Let's Do Mathematics 5 – Worktext A by Regal_Education

n at

Wo ork ktex t e xt

ffor o r lle e arners a r n e r s 10 - 11 year yea r s o l d

Re ga le du ca tio n

This book or parts thereof may not be reproduced in any form, stored in any retrieval ieval system, or transmitted in any form by any means – electronic, mechanical, photocopy, recording, cording, g, or otherwise otherwis – without prior written permission of the copyright owner. First edition 2021 This edition is published by Regal Education Inc. ISBN 978-1-953591-10-4

Regal Education Inc. 10 Pienza, Irvine, CA 92606, United States www.regaleducation.org

Let’s Do Mathematics

Re ga le du ca tio n

Let’s Do Mathematics is a series covering levels K-6 and is fully aligned to o the United States Common Core State Standards (USCCSS). Each level consists of two books boo (Book A and Book B) and combines textbook-style presentation of concepts oncepts pts as well as workbook practice.

Central to the USCCSS is the promotion of problem-solving skills ls and reasoning. Let’s Do Mathematics achieves this by teaching and presenting ng g concepts through throu a problem-solving based pedagogy and using the concrete-pictorial-abstract pictorial-abstract torial-abstract ((CPA) approach. Learners acquire knowledge and understanding a ng off concepts through thr th guided progression beginning with concrete examples and experiences which then w flow into pictorial representations and finally mastery at the and symbolic level. e abstract an a This approach ensures that learners develop a fundamental understanding of concepts damental ental understa underst rather than answering questions by learned procedures edures es and algorithms. algorit

Key features of the series include:

Anchor Task

Angles of Triangles h r Task hor Anchor

Open-ended activities serve as the starting point for understanding new vities concepts. Learners engage in activities e and discussions to form concrete experiences before the conceptt is formalized.

$5.25 per pack

$1.45 each

$0.75 each

Let’s Learn n

Concepts are presented sented in a clear and a colorful manner.. Worked rked problems problem provide learners step-by-step ers with ith guided step-by ste progression through Series gh examples. Ser mascots provide rovide de guidance through throug throu helpful comments observations omments ments and observa when new concepts oncepts are introduced. intro

Operations on Decima ls

Anchor Task

Multiplyi l ing

Let’s Learn

by 1-digit Nu

mbers

Step 3

A superma rket is sellin g pistachio will 3 kg of nuts for $21.3 pistachio nuts 0 per cost?

Multiply the

kilogram. How much We need to multiply 21.3 by 3 to find help find the out. Let’s use answer. a place value chart to Tens Ones Tenths . Each row rrepresents the . cost oof 1 kg of pista chio . nuts.

tens.

2 1 . 3

Tens

Find 77.4 x

6 using the

od.

Multiply the 2

tenths.

1 . 3

Tens

Tenths

4 using the

6 . 18 3

Step 2

Multiply the

ones.

2 1 . 3

Tens

Ones

3 . 9

6.83 x 4 = 27.32

3x1=3

Tenths

7 27 . 4

4 . 4

77.4 x 6 = 464.4

Find 6.83 x

Ones

. 9

. 4

3 x 0.3 = 0.9

$63.90.

7 27 . 4

$21.30

Tenths

column meth

7 27 . 4

21.3 x 3 = 63.9 So, 3 kg of pistachio nuts costs

Step 1

Ones

3 6 3 . 9

6 4 6 4 . 4

column meth

od.

6 . 18 3

. 3 2

6 . 18 3

4 2 7 . 3 2

We can use rounding and estimation to check our answers.

iii

Let’s Practice

Fill in the blanks.

Let’s Practice

(a)

Ones

Tens

dr Hundreds

Ten Thousands Thousands

Hundred Thousands

Millions

Fill in the blanks.

(a)

Learners demonstrate their understanding of concepts through a range of exercises and problems to be completed in a classroom environment. Questions provide a varying degree of guidance and scaffolding as learners progress to mastery of the concepts.

556,795

536,795

516,795

576,795

100,000 more

100,000 less

ds place

Look at the ten thousan

(b) Millions

n Ten Thousands sands Thousa

Tens

eds Hundreds

Ones

ed uc ati on

Hundred Thousands

The ten thousands digit The numbers increase

in each step.

increases by

(b)

2,824,575

1,574,575

The numbers increase

(c)

the pattern is The next number in

324,575

less 1 125,000

in each step.

more 125,000 m

ns Millions

4,074,575

Ten Thousands Thousands

eds Hundreds

Ones

Tens

1,500,000 more 1,500,00

00,000 less 1,500,000

in each step.

(d)

The next number in

Hundred Thousands

Millions

Ten Thousands Thousands

Hundredss

Ones

Tens

the pattern is

10,000 more

less 10,000 le

At Home

Classify each triangle .

Classify each triangle e.. Choose one cl classification per triangle. (b)

(a)

At Home

(a)

Right-angled

Scalene

Isoscele sceless

(b)

Right-angled Rig

Further practice designed to be completed without the guidance of a teacher. Exercises and problems in this section follow on from those completed under Let’s Practice.

