Multiplication and division math notebook

•

y

B ~

TOPH KAAC

1

. J

Ynpa>kHumeAHama mempagka "y.,a ce Da YMHO)l(aBaM H lleJlR "

e ogo6peHa om MUHucmepcmBomo Ha o6pa30BaHuemo, Haykama u

meXHoAoeuume c npomokoA N~ 6 om 02. 12. 1994 e.

Y"B

ce

aB YMHO)f(BBBM H aeJlR

Ha ........ ... ....... .... ........ .. ......... .

om ..... ...................... .. ..... kAac

Y4uAuLUe .............................. .

,

ttK 3..ulIliMllio IltlN

Da, maka e.

Ho a3 LUe 6u 3a6ega caMO go 2paguHama Ha 3aMbka.

A 6bmpe mpR66a ga npogbA>kume caMU. AHU, 6RPHO AU e, 4e HaO-AecHO LUe ce HaY4UM ga YMHo>ka6aMe U geAuM, ako omugeM 6 3aMbka Ha 36e3g06poe~a?

L

HRkbge, koO 3HaO kbge komeHua >ku8eJ\u g8e.

Ho CbC J\anu u onawku c6uJ\u ce 8egHb>k IoHawku.

6e3 o6a4e ga 6poumel Ka>keme kOJ\ko ca ywume?'

,

,

/ / JI " , ~/ I ~.~1~:- l tfJ___ W~J , : " rf::====j'{l I

I I

,

I \

-------足

2

=

4

72=

= VMHO)l(CHHC C 2

1

\

--

-\

\

\

-足

\

\

V揃"

0

At

I

\

I

\

I

.'

,I

I'

I

.足

--~~---

TOH40, npogbJ\>ku ga 3aka48aw no peg!

Ako npa8uJ\Ho 3a'ka4uM kbpnume u pewuM 3aga4ume, owe gHec we mpb2HeM kbM~_ '"'"~ 3aMbka.

= 2

1

I

I I

\

' \

3a ga BAe3eme B apaguHama Ha 3aMbka, Hanuweme kOAko 4epewku e UMaAO Ha Bceku kAOH omgfl~HO. Te ca 6UAU mOAkoBa, kOAkomo Ha kAOHa omMIBo U~~--......

•ge

e.

e Hagnuweme u ma6eA:k~~~~~~~~ Ha uBemfima. """A~~

Iku iawku. le! llume?

I

/1

I ~/ { ~

~ I

I

I I

\

I \

,

I

~

"

Vnpil}I(HeHHSI 3a YMHO)f(eHHe c

2

I

3a ga 6Ae3eme

6 3aMbka, 6ceku mpR66a

npa6uAHo ga u36epe 2 3HaMeHa.

BHuMa6aOme! To6a, koemo e

HanucaHO Ha 3HaMemo omAR60, ga

6bge pa6Ho Ha 4UCAomo 6bPXY

3HaMemo omgRcHo. CAeg kamo

npecMemHeme, ou6ememe

3HaMeHama no g600ku .

.QYMama nbTEKA UMa 0 epu4ku. BeRka epu4ka UMa 0 6yk6u.

KOAko ea 6yk6ume?

6pORm UM e HanueaH Ha eguH om kAlo406eme.

OmkpuOme 20.

.2 = 2 2.2 =4 3.2= 6 4 . 2= 8 5 . 2 = 10

6 . 2 = 12 7 . 2 = 14 8 . 2 = 16

9 . 2= 18 IIJ........

1

.2=

0.2=4 3.0= 6 4.2 = 8 .2= 6.0=

10

12

.2= 16 .0= 18 11---1----' •

VnpCl)KHCHMII 3a OTKpMoaHC Ha HCM38C(''TCH MHO)l(HTCA

0

=

2

3

= 9

7

3

= 2

4

3

=

6

3

YMHO)l(eHllle c

= 3

1

1

E,,,ame HaCaM, HO 2J\egaOme 4UCJ\ama, Kou om HanucaHume npou3足 6egeHus:l ca om ma6J\ullama 3a YMHo>keHue c 3? CaMo me3U cku ca go6pe 3ako6aHu, Cmbn6aOme 6bPXY

5 8

KOJ\ko nog Mocma?

I ' 13 1=

6mopa u I

KHwkkume Henpe6poeHu ca caMo nogpegeHu.

BMecmo mu ga au 6pouw, Mo>kew ga au YMHO>kUW.

.u06pe gowl\u 6 3aMbka Ha 4ucl\amal 3ag ma3U 6u61\uomeka UMa maOHa 6pama. Ho ms:l 1~___-w..41\~e ce om60pu, ako 6egHaa Hanuweme kOl\ko ca kHuaume Ha 6ceku """~IIIl::t,. pacpm.

rn

CbCTE3AHIf1E

C KOCTEHYPKIf1

Ha kOl\ko caHmu足

Mempa egHa om gpyaa

ca nbp6ama u 4em6bp足

mama kocmeHypka,

ako 3Haew, 4e 6CU4ku

me ce g6wkam Ha pa3足 CmOs:lHUe om no 3 CM.?

