƐŝŽŶ ůŝƚƚĠƌĂůĞ ĚĞ ƐŽŶ ƉĠƌŝŵğƚƌĞ Ğƚ ƌĠĚƵŝƐͲůĂ͘ ZĞĐƚĂŶŐůĞ •

• ϯǆ н ϱ н ǆ н ϭ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

dƌŝĂŶŐůĞ ŝƐŽĐğůĞ •

• Ϯ н Ă н Ϯ н ď с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

YƵĂĚƌŝůĂƚğƌĞ ƋƵĞůĐŽŶƋƵĞ •

• ϰǆ н Ϯǆ н ϱǆ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

>ŽƐĂŶŐĞ •

• ϱĂ н ď н ϱĂ н ď с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

dƌĂƉğǌĞ ŝƐŽĐğůĞ •

• Ă н Ă н Ă н Ă с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

dƌŝĂŶŐůĞ ƐĐĂůğŶĞ •

• ϯď н ϴ н ϯď с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

3 ZĠĚƵŝƐ ůĞƐ ƐŽŵŵĞƐ ĐŝͲĚĞƐƐŽƵƐ͘ ϯĂ н ϱĂ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϯǆ ʹ ǆ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϳĂ ʹ ϱĂ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϮĂ н Ă н ϱĂ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Ϯď н ϯď с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Ă ʹ Ă с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϰď ʹ Ϯď с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϱď ʹ ď ʹ ď с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϲǆ н ǆ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Ϯǆ ʹ ǆ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϯĐ ʹ Đ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ǆ н ϱǆ ʹ Ϯǆ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϯĐ н Đ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Ă н ϱĂ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϰĚ ʹ ϯĚ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Đ н Đ ʹ Đ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

4 ZĠĚƵŝƐ ůĞƐ ƐŽŵŵĞƐ ĐŝͲĚĞƐƐŽƵƐ͘ WŽƵƌ ƚ͛ĂŝĚĞƌ͕ ƚƵ ƉĞƵǆ ƐŽƵůŝŐŶĞƌ ĐŚĂƋƵĞ ƐĠƌŝĞ ĚĞ ƚĞƌŵĞƐ ƐĞŵďůĂďůĞƐ ĚĞ ŵĂŶŝğƌĞƐ ĚŝĨĨĠƌĞŶƚĞƐ͘ Ϯǆ н Ă н ϯǆ н ϮĂ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϮĂ н ϰĂ н ϱď ʹ ϯď с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ď н ϯď н ϰĐ ʹ Đ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϱĂ ʹ ϯĂ н ď ʹ ϮĂ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϯĂ н Ϯď н Ă н ϱĂ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϳď н Ϯ н ď н ϭ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Ě н ϱǆ н ϯĚ ʹ Ϯǆ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϯǆ н ϭϮ ʹ ϱ ʹ Ϯǆ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϯĂ ʹ Ă н Ϯď ʹ Ă с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϱǆ н ϯ н ǆ ʹ ϯ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϱď н Ϯǆ ʹ ϯď ʹ Ϯď с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Ϯ н ϮĂ н Ϯ ʹ ϮĂ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

5 ZĠĚƵŝƐ͕ Ɛŝ ƉŽƐƐŝďůĞ͕ ůĞƐ ƐŽŵŵĞƐ ĐŝͲĚĞƐƐŽƵƐ͘ ^ŝ ĐĞ Ŷ͛ĞƐƚ ƉĂƐ ƉŽƐƐŝďůĞ͕ ƌĞĐŽƉŝĞ ů͛ĞǆƉƌĞƐƐŝŽŶ͘ Ă н ď н Đ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Ϯǆ н ϱǇ н Ϯ ʹ ϯǇ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϳĂ ʹ ϳǆ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Ϯǆ н ϴ н Ǉ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϳĂ ʹ ϲĂ ʹ ϳ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϰǆ н ď н ǆ н ϰǆ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Ϯǆ н Ǉ ʹ ϱ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϱ н ϮĂ ʹ ϭ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Ϯ н ϯĂ ʹ ϮĂ ʹ ϭ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϯĂ ʹ Ϯď н ϯĐ ʹ ϮĚ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