(c)

Scalene Sca

(d)

Isosceles Isosce

(c)

Right-angled

Scalene

Isosceles

(e)

(f)

(d)

Right-angled d

Scalene

Isoscele sceless

Hands On

ps of 4-5. in your it number Work in grou mill n. w write a 7-dig n and 6 millio llion As a group, een 5 millio th that is betw notebook

t square. on the start forward the your counter . and move dice y Roll the dice Ro hown on your spaces show number of ber plete the num p must com oup grou the in fo ard. 4. Everyone order to move forw pattern in ber till o nal num the origi with 4 to steps 3 5. Repeat the finish. you reach

Learners are encouraged to ‘learn by doing’ through the use of group activities and the use of mathematical manipulatives.

ter Place a coun

Solve It!

(a) OPQR is a parallelo gram. SP is a straight line. Find OPQ O

Solve It!

118º

S Q

(b) MNOP is a trapezo id. NP is a straight line. Find t.

Re g

Activities that require learners earners ers to apply logical reasoning problem-solving. Problems ng and nd problem-solvin problem-s hich do o not have a rou are often posed which routine strategy rners are encouraged encourag enc for solving them. Learners to think creatively and apply problem-solving y a range of probl p heuristics.

Consolidated solidated practice where whe learners demonstrate on a emonstrate their understanding under u range ange of concepts taught taug within a unit.

N 38º

47º

(c)

GHIJ is a parallelogram. HJ is a straight line. Find G

56º H

m J

44º

120

pairs to plot the points 2. Use the ordered p

Looking Back 1. The line plot shows the distances the school fun run.

Looking Back

students in Grade 5 ran during the

Fun Run Distances

on the coordinate grid.

(a) A (1, 2)

(b) F (4, 4)

(c)

J (3, 7)

(d) W (3, 2)

(e) C (9, 9)

(f)

H (9, 6)

(g) E (4, 8)

(h) R (8, 4)

(i)

O (6, 5)

10 9

3 4

1 4

1 2

3 4

1 4

Miles

(a) How many students ran 2 miles? than (b) How many students ran further (c)

6 1

What is the combined distance ran by 1 mile of less?

1 miles? 2

the students who ran 4 3 mi

ran by (d) What is the combined distance or further?

3 the students who ran 1 4 miles

2 1 0

239 238

20º

Contents 2 4 15 26 30 42 55

Re ga le du ca tio n 1

Whole Numbers Numbers Beyond 1,000,000 Place Value Powers of 10 and Exponents Comparing and Ordering Numbers rs Number Patterns Rounding and Estimation

2 Operations on Whole Numberss n Addition and Subtraction Multiplying by 10s, 100ss and 1,000s Multiplying by 1 and 2-digit digit Numbers Numb nd 1,000s Dividing by 10s, 100ss and digit Numb Dividing by 1 and 2-digit Numbers tions ns Order of Operations Word Problems m

66 6666 75 89 101 111 120 128

3 Fractions Adding Fractions ctions acting ing Fracti Fractions Subtracting tiplying ying Fractions Frac Fraction Multiplying actions ons and Div Di Fractions Division Word rd Problems

146 148 168 180 197 208

4 Decimals ecima Hundredths and Thousandths Tenths, Hu Com Compar Comparing and Ordering Decimals und Rounding and Estimation 6

224 224 242 256 v

Whole Numbers

Anchor Task

al ed uc ati o Diameter of Planets

Planet Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune

Diameter (km) 4,879

12,104

12,742 6,779

139,820 116,460 50,724 24 49,244 44

Numbers Beyond 1,000,000

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Let’s Learn

Use place value disks to show numbers up to 1 million. 1

10 ones

1 ten

100

10 tens

100

1 hundred

100

100 0

1,000

100

100 10

100 00 0

1 thousand

10 hundreds reds

1,000

1,000 00 0

1,000 000

1,000 1,00

10,000

1,000

1,000 00 0

1,000 ,0 0

1,000 0

11,000

10 thousands

1 ten thousand

10,000 0,00 00 10,000 10,00 00 10,00 10,000 10 00 10,000 10,000

100,000

10,000 0 00 10,000 10 10,00 00 10 10,000 10,000 10,000

10 0 ten te thousands

1 hundred thousand

100,000 100,000 100,000 100,000 100,000

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1,000,000 000 0

100,000 100,000 100,000 100,000 100,000

10 hundred thousands

1 million

One million is a one followed by 6 zeros.

Find the number represented in the place ce value ue chart. (a)

Ten Thousands

Thousands

Hundreds

Tens ns

Ones

sand, d, five hundred hun hundr forty. We say: Thirty thousand, We write: 30,540.

(b)

Hundred Thousands

Ten Thousands

Thousands housa

Hundreds

Tens

Ones

y: Five hundre hundred fo We say: Five forty thousand, nine hundred one. We write: 540,901. 540,901.

(c)

Hundred Thousands

Te Ten Thousands Thou

Thousands

Hundreds

Tens

Ones

a ay: We say: Three hundred fifty-one thousand, four hundred four. We write: 351,404.

(d)

Hundred Thousands

Ten Thousands

Thousands

Hundreds

Tens

Ones

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Millions

We say: Three million, sixty thousand, forty-five. ve. e. We write: 3,060,045.