1 3 '1 . 13 1=

f

3anuwu kak60 e pa3CmOs:lHUemO Me>kgy kocmeHypkume: 6mopa u 4em6bpma nbP6a u 4em6bpma mpema u 4em6bpma

I 'I

1

1

1

1

1

1

B Hagnuca UMa 21

6ykBu, no 3 Ha Bceku kaMbk .

KOAko ca kaMbHume B Hagnuca?

1211

1

I : 13 = I .ll>kyg>kemo lUe u3Bagu om nell.\ma 14 xMI6a .

TpR6Ba ga au pa3geAu 3a 2 gHU no paBHo. KOAko xAR6a lUe cepBupa gHec?

3a mopmume UMa 18 4epewu.

C mRX ykpacu 2 mopmu kamo .ll>kyg>kemama ll.\e eAo>kam

au pa3geAuw no paBHo. nOAoBuHama ROua B 6aHuua足

ma , a oemaHaAume ll.\e eBa足 pRm. KOAko ROua ll.\e eBapRm?

I I I I I I

npeg g>kyg>kemo UMa 27 pe3eH4ema I\UMOH. nOMoaHU My ga au pa3g9J\U no paBHo 3a mpume Maeu .

ACI\CHHC C

2H3

I

no kOAko uBemR tUe noemaBu g>kyg>kemo BbB BeRka Ba3a, ako au pa3g9J\U no paBHo? - r - - ,. . - - ,. - - - ,. . . . - - , . . . - - - . ,

""--1

'pu geua HU am Ha aocmu.

NIX cma6aMe 15 gywu 3a 06Ag.

EgHO g>l<yg>l<e naAU mpu cBewu.

KOAko g>l<yg>l<ema ca 3anaAUAU cBewume B mpane3apuRma?

Wecm g>l<yg>l<ema we nogpe>l<gam Macume.

KOAko g>l<yg>l<ema we nogpegRm egHa Maca? Ha egHa om nokpuBkume e u36pogupaH omaoBopbm.

nOAOBuHama g>l<yg>l<ema ca c 4epBeHu wanku. KOAko ca CbC 3eAeHu?

I II I I I

, llBeg>l<yg>l<emawe m16 4UHUU B mpane3apuRma. no kOA­ ko mpR6Ba ga npeHece BCRko?

I I I I I I I ina U4e cAo>l<a m RQua B 6aHuua­ ~aAume U4e cBa­ Qua U4e cBapRm?

ll>l<yg>l<emama U meXHume aocmu we cegHam Ha 3 Macu no paBHo. no kOAko cmOAa mpR6Bam 3a BCRka Maca? Ha egHa om nokpuBkume e u36po­ gupaH omaoBopbm. Ha kOR?

~6bAkume ca

21 u g>l<yg>l<emo mpR6Ba ga au pa3geAu no paBHo B mpume cppykmuepu. no kOAko R6bAku we CAO>l<U BbB BCRka?

~

3BbH4emama no wan­ kume Ha g>l<yg>l<emama ca 3AamHU. cpe6bPHu u Om g>l<yg>l<emama CbC 3eAeHU­ 6POH30Bu no paBeH 6poo. me wanku nOAoBuHama ca C04U­ npe6poo 3BbH4emama.

Aa. KOAko om mRX uMam o4uAa? KOAko ca 3AamHl:.lme?

I I I I

I I

I I I I I I U4e nocmaBu Rka Ba3a, ako au

Aet\eHHe (2 H 3

I

I

I I I

I

I

Om g>l<yg>l<emama c OYU­ Aa nOAoBuHama ca kbCOaAegu , a gpyaume UMam gaAekoaAegcmBo. KOAko g>l<yg>l<ema uuam gaAekoaAegcmBo?

I I I I I I I I I I I I I

A3 nbk aomBA MHoao nO-AeCHo om g>kyg>kemama. O~ BCU4ko CJ\aaaM no 4 kUJ\oapaMa, HO Hukoaa He 3HaM kOJ\ko AgeHe l.l.\e ce nOJ\y4u. L-1 Bce He YJ\Y4BaM kOA meHg>kepa ga B3eMa. Ule MU nOMoaH9W J\U?

Ha 2 pa<j>ma

leA-e, AyK, 6ofi, 'lyWKU, opU3, Kapm(}g;u

=

2

Ako cna3Baw Aomo Ha 6poel.\a, Hanu ko nbmu l.l.\e IlOHegeAHuk ----足

=

3

IlOHeg8AHUk u

---足

n~g8AHUk,

=

1

=

2

8mopHUk

nOH8g8A 48m8~mbk,

= 4 0

A np83 npOA8mHam8 10 gHU?

B kUAepa Ha 6060 6culiku nakemu U mop6u ca no 4 kUAoapaMa. no kOAko kUAoapaMa om 6ceku npogykm UMa 6 kUAepa Ha 6060?

.-----.--....--r--"1.........---r--,.