6 ŽŵƉůğƚĞ ůĞƐ ƐŽŵŵĞƐ ĂůŐĠďƌŝƋƵĞƐ ĐŝͲĚĞƐƐŽƵƐ͘ ϮĂ н ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ с ϱĂ

ϳǆ ʹ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ с ϯǆ

ϯĂ н ď н ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ н ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ с ϰĂ н ϯď

н ϱď с ϲď

ϱĂ ʹ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ с ϮĂ

Ϯǆ н ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ н ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ʹ ϱǇ с ϯǆ н ϮǇ

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ǆ н ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ с ϯǆ

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹ Ϯď с ϲď

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹ Ϯ н ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ н ϰĂ с ϳ н ϲĂ

ϯĐ н ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ с ϲĐ

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹ Đ с ϰĐ

ϱĐ н ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ н ϯĚ ʹ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ с ϳĐ н ϮĚ 185

ACTIVITÉS

Chapitre 9 Calcul littéral

7 ĂͿ ĂůĐƵůĞ ůĂ ǀĂůĞƵƌ ŶƵŵĠƌŝƋƵĞ ĚƵ ƉĠƌŝŵğƚƌĞ ĚƵ ĐƌŽƋƵŝƐ ĐŝͲĚĞƐƐŽƵƐ ƉŽƵƌ ůĞƐ ǀĂůĞƵƌƐ ĞŶƚŝğƌĞƐ ĚĞ Ă ĂůůĂŶƚ ĚĞ ϯ ă ϲ Đŵ͘ 11a

7a ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ďͿ ĂůĐƵůĞ ůĂ ǀĂůĞƵƌ ŶƵŵĠƌŝƋƵĞ ĚƵ ƉĠƌŝŵğƚƌĞ ĚĞ ůĂ ĨŝŐƵƌĞ ĐŝͲĚĞƐƐŽƵƐ Ɛŝ Ă с ϵ͕ ď с ϳ Ğƚ Đ с ϴ͘ 5a

2b ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

4c 3b

5a b

6c + 10 ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ĐƚŝǀŝƚĠ ϯ ZĠĚƵĐƚŝŽŶ ĚĞ ƉƌŽĚƵŝƚƐ ĂůŐĠďƌŝƋƵĞƐ 1 ĐƌŝƐ ƵŶĞ ĞǆƉƌĞƐƐŝŽŶ ůŝƚƚĠƌĂůĞ ƌĠĚƵŝƚĞ ĚĞ ů͛ĂŝƌĞ ĚĞƐ ƌĞĐƚĂŶŐůĞƐ ĐŝͲĚĞƐƐŽƵƐ͘ a

9 ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

a 3b

186

p.74

ACTIVITÉS

Chapitre 9 Calcul littéral

2 ZĠĚƵŝƐ ůĞƐ ƉƌŽĚƵŝƚƐ ĐŝͲĚĞƐƐŽƵƐ͘ a . ď с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϯď . ϮĂ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϮĂ . ϮĂ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

d . Đ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϮĂ . ϯĐ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϯď . Ϯď с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

a . ϮĂ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ď . ϭϬ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϱǆ . ϯǇ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϰǆ . ϯǆ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

a . Ϯ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

d . Ě с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Ϯǆ . ϯǆ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϰǆ . ǆ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

a . Ă с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

d . ϭ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϯĂ . ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ с ϲĂ

3 ŽŵƉůğƚĞ ůĞƐ ƉƌŽĚƵŝƚƐ ĐŝͲĚĞƐƐŽƵƐ͘ ϯĂ . ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ с ϲĂď

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

. ϱĚ с ϰϱĐĚ

ϯĂ . ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ с ϲĂϮ

ϯĂ . ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ с ϯĂď

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

. Ǉ с ǆǇ

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

. ϯď с ϭϮďϮ

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϰǆ . ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ с ϭϮǆǇ