(e)

Millions

Hundred Thousands

Ten Thousands

Thousands

Hundreds dre

Tens T

Ones

We say: Five million, five thousand, hundred eighty-nine. usand, four h hund We write: 5,005,489.

(f)

Millions

Hundred Thousands

Ten Thousands nds

Thousands Thousand

Hundreds

Tens

Ones

We say: Six million, fifty-four thousand, eight hundred. n, nine hundred h We write: 6,954,800. 4,800.

(g)

Millions

Hundred Thousands

Ten Thousands

Thousands

Hundreds

Tens

Ones

We Nine million, eight hundred thousand, six hundred fifty. e say: s We write: 9,800,650. 9 9,8

Count on in hundreds. (a)

+100

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+100 23,098

(b)

23,198

23,298

+100

158,987

+100

23,398

00 +100

+100

159,087

159,187

23,498 3,498

159,287 87

159,387 159,3

Count on in thousands. (a)

+1,000

14,890

(b)

15,890

16,890 890

1,000 00 +1,000

+1,000

166,213

000 +1,000

+1,000

167,213

+ +1,000

17,890 17

+1,0 +1,000

168,213 168,21

18,890

+1,000

169,213

170,213

Count on in ten thousands. housands. ands. (a)

+10,000 000

46,986 6

(b)

56,986

+10,00 +10,000

587,563 58

+10 +10,00 +10,000

66,986

+10,000

597,563

+10,000

76,986

+10,000

607,563

+10,000

86,986

+10,000

617,563

627,563

Count on in hundred thousands. (a)

+100,000

Re ga le du ca tio n

+100,000 87,620

(b)

187,620

+100,000

785,562

287,620

+100,000

885,562

387,620

+100,000

985,562

487,620 87,620

100,000 +100,000

1,085,562 562

1,185,562 1,185

Count on in millions. (a)

0,000 +1,0 +1 0 +1,000,000 +1,000,000 +1,000,000 +1,000,000

1,564,236

(b)

5,564,236

6,264,123

7,264,123 7,264,12

8,264,123

9,264,123

1,000,022

2,000,022

3,000,022

4,000,022

+1,000,000 +1,000,000 +1,000,000 +1,000,000 0,000 +1,00 +1,0

2,425,352

4,564,236 4,56

000 +1,000,000 +1,000,0 +1,000,000 +1,000,000 +1,000,000

(d)

3,564,236 4,236

00,000 00 +1,000, +1,000,000 +1,000,000 +1,000,000 +1,000,000

5,264,123

(c)

2,564,236

3,425,352 3

4,425,352

5,425,352

6,425,352

Let’s Practice Write as numerals and words.

Re ga le du ca tio n

(a)

(b)

Hundred Thousands

Ten Thousands

Thousands

Hundreds

Tens

Ones

Hundred Thousands

Ten Thousands

Thousands

Hundreds dreds

Tens Te

Ones

Millions

Hundred Thousands ousands

Ten Thousands Thou

Thousands

Hundreds

Tens

(c)

Ones

Write the numbers.

Re ga le du ca tio n

(a) One hundred thousand, fifty-six.

(b) Four hundred sixty thousand, eight hundred fifty-four. y-four. ur.

(c)

Nine million, four thousand, eighty-one.

(d) Five million, seven hundred eighty thousand, usand, two h hundred twelve.

(e) Two million, seventy thousand, d, nine e hundred thirty-five.

(f)

Eight million, six hundred ed forty-five orty-five thousand, tho th eight hundred eleven.

Write in words.

(a) 1,758,284

(b) 4,576,264 576,264 64

(c)

9,649,538 9,649,538 ,649,53

Count on in 1,000s.

5,856,

Re ga le du ca tio n

(a)

(b)

254,

(c)

87,934,

(d)

563,573,

Count on in 10,000s.

(a)

98,546,

(b)

89,354,

(c)

8,345,

(d)

265,925,

Count on in 100,000s.

(a)

530,

(b)

640,240,

(c)

64,012,

(d)

1,542,155 55 5,

Count on n in 1,000,000s. ,000,000s.

(a)

1,754,899 ,754,899 4,8 ,

(b)

5,983,085 983,085,

(c)

879,690,

(d)

3,958 3,958,684 ,

Hands On

Re g

tio n

Form pairs of students. Each pair receives a dice and a place value chart. Roll the dice ice 7 times to form a 7-digit number. Write the number in the place lace e value chart. Your teacher will say a count on number. Take turns ns counting ounting on from your number.

Millions Mil

Hundred Hu Thousands Thousa

Ten Thousands

Thousands

Hundreds

Tens

Ones

Match.

seven hundred ninety thousand, thirty eight

230,400 2

two hundred thirty thousand, four hundred ndred

8,444,080

eight million, four hundred forty-four ty-four thousand, th eighty

650,366

Re g

le du ca tio n

At Home

nine million, on, two hundred thousand, six hundred two

790,038

six hundred fifty thousand, three hundred sixty-six

9,200,602

Write as numerals and words. Hundred Thousands

Ten Thousands

Thousands

Hundreds

Tens

Oness

Millions

Hundred Thousands

Ten Thousands

Thousands ds

Hundreds ndreds

Tens

Re ga le du ca tio n

(a)

(b)

Count on in 10,000s.