6paWHO - 9 nakema Mopko6u - 5 mop6u s:l6bAku - 6 mop6u 3axap - 8 nakema

Peuenma N2 2 Kapmoffjll, fiofi It Opll3

I I I

Ha 2 pacpma 6 kUAepa Ha 6060 UMa 4 pega no 4 6ypkaHa c kOMnom.

KOAko ca kOMnomume?

~~I~I~I

~I~II~I~I~·

Ha gpyau 2 pacpma UMa 4 pega no 3 6ypkaHa c mYPwuR

KOAko ca 6ypkaHume c mYPwuR?

~II~I~~I~I I~I~I~I~I~I~I _ KOAko ca 6culikume 6ypkaHu 6 kUAepa Ha 6060?

I

I

,I

1

I

I

I

1

1

Ako cna36aw npa6u­ Aomo Ha 36e3go­ 6poeua, Hanuwu kOA­ ko nbmu !..Ue Rgew 6:

4 = 4 1 -----------+-+---t---+--+--+---4

nOHegeAHuk

2

noH6geAHuk u 6mopHuk

=

------------+-f---+---+-+--+-........-4

nOHegeAHuk, 6mopHuk u cpRga

-----------+-+---+---+--+--+---4

nOHegeAHuk , 6mopl-luk, cpRga u 4em6~mbk _ _ _ _ _ _ _ -t --t­ --t­ --t­ -+­ -+­ --4 nn~'.nA"'Huk, 6mopHuk, cpRga, em6~mbk ~e.!!!.bL _ _ _ _ -I --+­ --t­ --+ --+ --+­ --4 nOHegeAl-luk, 6mopHuk, cpRga, 4em6~mbk, nembk ~cb6oma _ _ -f----,-+--+--+--+~I__-l nn~'~(]A"'l-Iuk , 6mopHuk, cpRga, L4EIrllBl.pmbk ~mbk,~b6om~~eAR -t-+--+--+--+~I__-l A npu npOAeml-lama 6akaHuuR, kORmo e 10 gl-lu?

Vnpil)I(HeHHSl 3a YMHO)KeHHC C

4

3Be3g06poeUbm e kynuA 28 3aaagb4Hu oaAegaAa U au e pa3geAuA no paBHo Ha 4emupume ema~a Ha 3aMbka. no kOAko oaAegaAa UMa Ha Bceku ema~? BepHURm omaoBop e ckpum HRkbge. HaMepu ao . .

n

AHU MU 6ewe ka3aAa, 4e 6e3 ga 6POUM, Mo~eM ga .......'''路路emHeM kOAko cBe~u naARm g~yg~emama B 3aMbka BCRka Be4ep.

,

Ako npou3BegeHuemo Ha 5 U 4 HaMaAUme 2 nbmu, nOAY4eHomo YMHo~ume no 3 U npu6aBume 50, ~e nOAY4ume 6POR Ha cBe~ume B 3aMbka.

5

5

6

5

= = = = = =

3

5

= =

=

4

5 2

3

5

j

I

,

7 9 VMHO)l(eH ....e c

5

5

1 1 2

4

.

Ha ma3U kapma 36e3g06poe足 Ubm e Om6el\~3al\ 36e3gume, koumo e Ha61\loga6al\ npe3 Howma c mel\eckona cu.

3an04Hal\ ega au apynupa no 5, 3a ga au npecMemHe nO-I\eCHO. OnumaO u mu.

I I I I

geHuemo Ha 5 u 4 . nbmu, nOl\Y4eHomo 103 u npu6a6ume 50, Ie 6po~ Ha c6ewume

npo

=

5

2

=

1

0

3

=

1

5

5 =

2

0

5

.

I

onbAHU CHamume 4UCAa

1

5

5

=

6

5

-

7 5 9 VMHO)l(eHHe c 5

1足

=

3

=

4

0

=

4

5

36e3g06poeUbm He e cnal\ URI\8 HOW. Ho kOl\ko MUHymu e al\eg8l\ npe3 mel\eckona? ~34UCI\U no gHe6Huka My.

II IIIII

OuBemu c >kbAmo me3U 3Be3gu, Ha koumo UMa BepHU omaoBopu. n03Ha AU koe e moBa cb3Be3gue?

3Be3g06poeUbm epa3wucppoBaA cuaHaAU om kOCMoca U e Ha4epmaA no mAX me3U cpuaypku. Ho 3a egHa cuaHaAbm e 6UA HeAceH. nOMoaHU My ga omaamHe kak u3aAe>kga AuncBaLUama cpuaypka.

5.3-15

fr. t; .. . .,

")\,27

V

5.4-20

AS ¢ , .

V

A "'-------'

V >kumel\ume l-'136bH3eMHume ca om6eAA3al\U Ha 3eMAma c uuCPpu, koumo

2 7.3_ 1

¢

¢:

' * -¢2.3-8

3. ..

)KumeAume Ha gaAe4Hama nAaHema He npUI\U4am Ha 3eMHume. Te ca 03Ha4UI\U ce6e cu c uucppu, koumo ca npou3BegeHuA om ma6Auuama 3a YMHo>keHue c 5.

Ou6emu au.