Ϯď . ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ с ϭϬďĐ

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

. ϱĐ с ϱĐϮ

ϭϮǆ . ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ с ϯϲǆ

ϮĂ . ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ с ϮĂĚ

a . ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ с ϯĂϮ

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

. ϭϱĐ с ϭϱĐĚ

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

. ϱď с ϭϱď

. ϱǇ с ϮϱǇ

4 ĂůĐƵůĞ ůĂ ǀĂůĞƵƌ ŶƵŵĠƌŝƋƵĞ ĚĞ ů͛ĂŝƌĞ ƚŽƚĂůĞ ĚĞ ĐŚĂĐƵŶĞ ĚĞƐ ĨŝŐƵƌĞƐ ĐŝͲĚĞƐƐŽƵƐ Ɛŝ Ă с Ϭ͕ϳ Đŵ Ğƚ ď с Ϯ Đŵ͘ b 5a b b b a a 2b b a b b

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

a 4a

5a 2b

b 3a

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

187

ACTIVITÉS

Chapitre 9 Calcul littéral

ĐƚŝǀŝƚĠ ϰ Expressions littérales et nombres entiers 1 hŶ ĐĂƌƌĠ ĞƐƚ Ěŝƚ ͨ ŵĂŐŝƋƵĞ ͩ ƉŽƵƌ ů͛ĂĚĚŝƚŝŽŶ Ɛŝ ůĞƐ ƐŽŵŵĞƐ ĚĞƐ ŶŽŵďƌĞƐ ĚĞ ĐŚĂƋƵĞ ůŝŐŶĞ͕ ĚĞ ĐŚĂƋƵĞ ĐŽůŽŶŶĞ Ğƚ ĚĞ ĐŚĂƋƵĞ ĚŝĂŐŽŶĂůĞ ƐŽŶƚ ůĞƐ ŵġŵĞƐ͘ ĂͿ sĠƌŝĨŝĞ Ɛŝ ĐĞ ĐĂƌƌĠ ĞƐƚ ŵĂŐŝƋƵĞ ƉŽƵƌ ů͛ĂĚĚŝƚŝŽŶ͘ ʹϮĂ ʹ ϯ ʹϯĂ ʹ ϰ ϮĂ н ϭ

ϯĂ н Ϯ ʹĂ ʹ Ϯ ʹϱĂ ʹ ϲ

ʹϰĂ ʹ ϱ

ʹϭ

ďͿ ;ϭͿ ĨŝŶ ĚĞ ĐŽŵƉůĠƚĞƌ ůĞƐ ĂƵƚƌĞƐ ĐĂƌƌĠƐ ƉĂƌ ĚĞƐ ŶŽŵďƌĞƐ͕ ĐĂůĐƵůĞ ůĂ ǀĂůĞƵƌ ŶƵŵĠƌŝƋƵĞ ĚĞ ĐŚĂƋƵĞ ĞǆƉƌĞƐƐŝŽŶ Ɛŝ Ă с Ϯ Ğƚ Ɛŝ Ă с ʹϮ͘ Ă с Ϯ

Ă с ʹϮ

ʹϮĂ ʹ ϯ

ʹϯĂ ʹ ϰ ϮĂ н ϭ ϯĂ н Ϯ ʹĂ ʹ Ϯ ʹϱĂ ʹ ϲ ʹϰĂ ʹ ϱ ;ϮͿ ĠƚĞƌŵŝŶĞ ůĂ ƐŽŵŵĞ ͨ ŵĂŐŝƋƵĞ ͩ ŽďƚĞŶƵĞ ƉŽƵƌ ĐŚĂĐƵŶ ĚĞƐ ĐĂƌƌĠƐ Ɛŝ͙ Ă с Ϯ ͗

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Ă с ʹϮ ͗

p.75 D

188

ACTIVITÉS

Chapitre 9 Calcul littéral

2 ŽŵƉůğƚĞ ůĞƐ ƉǇƌĂŵŝĚĞƐ ƐĂĐŚĂŶƚ ƋƵĞ ĐŚĂƋƵĞ ďƌŝƋƵĞ ĞƐƚ ůĞ ƉƌŽĚƵŝƚ ĚĞƐ ďƌŝƋƵĞƐ ƐƵƌ ůĞƐƋƵĞůůĞƐ ĞůůĞ ƌĞƉŽƐĞ͘