(a)

98,546,

(b)

89,354 4,

Count on in 100,000s. 100,000 00,000s. s.

(a)

54,570 70,

(b)

2,316,546 316,546,

C Count ount nt on in 1,000,000s. 1,000

(a)

2 24,641 ,

(b)

4,234,231, 4, 4,234

Ones

Place Value

Re ga le du ca tio n

Let’s Learn

Find the value of each digit in the numbers shown. (a)

Millions

Hundred Thousands

Ten Thousands

Thousands

Hundreds

Tens

Ones

The digit in the millions place is 3. It represents presents ents 3,000,000. 3,000,0 The digit in the hundred thousands place is 1. It represents 100,000. repre rep The digit in the ten thousands place 20,000. ce is 2. It represents represe The digit in the thousands place is 4.. It represents represe represent 4,000. The digit in the hundreds place e is 6. It represents represen 600. The digit in the tens place is 8. It represents 8 80. The digit in the ones place is 7. Itt represents represen represent 7. 3,000,000 + 100,000 + 20,000 000 + 4,000 + 600 + 80 + 7 = 3,124,687

The number c be found by adding can the place values of each digit!

Re ga le du ca tio n

(b)

HTh TTh

The digit in the millions place is 4. Itt represents 4,000,000. resents 4,0 The digit in the hundred thousands 600,000. nds place is 6. IIt represents r The digit in the ten thousands place is 3. It represents 30,000. repr rep The digit in the thousands place 1,000. ace is 1. It represents repres The digit in the hundreds place is 2. It represents 200. repr repre The digit in the tens place represents 50. e is 5. It represen represe The digit in the ones place 1. ace is 1. It represents repres repre

4,000,000 + 600,000 00 + 30,000 000 + 1,000 1,0 + 200 + 50 + 1 = 4,631,251

What is the value of the digit in the millions place?

Let's find the value of each digit in the number. 5

1 0 0 0 0 0

Re ga le du ca tio n

(a)

2 0

4 0 0

6 0 0 0

9 0 0 0 0

The value of the digit 5 is 500,000. The value of the digit 2 is 20,000. The value of the digit 4 is 4,000. The value of the digit 6 is 600. The value of the digit 9 is 90. The value of the digit 1 is 1. 500,000 + 20,000 + 4,000 + 600 + 90 + 1 = 524,691 524,69 524,

(b)

2 3 0 6 0 0 4 0 0 0 1 0 0 0 0

9 0 0 0 0 0

0 0 0 0 0 0 0

The value of the digit 1 is 1,000,0 1,000,000. 1,0 The value 400,000. e of the he digit 4 is 400 The value 60,000. ue off the digit 6 is 60 The value alue off the digit 3 is 3,000. The value ue of the digit 2 is 200. The he value lue of the digit 9 is 90. The value v lue of the digit dig 0 is 0. 1,000,000 + 400,000 400,0 + 60,000 + 3,000 + 200 + 90 = 1,463,290 40

(c)

Re ga le du ca tio n

4 1 0 2 0 0 8 0 0 0 7 0 0 0 0 6 0 0 0 0 0

3 0 0 0 0 0 0

The value of the digit 6 is 6,000,000. The value of the digit 7 is 700,000. The value of the digit 8 is 80,000. The value of the digit 2 is 2,000. The value of the digit 1 is 100. The value of the digit 4 is 40. The value of the digit 3 is 3. 6,000,000 + 700,000 + 80,000 + 2,000 + 100 + 4 40 + 3 = 6,782,143

(d)

1 0

4 0 0

9 0 0 0

2 6 0 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0

The value of the 8,000,000. he digit 8 is 8,00 The value 100,000. e off the digit 1 is 100 The value alue off the digit 4 is 40,000. 4 The value e of the digit 9 is 9,000. The e value lue of the digit 7 is 700. The he value lue of the digit 6 is 60. The value value of the th digit di 2 is 2. 100,000 + 40,000 + 9,000 + 700 + 60 + 2 = 8,149,762 8,000,000 + 100,0

Let’s Practice Write the numbers shown in the place value abacus.

Re ga le du ca tio n

(a)

(b)

HTh TTh

(c)

HTh HT h TTh T h TT

Th h

HTh TTh

(d)

HTh TTh

(e)

(f)

HTh HTh TT T TTh h

Th T

Write the number in its expanded form.

Re ga le du ca tio n

(a) 546,540

(b) 5,265,640

(c)

4,729,572

(d) 1,730,275

(e) 6,289,365

Write the value alue of the digit. digit

(a)

(b)

(c)

(d)

Write the value of each digit. Then add the values. 4

Re ga le du ca tio n

(a)

(b)

Solve It!

Re ga le du ca tio n

Halle is helping her father paint the house. She accidentally spills pills some ome paint onto the brochure containing the price for her new house. use. The real r estate agent leaves some clues to help Halle and her father er find nd the price pric of the house. Use the clues to help them find the house price! e!