OnumaO oU.\e npecMemHu. HaO· 4acmHO cbomBen HaO-MaAkama n. nogpegu au no ( om HaO-aOMIMc HaO-MaAkal

nAaHema I YacmHO

I

~

no I

Hen"1rH~~~: ~ =-~

__

IOnumep 150 : 5 = I --------t-Mapc 130 : 5 = I - - - - - - ---i-­ 3eMR__ I~~: ~ ~ ...j _ _ BeHepa 35: 5 =

Macau

ca npou36egeHuA om ma6Auuama 3a YMHo>keHue c 3. Kou ca me?

5.2-10

-¢'

'.3•••

KOAko. e uHmepecHol Mo>ke nbk, kamo nopacHa, ga cmaHa acmpoHoM!

~

BpeMe e ga cu npunoMHuM, 4e koaamo B egHa 3aga4a UMa ck06u, nbpBo ce u3BbpwBa geQcmBue­ mo B ck06ume. Ako HAMa ck06u, nbpBo ce

u36bpwBam geocmBuAma YMHo>keHue u geAeHue.

Vnpa)I(HeHHR 3a YMHO>KeHHe c '1, 3, 4, H 5

npaBUAHO AU nogp' npoBepu! Ako peWl >kbAmama AeHma LMe nAaHema B CAbH4eBa caMo nem. 3Haew AU

1. EgHa om nocokumf 3aAR3Ba CAbH~emo caMOAem 5. CBogbm ~ mo u 3Be3gume 6. n Ae"eHHe c 5

~Q

28

8

06SA cuaHaJ\U no m~x me3U HSAbm e 6UA maamHe kak laypka.

, MaHema He ca 03Ha"lUAU Ipou36egeHuR 損keHUe c 5.

OnumaO o~e ceaa. npecMemHu. HaO-MaAkomo 4acmHO cbomBemcmBa Ha HaO-MaAkama nAaHema. nogpegu au no aOAeMUHa om HaO-aOA~Mama go HaO-MaAkama.

n"aHema I 4acmHO

I

Nv no peg

Hen~H-l~~:~ =--1-足 IOnumeE...I.?~: ~ =-~

__

Map~ _I ~~: ~ ~~ _ _ 3eM~ _I~~: ~ =---1- _

Kamo u36bPWUW npeCMRmaHURma, ~e nOAY"lUW "IUCAO. To noka36a 3a kOAko Meceua 3eMRma ...B _e_H_ ep_a_...3_5_:_S_=....I._ _...... 06ukaAR OkOAO CAbHuemo.

)m6eAR3aAU u$pu, koumo ,6Auuama 3a

\f/

~?

- .0-足 / I "

npa6UAHO AU nogpegu nAaHemume no 20AeMUHa?

npo6epu! Ako peLUUUJ 6RPHO kpbcmocAo6uuama, 6

>kbAmama AeHma we nOAY4uLU UMemo Ha HaO-BOARMama 12 nAaHema 6 CAbH4e6ama cucmeMa. Ho 6 3aga4ama me ca

caMO nem. 3HaeLU AU kOAko ca Ha 6poO nAaHemume?

1. EgHa om nocokume Ha c6ema 2. nocokama, 6 kORmo

3aAR36a CAbHuemo 3. EgUH om ce30Hume 4. nUAom Ha

CaMOAem 5. C60gbm Hag Hac, Ha koOmo 6u>kgaMe CAbHue足

mo U36e3gume 6. nmuuama, CMRmaHa 3a uap Ha He6emo.

AeAeHllle c 5

1

3

14 5 6

6060 e nonpa6 kpaH06eme e 3a UMa npOU30e~Je"lu

I

M'bHU"4kume 4»eu om 3aM'bka c'b6upam 6uI\ku u au npeHacRm 8 mop6u"4ku no B apaMa.

I

KOAko 6UAku ca cb6pMU mpume cpeu 06LUO?

KOAko ap 6UAku LUe cb6epe egHa cpe~ 6 9 mop6u4ku?

CAeg kamo u3cywam 6uAkume, cpeume au HacunBam BaOAeMU kHU>kHU nAuko6e U maka au cbxpaH~Bam npe3 3UMama, Bceku nAuk cb6upa 7 mop6u4ku, KOAko apaMa cb6upa 1 nAuk? nonbAHU nponycHamume 4UCAa

1

6

2

6 4

6

5

= = = = :;::

~

= =

8 9

6

VMHO)l(CtUtc

= c6

, \

1

2

1

8

3

0 1 cyweHume

3 4 4

6

2

8

Cl>eume npoga6am

6uAku.

EgUH apaM cmpy6a 6

cmomuHku, Ako 3a

cympewHuR "480 cu

kynuw 4 apaMa, kOAko

~e mu cmpy6a moO?

I I I I I I I

Vnpa>KHCHMC la YMHO)l(C I

- -- - -- = = =C-=::"II'I

6060 e nonpaB~A BogonpoBoga 3a q>oHmaHa. Ho e 3a6paBuA koO om kpaHoBeme e 3a Heao. nogcka>ku My. ToO e 3a mpb6ume, BbPXY koumo UMa npou3BegeHuR caMo c 4UCAomo 6.