ʹϭ

ʹĂ

ʹϮ

3 ĂͿ ZĠĚƵŝƐ ůĞƐ ƐŽŵŵĞƐ ƐƵŝǀĂŶƚĞƐ͘ ϳĂ ʹ ϱĂ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϮď н ϴď с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϯď н ϱ н ď ʹ ϳ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϯĂ ʹ ϳĂ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϯĂ н Ă с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϴ ʹ ϮĂ н ϱĂ ʹ ϭ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϰĂ ʹ ϱĂ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϮď ʹ ď с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹď н ϴ ʹ ϯď ʹ ϱ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ďͿ ZĠĚƵŝƐ͕ Ɛŝ ƉŽƐƐŝďůĞ͕ ůĞƐ ƐŽŵŵĞƐ ĐŝͲĚĞƐƐŽƵƐ͘ ^ŝ ĐĞ Ŷ͛ĞƐƚ ƉĂƐ ƉŽƐƐŝďůĞ͕ ƌĞĐŽƉŝĞ ů͛ĞǆƉƌĞƐƐŝŽŶ͘ ϯĂϮ н ϱĂϮ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϮĂϮ ʹ ϯĂϮ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹĂϮ ʹ ϯďϮ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϱĂϮ ʹ ϯĂϮ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϰď н ϯďϮ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϮĂϮ ʹ ϮĂϮ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

aϮ ʹ ϲĂϮ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϯĂ н ϱĂϮ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϮĂϮ ʹ ϮĂϮ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϯĂϮ ʹ ϱďϮ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹďϮ ʹ ϮďϮ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ď ʹ ϳďϮ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ĐͿ ƐƐŽĐŝĞ ĐŚĂƋƵĞ ĞǆƉƌĞƐƐŝŽŶ ă ƐĂ ĨŽƌŵĞ ƌĠĚƵŝƚĞ͘ ϮĂ ʹ Ϯ н ϯĂഩͻ

ͻഩʹĂ ʹ Ϯ

aϮ ʹ ϯĂ ʹ ϰ н Ă ʹ ϮĂϮഩͻ

ͻഩʹĂϮ ʹ ϰĂ ʹ ϰ

ϮĂ ʹ Ϯ ʹ ϯĂഩͻ

ͻഩĂ н Ϯ

aϮ ʹ ϯĂ ʹ ϰ ʹ Ă ʹ ϮĂϮഩͻ

ͻഩʹĂϮ ʹ ϮĂ ʹ ϰ

ϮĂ н Ϯ ʹ ϯĂഩͻ

ͻഩϮ ʹ Ă

ʹĂϮ ʹ ϯĂ ʹ ϰ н Ă н ϮĂϮഩͻ

ͻഩĂϮ н ϰĂ ʹ ϰ

ʹϮĂ н Ϯ н ϯĂഩͻ

ͻഩϱĂ ʹ Ϯ

ʹĂϮ н ϯĂ ʹ ϰ н Ă н ϮĂϮഩͻ

ͻഩʹϯĂϮ ʹ ϮĂ ʹ ϰ

ʹϮĂ ʹ Ϯ ʹ ϯĂഩͻ

ͻഩʹϱĂ ʹ Ϯ

ʹĂϮ ʹ ϯĂ ʹ ϰ н Ă ʹ ϮĂϮഩͻ

ͻഩĂϮ ʹ ϮĂ ʹ ϰ

ĚͿ ZĠĚƵŝƐ ůĞƐ ƉƌŽĚƵŝƚƐ ƐƵŝǀĂŶƚƐ͘ ʹϰĂ . Ϯď с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϮď . ϯď с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϰĂ . ;ʹϰĐͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

;ʹϮĂͿ . ;ʹϯďͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϰĐ . ;ʹϮĐͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϰĂ . Ă с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϮĂ . ;ʹϱďͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϯĂ . ď с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϮĂ . ;ʹďͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϯĂ . ϮĂ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Ϯď . ;ʹϰďͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϯ . ;ʹϮĐͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