• The price has 7 digits. ts. • The price is greater and less than 3 million. ter than 2 million m • The price iss an even number. numb num • The sum of the e digits in the t hundreds, tens and ones place is 8. • The digit place is 5 . git in the ten g en thousands thou • No digit 4. gitt is equal eq equ to 4 • All digitss are less than 8 and no 2 digits are the same. t

House price e$

At Home Match the numbers in two ways.

Re ga le du ca tio n

five hundred d sixty-three xty-three thousand, eight ht hundred fifty-nine e

563,859

3,000,000 000,000 000 + 700,000 700,0 + 40,000 + 8,000 00 + 100 + 60 6 +7

five hundred hundre sixty-nine thousand, thousand one hundred ninety-four ninety-f

3,748,167

5,178,193 93 3

5,000,000 + 100,000 + 70,000 5 5,0 + 8,000 + 100 + 90 + 3

three million, seven hundred forty-eight thousand, one hundred sixty-seven five million, one hundred seventy-eight thousand, one hundred ninety-three

569,194

500,000 + 60,000 + 3,000 + 800 + 50 + 9

500,000 + 60,000 + 9,000 + 100 + 90 + 4

Write the numbers shown in the place value abacus. (b) b)

(a)

HTh TTh

HTh HT h TT TTh Th

Th Th

Re ga le du ca t

Write the numbers represented by the e place ace value disks. dis (a)

100

100,000 100,000 10,000 10,00 10,000 00 1,000 0

100

100,000

10,000 ,00 00 10,00 10 00 1,00 10,000 1,000 1,0

100

100,000

10,00 00 00 10,000

1,000

100

100,000

10,000 ,00 00 00

1,000

100

1,000,000 00 0

1100,000 00,00 00 0 1,000 0

1,000 1,0

1,000,000 00,000 0

1100,000 00,00 00 0 1,000 0

100

11,000,000 ,000,0 ,00 00 0

1100,000 00,00 00,00 00 0 0 1,00 1,000

11,000,000 ,000,0 00 00 0

1,000,000

100,000 100,000 10,000 10,000 ,00 00 1,000 000 0

1,000,000

1,000 1,00

(b)

100

1100,000 00,00 00 0 1,000

100

1,000

100

Write the value of each digit. Then add the values. 5

Re ga le du ca tio n

(a)

Add the place values.

(a) 40,000 + 2,000 0 + 200 + 50 =

(b) 100,000 + 60,000 0,000 0 + 1,000 1,00 1,0 + 7 = (c)

400,000 0 + 50,000 0,000 + 300 + 60 6 +1=

(d) 500,000 000 + 80,000 + 3,000 3,00 3 =

(e) 3,000,000 000,000 000 + 20,000 20,00 + 800 + 4 = (f)

400,000 0,000 + 70,000 + 400 + 30 + 2 =

(g) 7,000,000 + 600 600,000 + 10,000 + 8,000 + 800 + 20 + 2 =

(h) ( 4,000,000 + 500,000 + 40,000 + 7,000 + 500 + 60 + 6 = 4,000,0

Powers of 10 and Exponents

Re ga le du ca tio n

Let’s Learn

We can show repeated addition using multiplication. 10 + 10 + 10 + 10 = 40 4 x 10 = 40

Similarly, we can show repeated multiplication with exponents. Halle uses place value disks to show repeated multiplication tion of 10.

x 10

1 x 10 = 10

x 10

100

x 10

1,000

10 x 10 x 10 = 1,0 1,000

1,000 x 10

10,000 ,00 0 00

10 x 10 0 x 10 1 x 10 = 10,000 00

10 x 10 0 = 100

exponent.

10 x 10 x 10 0 x 10 = 104 = 10,000 base

The number that is repeatedly multiplied. e base is the nu numbe The exponent how many times the base is multiplied. ponent tells te h We write: rite: 104 We say: the fourth power of 10

What pattern can you see?

Let's look at the powers of 10 to 1,000,000. 100 = 1

Re ga le du ca tio n

1 1 x 10

101 = 10

1 x 10 x 10

102 = 100

1 x 10 x 10 x 10

103 = 1,000

1 x 10 x 10 x 10 x 10

104 = 10,000

1 x 10 x 10 x 10 x 10 x 10

105 = 100,000

1 x 10 x 10 x 10 x 10 x 10 x 10

106 = 1,000,000

Dominic read in his space book that the distance from Earth to the moon iss about 4 x 105 km. Write the distance as a whole number. 105 = 100,000

4 x 105 = 4 x 100,000 = 400,000

ar to the he moon is about 400,000 km. So, the distance from Earth Blue whales can reach each h a mass of 150,000 kg. Find the mass as a whole whol number multiplied plied by a power powe of 10. 1 150,000 = 15 5 x 10,000 ,0 = 15 x 104

So, blue ue whales can reach reac a mass of 15 x 104 kg.

Let’s Practice Write in exponent form in numbers and in words.

Re ga le du ca tio n

(a) 10 x 10 x 10

Exponent form:

Word form:

(b) 10 x 10

Exponent form:

(c)

Word form:

10 x 10 x 10 x 10

Exponent form:

Word form: m:

(d) 10 x 10 x 10 x 10 x 10 x 10 Exponent form:

Write the number.