I

~aCAm

6

mop6u~ku

I I I I

I I I I

9MU kHU>kHU

l1J\uko6e

I I I I

HRk oO >K uBee B kYAama Ha aaMbka. LUe HaY4Uw koo e moO, ako npaBuAHo pewuw aaga4ume. nOAY4eHomo 4UCAO we mu noka>Ke kOR no peg 6ykBa om a36ykama ga Hanuwew.

0 7+60:6=0 0 54:6=0 0 48: (30: 5) = ,0 0 9+48:6=0 0 18:6-2= 0 0 ,_-u 36 : 6 + 5=0 0

I

42:6+9=0

I'

TOH40 Mo>ke ga ce ka4u go kYAama, caMo ako npa6uAHo pewu aaga4ume.

Lr1Ha4e cmbnaAama we ce cpymAm.

I I

opaH>k

. 36 : 4=

54: 6

=

AUAa6 .9: 3 =

,

.24 : 6 =

6 :6 =

1路 1 1=1 ,I

12: 6 = . ACt\C HIitC C 6

,.1 1=1 I

I+1 I 1= I

1 <l>eume ca nOpb4aAU Ha l\uAu

~----, 2 ga ouBemu gbaama. Ho ~---"""1 3 nbpBo

- -足 --I ------I

__----J

ga mpR6Ba 4 npecMemHe u3pa3ume. ~ nOMoaHu Q. Hanuwu cpell-'Y 7 BCRka UUQ>pa cbomBemHuR uBRm. A nOCAe au ouBemu.

44epBeHo

9

...

6 5

10 Mo>ke ga CS I go kYAama, ) ako npaBUAHo U 3aga4um e. ~e cmbnaAama :e cpymAm.

I I

opaH>k 36 : 4=

I

AUAaB 9 :3 =

I

3SASH 15 : 3=

I

cB. CUH 28 : 4=

I

___- - - , nOM08HU Ha g>kyg>kemama ga npscMemHam ueHume.

::=:::==:::::

A a3 mpR6Ba ga cspBupaM 2 cynu no 5 AsBa, 3 RcmUR no 4 AsBa, 3 4aR no 6 AsBa U 1 cAagoAsg om 9 AsBa.

\ \.\ \=\ \

\ \.\ \=\ \ \

\ \+\ \ \= I I I Vnp(\)I(HeHIltSi 3a YMHO)l(eHllte lit AeAeHllte c

L-I..1.-1. .L.+I .:.....1.I--L-~1+.. .1-\--L-...I_+.1-.1...L-I-~--,

2, 3, 4, 5,

lit

6

6060 3an04HaA ga cnecmRBa napu B 2 kacu4ku. nycHaA BbB BCRka no 7 AeBa. KO Ako AeBa UMa B gBeme kacu4ku?

KoO AU cmou 3ag 6060?

CbeguHu nocAegoBameAHO 3anUCaHUme 4UCAa U U,(e pa36epew. BCRko cAegBaU,(o 4UCAO e CbC 7 noBe4e om npeguwHomo.

49.

56. Q

V1MaA B g>ko6oBeme cu OLUe 28 AB. Cb6paA Bcu4kume napu B egHa kacu4ka. KOAko AeBa ca cmaHaAu?

+~

nonbAHU Hamume 4UCAa

1

7

2

7

3 7

6

7 7

8

7

= = =

G;>

.7 peCMemHU 3pa3ume U oapagu caMO me3U 4UCAa BbPXY 3HaMemo, Koumo ca paBHu Ha omaoBopume.

,.

2

1

3+3.4=

:;

2

8

9-4.2=

= = = =

3

5

=

6

VMHO)l(eHMe ChC 7

4

9

2.6+4= 2.7+3.7足 4.7+5.7足

3

.ll>kyg>kemama ~ MeAHuu.ama n aoguHu. lile Hi kOAko om omaol

3a BCRka peg apu>kam 14 <l>eu <l>eu ce apwkam kowep?

6.7+7.7足 AeAeHMe (bC 7

r---------~------~~----------~~~~~~~~.

ToBa e B~mbPHama MeJ\HU14a Ha aaMbka. npeCMemHU UomkpuO koe om kpuJ\ama mp~66a ga ce nonpa6u. 0146emu eo.

G BCU4kume cu napu 6060 kynuJ\ "-_~ 7 6a<t>J\u . KOJ\ko cmpy6a egHa

6a<t>J\a?

-28

.7 npeCMemHU aume U oepagu MO meau YUcJ\a pxy aHaMemO, mo ca pa6HU Ha maoBopume.

.4

n>kyg>kemama ca nocmpouJ\u MeJ\HU14ama npegu MHoao aoguHu. W.e HaY4uw npegu kOJ\ko om oma060pa Ha 6~PHO peweHama aagaya.