4 ZĠĚƵŝƐ͕ Ɛŝ ƉŽƐƐŝďůĞ͕ ůĞƐ ĞǆƉƌĞƐƐŝŽŶƐ ĐŝͲĚĞƐƐŽƵƐ͘ ^ŝ ĐĞ Ŷ͛ĞƐƚ ƉĂƐ ƉŽƐƐŝďůĞ͕ ƌĞĐŽƉŝĞ ů͛ĞǆƉƌĞƐƐŝŽŶ͘ ϯĐ ʹ ϮĐ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϮĂ н ϱĂ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϮĂ ʹ ϯĂ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϱď н ϯď с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

a . ϰĂ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϮĂ . Ă с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϯĂ . Ϯď с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

a . ;ʹϯďͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϰĐ . ;ʹϮĐͿ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϱď . ϯĐ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ϱ ʹ ϮĂ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϰĐ ʹ ϮĐ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϯĂ н Ϯď с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

Ϯď . ϯĂ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘

ʹϯ . ;ʹϮĂ Ϳ с ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ 189

ACTIVITÉS

Chapitre 9 Calcul littéral

ĐƚŝǀŝƚĠ ϱ Priorités des opérations et calcul littéral 1 hŶĞ ĞŶƚƌĞƉƌŝƐĞ ĨĂďƌŝƋƵĞ ĚĞƐ ďŽŠƚĞƐ ĞŶ ĐĂƌƚŽŶ ĚĞ ĚŝĨĨĠƌĞŶƚƐ ĨŽƌŵĂƚƐ͘ WŽƵƌ ĐŚĂƋƵĞ ŵŽĚğůĞ͕ ŽŶ ƉĞƵƚ ĨĂŝƌĞ ǀĂƌŝĞƌ ůĞƐ ǀŽůƵŵĞƐ ĞŶ ĂƚƚƌŝďƵĂŶƚ ĚŝĨĨĠƌĞŶƚĞƐ ǀĂůĞƵƌƐ ĂƵǆ ĚŝŵĞŶƐŝŽŶƐ Ă Ğƚ ď͘ DŽĚğůĞ &

DŽĚğůĞ ,

DŽĚğůĞ <

DŽĚğůĞ W

DŽĚğůĞ Z

b a

2a 3a

2a b

ĂͿ ŽŵƉůğƚĞ ůĞ ƚĂďůĞĂƵ ĞŶ ƐƵŝǀĂŶƚ ůĞƐ ĠƚĂƉĞƐ ĐŝͲĚĞƐƐŽƵƐ͘ ;ϭͿ ǆƉƌŝŵĞ ůĞ ǀŽůƵŵĞ ĚĞ ĐŚĂƋƵĞ ďŽŠƚĞ ƉĂƌ ƵŶĞ ĞǆƉƌĞƐƐŝŽŶ ůŝƚƚĠƌĂůĞ ƌĠĚƵŝƚĞ͘ ;ϮͿ ^ŝ Ă с ϭϬ Đŵ Ğƚ ď с ϭϱ Đŵ͕ ĐĂůĐƵůĞ͕ ă ƉĂƌƚŝƌ ĚĞ ƐŽŶ ĞǆƉƌĞƐƐŝŽŶ ůŝƚƚĠƌĂůĞ ƌĠĚƵŝƚĞ͕ ůĞ ǀŽůƵŵĞ ĚĞ ĐŚĂƋƵĞ ďŽŠƚĞ͘ sĠƌŝĨŝĞ ĞŶƐƵŝƚĞ ƚĞƐ ƌĠƉŽŶƐĞƐ ĞŶ ĐĂůĐƵůĂŶƚ ůĞ ǀŽůƵŵĞ ĚĞ ĐŚĂƋƵĞ ďŽŠƚĞ ă ƉĂƌƚŝƌ ĚƵ ƉƌŽĚƵŝƚ ĚĞ ƐĞƐ ƚƌŽŝƐ ĚŝŵĞŶƐŝŽŶƐ͘

ǆƉƌĞƐƐŝŽŶ ůŝƚƚĠƌĂůĞ ƌĠĚƵŝƚĞ ĚƵ ǀŽůƵŵĞ

sĂůĞƵƌ ŶƵŵĠƌŝƋƵĞ ĚƵ ǀŽůƵŵĞ ;Đŵϯ)

sĠƌŝĨŝĐĂƚŝŽŶ

͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘ ͘