(a) 101 =

(b) 102 =

105 =

(d) ( 104 =

(c)

(e) 103 =

(f)

(g) 100 =

(h) 107 =

106 =

Write the number. mber

(a) 2 x 102 = (c)

Word ord form: o

15 x 103 =

(b) 3 x 101 =

(d) 25 x 103 =

(e) e) 9 x 105 =

(f)

3 x 106 =

(g) ( 99 x 102 =

(h) 10 x 104 =

At Home

Re ga le du ca tio n

Match the numbers in two ways.

102

1,000 000

10 x 10 x 10 1

104

10,000 10

1 x 10

100

103

10 x 10 x 10 x 10

10 x 10

Comparing and Ordering Numbers ers

Re ga le du ca tio n

Let’s Learn

(a) Compare 1,422,645 and 1,432,523. Which number is greater? Millions

Hundred Thousands

Ten Thousands

Thousands

Hundreds

Tens Te

Ones

First, compare the values in the millions ons place. ace. The values v in the millions place are the same. Compare the values ues in the next ne place – hundred thousands. The values in the hundred ndred ed thousands thousan place are also the same. Compare the values in the he ten thousands thousan thousand place. 3 ten thousands is greater than 2 ten thousands. nds. So, 1,432,523 is greater than han 1,422,645. 422,645.

(b) Compare the numberss 3,619,381 619,381 and 3,619,728. Millions

Hundred Thousands

Ten Thous Thousands

Thousands

Hundreds

Tens

Ones

The values alues in n the million millions, hundred thousands, ten thousands and thousands usands nds are the same. sam Compare the values in the hundreds place. 3 hundreds than 7 hundreds. undreds eds is smaller th 3,619,381 3,619,728 3,619 9,381 < 3,6 3,619,72

3,619,728 > 3,619,381

Compare the numbers in the place value chart. Order the numbers from the greatest to the smallest. Millions

Hundred Thousands

Ten Thousands

Thousands

Hundreds

Tens

Ones O

Re ga le du ca tio n

(c)

ns place. ace. First, compare the values in the millions llions plac 540,571 does not have any digits in the millions place. So, it is the bers both ha smallest number. The remaining numbers have 5 millions. Compare the values in the hundred dred thousands place. The remaining numbers both have 3 hundred Compare the values in the d thousands. Co ten thousands. 3 ten thousands than 1 ten thousand. nds is greater th So, it is the greatest number. er. 5,334,627 greatest

5,315,763 5,315,

540,571

smallest

Always start by comparing the digits in the highest place value.

(d) Compare the numbers using a bar model.

Re ga le du ca tio n

What number is 500,000 greater than 367,194?

367,194

500,000 500

0 0 0 0 0

4 is 500,000 gre 867,194 greater than 367,194.

What number is 0 less tha 1,000,000 than 85? 5,234,285?

5,234,285

1,000,000

0 0 0 0 0 0

4,234,285 is 1,000,000 less than 5,234,285.

Let’s Practice Write the number represented by the base ten disks. Check the smaller number.

Re ga le du ca tio n

(a)

100,000 100,000 100,000 1,000

1,000

100

1,000,000 1,000,000 ,000 00 ,000,0 0

10,000 00 00 1,000 1,000

100,000 100,00 00 0 10 110,000

1,000 1,000

1,000 10

100 0

(b)

1,000,000 1,000,000 1,000,000 11,000,000 ,000,000 0

1,000,000 1,000,000 1,000,000 100,000 11,000,000 ,000,000 0

100,000 100,000 100,000 00 00 0 1100,000 00,00 00 0

100,000 100,000 100,000 100,000

100,000 10,000 10,00 10,000 10,000 10 00 00 0

10,000 10,000 10,000 10,000

1,000

1,000 000 0

1,000 1,000

1,0 1,000

1,000

100

100 100

10 0

110

Write the numbers in the place value chart and compare.

Re ga le du ca tio n

(a) Compare 275,195 and 2,275,195. Millions

Hundred Ten Thousands Thousands Thousands

Hundreds

Tens ens

Ones On

Hundreds

Tens

Ones

(b) Compare 5,395,295 and 5,395,205. 95,205. Millions

Hundred Ten Thousands Thousa Thousands Thousands ds

Use the e symbols mb >, >, < and a = to fill in the blanks.

(a) 376,296 6,296

496,285 496

(b) 274,294

3,658,496

(d) 4,295,275

3,496,251

(f)

5,933,275

4,583,840

(h) 3,593,183

4,393,285

653,450 53,450

((e) 8,385,295 8,385,29

(g) 9,758,291 9

4,834,029

3,958,382

3,195,304

Check the smaller number. (a)

485,295

(b)

1,383,294

449,294

(c)

1,589,302

1,594,391 4,391 391

(d)

4,294,024

4,194,284 ,194,284 4,284

(e)

3,833,203

5,374,294 374,29

(f)

4,352,205

5,194,394 5,194, 5,194

Re ga le du ca tio n

275,194

Fill in the blanks.

(a)

145,600

100,000

is 10 100,000 more than 145,600. 100,00

(b)

1,520,080

200,000

is 200,000 less than 1,520,080. 35

(c)

500,000

Re ga le du ca tio n

2,222,500

is 500,000 more than 2,222,500. 500. 00.