21 : 7 14

+

9 . 7

+ +

23 6

=7 +

=3 +

23

=

31

6 = 18

21 : 7 = 35 : 7 = 5

+

63 : 7 = 63

+

9 = 72

B apaguHama aag MeJ\HU14ama ca kowepume Ha nyeJ\ume. Te ca 06wo 49 U ca 6 7 pegu14u. no kOJ\ko kowepa UMa 6b6 6c~ka pegu14a?

I I I I I I I

足

2=

. 4足 7

足 足

7. 7

..-

3.7 5

49 : 7

3a 6c~ka pegU14a ce apu>kam 14 <t>eu. KOJ\ko <t>eu ce apu>kam 3a eguH kowep?

I I I ACAeHHe CbC

7

CaMO egHa Bpama e omk'''04eHa. ToBa e Bpamama, Ha kORmo BCU4ku 3aga4u ca peweHu BRpHO. Ako R omkpURm, AUAU, T0H40 U Becko we Moaam ga BAR3am B apaguHama c kowepume. A mu we R om6eAe>kuw AU? Oapagu apewHume omaoBopu.

9.6==54 36: 4 == 9 9.3== 18 3.5==25 nog4epmaO apeWHume omao6opl

60 60 ce e U3xumpUA. 3an04 HaA e ga konae mYHeA nog cmeHama.

TpR6Ba ga u3konae 06wo 12 Mempa nog 3eMRma. 3a eguH geH u3konaBaA 3 Mempa. npecMemHu kOAk o gHU mpR6Ba ga pa60mu 5060?

VnpCl)I(HCHHSI 3a YMHO>KCHHC H AeAcHHc C

2, 3, 4, 5, 6 H

7

2

8

=

1 Ii

6

8

=

6

3

8

=

5

8

=

2 I 4

8

8

=

7

6

8

=

4

4

8

=

3

9

8

=

7

2

8

=

1

VMHO>KeHHe C 8

I

mkJ\104eHa. To6a e 3CU4ku 3aga4u ca kpURm, AUJ\u, TOH40 IR3am 6 apaguHama R om6eJ\e>kuw J\U? !o6opu.

'>---.1.

nog4epmaa apeWHume omao6opu

3Haew J\U, 4e koaamo n4eJ\ama "emu 6 kpba, mR cbo6U4a6a, 4e Hekmapbm e 6J\U30. A koaamo onuc6a oCMopka,

36e3go6poeUbm e omxJ\ynuJ\ egUH kowep.

KOR om kUJ\uOkume ce pa3J\u4a6a om OCmaHaAUme? Ou6emu R.

2 '

8

=

1

2

6

8

=

6

4

3

8

=

2

4

5

,8

=

4

0

8

8

=

7

2

6

8

=

4

8

4

8

=

3

2

9

8

=

7

2

Ho

2

8

=

1

6

11 101

,

06ukHo6eHo om eguH kowep ce nOJ\y4a6am 121 . 181=

UMa

I I I kUJ\oapaMa Meg. U pekopgHu

go6u6u

路lsl= I I I kUJ\oapaMa Meg.

om

~

..

BHUMal11 noaAegHu gBe CBuBaw m03U n noka3Ba koe 4UC Baw no 9, kamo ~ HagRcHo. OmaoBo npbcmume omARB noka3Bam gece"l gRCHO, noka3Ba CBumuRm He ce 6

T03U, koOmo e HapucyBaH B M03aOkama, U4e mu omkpue MaaURma Ha 4UCAomo 9. Ho mpR6Ba ga BHuMaBaw npu ou,BemRBaHemo.

TaM, kbgemo 4UCAomo ce geAu Ha 8, ou,Bemu CbC cBemAo CUHbO. A kbgemo He ce geAu Ha 8, ou,Beniu c kacpRBo.

Kou npou3BegeHufi ca BepHu?

9

9

=

9

1

4

9

=

3

6

2

9

1

9

7

9

= =

6 3

3

9

=

2

7

8

9

7

2

2

9

1

8

15

9

= = =

4

0

9

9

=

8 1

VMHU)I(CHMe c 9

BHUMameAHO

n02AegHu gBeme MU Pbu,e.

CBuBaw m03U npbCm, koOmo

noka3Ba koe 4UCAO w.e YMHo>ka足

Baw no 9, kamo 6pouw omMIBo

HagRcHo. Om20Bopbm e npeg me6.

npbcmume omARBo Ha C2bHamUR

noka3Bam gecemuu,ume, a om足

gRCHO, noka3Bam eguHuu,ume.

CBumuRm npbcm.__.-li~::::'" He ce 6pou.

Om20Bopu AU Ha Bbnpoca kOAko ca nAaHemume' B CAbH4e6ama cucmeMa? Ako He cu 3HaeA, ce2a 3anOMHU . Te ca 9.

onumaM!

[3U, HapucyBaH lwe mu omkpue UCAomo 9. Ho uMaBaw npu BaHemo.

:I\omo ce geAu Ha 8, CUHbO. A kbgemo oL\Beniu c ka蔵RBo. 1\0

Kou npou36egeHuR ca 6epHu?

=

9

1

9

3

6

2

9

7

9

3

9

8

9

= 1 9 = 6 3 = 2 7 = 7 2

2

9

5

9

= =

9

9

9

9

4

VMHO)l(CHHC C9

1

8

4

0

= 8

1

Ako pewuw' npaBuAHO 3aga4ama, w.e omkpuew Ha kOAko 20gUHU e Becko.

5.9-4.9= npecMemHu kOAko cmbnaAa u3ka4Ba npu3pakbm, k02amo ce npu6upa B cBoRma kYAa.

3.9+8.9 足

6060 e BMI3bA B Aa60pamopuRma Ha 3Be3g06poeua, 3a ga cu Hagye 6aAoHa. Ako HanucaHume BbPXY kOA6ume 4UCAa ce geMlm Ha 9, 6MoHbm My we nOAemu. Ho ako UMa apewka, we u36yxHe. CnpaBUA AU ce e 6060?

~~

Oapagu BepHUR omaoBop.

BepHU AU CG paBeHcmBam.

30 - 3 = 3 .

70 - 7 = 7 .

4.9=40-足 50 - 41 = 1 .

36-4=4.

63-7=7.

8 .9=9.8 3.8=6.4

. ~~

AB Aa60pamopURma oe14a, 3a ga CU Hagye HanucaHume BbPXY :Aa ce geARm Ha 9, ~e nOAemu. Ho ako ~ a, U4e u36yxHe. pe e 6060?

CAeg onuma c 6aAOHa 6060 e pewuA ga nOAemu c XBbp4uA a. Ho XBbp4uAama lUe U3AemRm, aka omaoBopume BbPXY rTmX ca BepHu.

~ยงJ

omaoBop.

BepHU AU ca paBeHcmBama?

30 - 3 = 3 . 9 70 - 7 = 7 . 9 4.9=40-4 50 - 41 = 1 . 9 36 - 4 = 4 . 8 63-7 = 7.8 8.9=9.8 3.8=6.4

~~ Vnpil)KHeHHSl 3a YMHO)l(eHHe H AeAeHHe c

8

H

9

.

<beume ca OpaaHU3UpaAU AOmapU R. Bceku 6uAem ne4eAU m03U npegMem, BbPXY koOmo e HanUCaH omaOBOpbm Ha 3aga4ama.

npu3pakbm e 3aMbkauce 3aga4ama, U4e U4e ce cb6ygu

5 . 10 - 2 . 10

9

6

1

0

5

1

0

8

1

0

3

1

0

1

1

0

= = 7 = 8 = 3 = 1

5

1

0

2

1

4

=

npegu ga 3acnu, ' , Ha 3aMbka.

0 0 0

=

5

0

0

=

1

0

1

0

=

4

0

HMC

c 10

Hanuwu koO kakBo cne4eAU I\UAU ' Becko-------------­ TOH40­ - - - - - - - ­ - - - - ­

--- - --- -- - -- ­

6060 - 5060 - - - ­ - - - ­ - - - ­ - - -

ToO mu npUnOMH~ UMa cb6upaHe, U geAeHue U HRMa cl geOcmBuRma YMHC ck06u, nbpBo ce ck06ume.

Aei\eHHe c 10

Ako YUCAama BbPXY kaMbHume ca yaCmHU om ma6Auuama 3a geAeHue c 10, nupaMugama HRMa ga ce cpymu . .llo6pe AU au e u36pal\ TOHYo?

~~ Oapagu BepHuR omaoBop.

npu3pakbm e YMopeH om mOAkoBa WYM B 3aMbka U ce npu6upa ga cnu . Ako pewuw BRPHO 3agayama, we pa36epew cAeg kOAko aoguHu w e ce cb6ygu nak.

5 . 10 - 2 . 10

=

npegu ga 3acnu , moO 06ukaAR BcuYku cmau Ha 3aMbka. npecMemHu kOAko ca cmaume.

(12 - 7) . 10 (ak60 cnSYSI\U

=

ToO mu npunoMHR, ye koaamo B egHa 3agaya UMa cb6upaHe , u3Ba>k g aHe, YMHo>keHue u gel\eHus u HRMa cko6u , nbpBo ce u3BbpwBam geOcmBuRma YMHo>keHue u geAeHue. Ako UMa cko6u , nbpBo ce u3Bbpw Ba geOcmBuemo B cko6ume.

W:: " Pewu 3aga4ume

5

1

1

1

= =

9

1

=

6

1

5

1

= =

5

TpA66a ga 3anOMHAI ToBa e MHoao Ba>kHO! Koaamo eguHuRm om MHo>kumei\ume e 0, mo u npou3BegeHuemo e O. 5.0=0.5=0 C 4UCAomo 0 He MoJke ga ce geAul 5 : 0 e HeBb3Mo>kHo geOcmBue.

@

7.2 + 3

7.(2+~

VMHO)KeHHe H AeAeHHC C

1

H

0

9

0

8

0

6

0

3

0

4

0

= = = = =

0 0 0

9:3-1=

6+6.0=

0 4

(6 + S) . ( Vnp(\)I(HeHHII 3a

I

Pewu 3aga4ume

5

1

=

1

1

=

9

1

=

6

1

5

1

= =

5

Sue o6ukOAuxme

Ako HRMa cko6u, nbP80 geAuM U YMHo)\(a8aMe, a nOCAe u38a)\(gaMe U cb6upaMe.