6,720,500

(d)

4,000,00 4,000,000

is 4,000,000 000 0 less than 6,720,500. 6, 6

Check the greatest number, mber, er, cross tth the smallest number.

(a)

264,294 ,294 294

478,294

284,294

(b)

4,289,192 89,192

272,292

349,391

(c)

4,193,193

453,294

5,395,291

(d) d)

5,384,123 5,384,1

5,393,102

5,393,100

(e) (

2,693,391 2,69 2

284,933

2,942,203

(f)

5,293,291

355,203

5,100,100

Arrange the numbers from the greatest to the smallest. 105,558

110,598

Re ga le du ca tio n

(a) 109,558

(b) 753,186

119,060

401,306

(c)

145,558

93,002

930,001

(d) 29,158

19,414

9,455

Use numbers to fill in the blanks. s.

(a)

is 10,000 greater reater ter than 859,294. 859,

(b) 583,495 is 100,000 less ss than n (c)

592,395 is 1,000,000 00 less le ess than

(d) 5,339,495 is 1,000,000 0 00 more th than

(e) 2,530,395 iss 300,000 less than ,000 le

(f)

is 3,000,00 3,000,000 g greater than 3,583,595.

(g)

is 20,00 20,000 le less than 7,896,384.

(h)

iss 300 m more than 5,495,221.

(i)

is 1,00 1,000,000 less than 9,584,833.

(j)

is 900,000 more than 5,995,933.

At Home Write the number represented by the place value abacus. s. Check the greater number.

Re ga le du ca tio n

(a)

HTh TTh

HTh HT h TTh TTh

HTh TTh

HTh HTh TTh TTh

HTh TTh

(b)

(c)

Write the numbers in the place value chart and compare.

Re ga le du ca tio n

(a) Compare 1,316,200 and 475,950. Hundred Ten Thousands Thousands Thousands

Millions

Hundreds

Tens ens

Ones On

Hundreds Hu

Tens

Ones

(b) Compare 6,693,017 and 6,693,710. 710.

Hundred Ten Thousands housa Thousands Thousands nds

Millions

Fill in the blank. ank.

145,600 45,600

100,000

is 100,000 more than 145,600.

Check the numbers greater than 4,365,385.

3,743,575

5,275,293

7,296,395 6,395

2,352,183

4,365,384

4,365,38 4,365,387

4,654,292

5,385,184

4,234,580 4,23 4,234

Re ga le du ca tio n

Use the words is greater than, is smallerr than n and is equal eq e to to fill in the blanks.

(a) 3,583,395

4,275,285 4,275,28

(b) 5,284,305

6,253,194 6,253,1 6,253,19

(c)

4,691,911

202,113 202,11

(d) 6,375,395

6,375,385 6

(e) 1,295,294

563,385

(f)

3,704,406

7,964,860

Arrange the numbers umbers bers from the t greatest to the smallest.

(a) 4,203,529 529

4,284,495 4,284,4 ,

(b) 7,595,395 95

8,190,641 8,190 8,19 ,

(c)

542,120

4,451,560 ,

(d) 6,5 6,512,48 6,512,481

6,516,384 ,

7,285,395 ,

7,645,120 ,

4,442,150 ,

6,512,484 ,

Solve It!

ed uc ati on

Read the table and answer the following questions. Distance from New York City (kilometers) Chicago

1,146

New Orleans

1,169 69

San Francisco

4,130

Miami

1,757 757

Los Angeles

3,937

Boston

306

(a) What city is furthest from New York City? ty?

(b) Which cities are further than 3,000 ,000 000 km away ffrom New York City?

(c)

rtherr from New York City than Boston? What city is 1,451 km further

Number Patterns

Re ga le du ca tio n

Let’s Learn

What is the next number in the pattern? (a)

125,800

126,800

127,800

128,800 0

Let's look at the thousands place!

C you Can see a pattern with the digits in the thousands place?

The thousand digit increasess by 1 ep. each step.

+1,000

128,800 + 1,000 = 129,800 12 The next in the pattern is 129,800. next number nu

So the numbers increase by 1,000 in each step.

(b) 732,594

1,032,594

1,332,594

Re ga le du ca tio n

432,594

Look at the hundred thousands place.

The hundred thousand digit increases by 3 each ch step. The numbers increase by 300,000 each step. 1,332,594 + 300,000 = 1,632,594 The next number in the pattern is 1,632,594. 32,594. 4.

(c)

5,385,395

5,635,395

5,885,395 85,395

6,135,395 35,3

The numbers increase by 250,000 000 each step. st s 6,135,395 + 250,000 = 6,385,395 85,395 e pattern ttern is 6,385,395. 6,385 The next number in the

(d)

3,684,229

3,671,729 1,729

3,659,229

3,646,729

The numbers ers decrease by 12,5 12,500 each step. 3,646,729 9 - 12,500 2,500 = 3,634,229 3,634 The next the pattern is 3,634,229. xt number mber in th pa

(e)

7,562,595

7,529,595

7,496,595

7,463,595

The numbers numbers decrease by 33,000 each step. 7,463,595 = 7,430,595 463,5 – 33,000 463,595 3 The next in the pattern is 7,430,595. ext number n

What is the missing number? ?