(HO! Koaamo 1eAume e 0, mo lemo e O. 5=0 ke g8 ce geAu!

IMO)\(HO

Je.

7.2+ 3 = 7 . (2 + 3) 9

0

=

0

,8 ,6

0

=

0

0

=

0

3

0 =

0

4

0

=

4

9 :3 -1

8.4+5.6=

-

35:5+2=

足

6 + 6.0= (6 + 6) . 0 = Vnpa)I(HeHHSl 3a pewaBaHe Ha 3aAa~H CbC CKo6H

= 70 : 10 = 7: 0 =

• 1.3=3 2.3=6 '3.3=9 4.3=12 5.3=15 6.3 = 18 7.3=21 8.3=24 9.3=27 10.3 =30 1.6=6

2.6 = 12 3.6=1 8

4.6=24 5.6=30 .6 .6=36

7.6=42 8.6=48 9.6=54 10.6=60

1.7=7 2.7=14 3.7=21 4.7=28 5.7=35 6.7=42 7.7 = 49 8.7=56 9.7=63 10.7=70

1.4=4 .2.4=8 3.4=12 4.4=16 5.4=20 6.4=24 7.4=28 8.4=32 9 .4=36 10 .4 =40

1.5=5 2.5=10 3.5=15 4 .5=20 5.5=25 6.5=30 7.5=35 8.5=40 9.5=45 10.5=50

1.10=10 2.10=20 3.10=30 4.10=40 5.10=50 6.10=60 7.10=70 8.10=80 9.10=90 0.10=1

t=---­ Ynpa>kHUmel\Hama mempagka no MarneMamuka 3a Bm09u kl\ac "Y&.fA CE fJ.A YMHO>KA BA M '" AEI\A" e He06xOguMO u nOllc33HO nOMaZal\O

38 Y<iumel\ume, Y'IeHUUUme u pogurnel\ume, koumo g06pe nOOHaBam

u npegnollumam cepuAma om ynpa)!(Humel\Hu mempagku

Ha Vl K "3AamHOmO name"

nognoMaeaHO om cBourne BpbCmHuuu om cmpaHuuume Ha mempagkama,

gememo C I\ekoma OCMUCI\R u ycBoABa geucmBuRma

YMHo>keHue U gel\eHUe, koumo ocBeH naMem u3uckBam u kOM6uHamuBHocm.

C me3U cBou npUAmel\U Bawemo geme w.e npoHukHe B 3aMbka Ha 'iUCl\8ma

om 1 go 100, kamo ce cnpaBR C Pa3I\UllHU aaeagku no nbmR Clj

T£: u B CAeyBaw.urne kl\ac06e LL(e 6bgam 3oogHo C Heeo B ~I\OCmHama cePUR

om Y'ie6HU MamepUal\u. koumo ca 06Bbp3aHu B eguHHa

npoBepeHa npakmukama Memoguka.

a

,

I

OT CepIUITa Yge6HH nOMaraJ1a Ha 11 K "3J1aTHOTO naTe"

Ta3H ":, Ja oeq(lma

6

rO~HHa

me HaMepHTe:

llPERYf.{HJlHmHA B'b3PACT u fl'hPBH KJIAC :

"A3 me 6'b.na n'bpBoKRacHHK"-l, "A3 lUI; 6 'b,lla flbpBoKRacHHK"-2,

"A3 '-leTa H CMRTaM", "Il'bpso 6yr(f~ap'te"

3a Y'Ienuqume 8 ll'hPBH KJlAC: "Y'fa ce )la llHwa"-l, "Y'-Ia ce tla lIHilla" -~, "Y'Ia ce .na nHwa"-3,

"PO.at:H Kpaii 3a ITbpBH KRac" - Yll pail<HI1Tt:J1HH TeCTO Be,

"Y'fa ce .lI.a CMJlTaM t.

3a y'leHUqume

3M

BTOPH KJlAC:

"Y'fa ce .lI.a YMHox<aaaM H .lI.eRJI",

npO.ll.eH Kpaii 3a STOPH KRach - ynpa)KHI1TeRHH TeCTOBe ,

"Y'ta ce .aa KOM6HHHpaM" - 3aHlfMa1eRHa TeTpaJJ;Ka

no MaleMaTHKa II TPY.lI. H TBop'teCTBO

I

Co¢w. 199-1

IO( "3.llJ1tJNlHlU1lWJ1W", 0 Muw.:a

~ CIUIa Cmelfiw'oo -

,,"C),IlKU,

e

K4.JOJlIlOiJ4 - UllmlJp. '" CmDJUI

H_

_ dJltnOp.

rfLW:I<U 3.JCll7UIIlIl - ClO....·emJUJ KDIUjI!JuptJl " DglOp....U!IUU

ISBN 954-431-082-7