, 1,573,489 , 1,073,489 3,489 9

Re ga le du ca tio n

(a) 3,573,489 , 3,073,489 , 2,573,489 ,

ep. The hundred thousand digit decreases by 5 in each step. The numbers decrease by 500,000 in each step. 2,573,489 - 500,000 = 2,073,489 The missing number is 2,073,489.

(b)

, 98,700 , 94,200 , 89,700 , 85,200 , 80,700 ,700

The numbers decrease by 4,500 each step. p. 98,700 + 4,500 = 103,200 The missing number is 103,200.

(c)

53,275 , 253,275 , 453,275 ,

,8 853,275 53,275 , 1,053,275

The hundred thousand digit git increases reases by 2 in each step. The numbers increase by y 200,000 0,000 each step. 453,275 + 200,000 = 653,275 3,275 75 The missing number is 653,275. 3,275.

(d)

, 3,564,590 4,590 , 3,564,2 3,564,290 , 3,563,990 , 3,563,690 , 3,563,390 3,564

The hundred ed digitit decreases decrease by 3 each step. The numbers 300 each step. bers decrease by b 30 3,564,590 90 + 300 = 3,564,890 3,564 The missing 3,564,890. g numb number er is 3,5

(e) 450,404 , 1,700,404 1,700,4 , 2,950,404 ,

, 5,450,404 , 6,700,404

increase by 1,250,000 each step. The e numbers numbe inc 1,250,000 = 4,200,404 2,950,404 2, 950 + 1,25 The m missing number is 4,200,404.

What are the missing numbers? ?

, 1,282,293,

The numbers increase by 650,000 in each step.

, 2,582,293, 3,232,293, 3,882,293 3

ed uc ati on

(a)

Subtract 650,000 from and add 650,00 650,000 to 1,282 1,282,293.

1,282,293 – 650,000 = 632,293 1,282,293 + 650,000 = 1,932,293

The missing numbers are 632,293 93 and 1,932,293. 1,93 1,9 (b)

, 658,165, 888,165, 65, 1,118 ,118 ,165 ,165, ,16 ,

, 1,578,165

Re ga l

The numbers increase by 230,000 each step.

Subtract 230,000 from 658,165 and add 230,000 to 1,118,165.

658,165 – 230,000 230,0 = 428,165 2 1,118,165 = 1,348,165 1,118,16 + 230,000 230

The missing ssi numbers are 428,165 and 1,348,165. 45

Let’s Practice Fill in the blanks.

Re ga le du ca tio n

(a)

516,795

536,795

556,795

576,795

Look at the ten thousands place

The ten thousands digit increases es by

The numbers increase by +

in each step.

in ea each step.

The next number in the pattern is

(b)

324,575

1,574,575 ,574,5

2,824,575

The numbers mbers rs increase by +

in each step.

The e next next number iin the pattern is

4,074,575

Fill in the blanks. (a) Hundred Thousands

Ten Thousands

Re ga le du ca tio n Millions

Thousands

100,000 less

Hundreds

Tens

Ones

100,000 00,000 ,000 more

(b)

Millions

Hundred Thousands

Ten Thousands

Thousands

125,000 less

Hundreds

Tens

Ones

125,000 more

(c)

Millions

Hundred Thousands

Ten Thousands ousand

Thousands Th

1,500,000 less le

Hundreds

Tens

Ones

1,500,000 more

(d)

Millions

Hundred dred Thousands

Ten Thousands

10,000 less

Thousands

Hundreds

Tens

Ones

10,000 more

Fill in the blanks. (a)

220,000 less

Re ga le du ca tio n

3,019,392

220,000 more e

(b)

3,000 less

(c)

325,000 less

(d)

1,200,000 less

(e)

250,000 less

(f)

100,500 less

485,830

3,000 more e

325,000 25,000 5,000 more

325,002

1,249,102 102

5,140,001 40,001 0,001 583,293

1,200,000 ,200,000 mor more m

250,000 0,0 more

1100, 500 more 10

Find the number that comes mes next ext in the pattern.

(a)

462,395

439,395 5

416,395 416

393,395

(b)

4,298,358

23,35 4,423,358

4,548,358

4,673,358

(c)

278,491

1,728,491 ,728,4

3,178,491

4,628,491

(d)

020 9,472,020

7,372 7,372,020

5,272,020

3,172,020

(e) e)

245,053

490,053

735,053

(f)

789,465 7894

677,465

565,465

453,465

Write the rule for the number pattern. The first one has been done for you.

Re ga le du ca tio n

(a)

+6,200

248,300,

+6,200

254,500,

+6,200 0

260,700, 0,

266,90 266, 266,900 90

2,444,482, 444,482,

2,024,482

(b)

3,284,482, 2,864,482,

(c)

34,

2,100,034, ,034, 4,

4,200,034, 4,2 4,200 6,300,034

(d)

365,294,

317,794, 317 3 4

270,294,

222,794

Find the missing sing numbers numbers in the number pattern.

(a)

, 909,785 909,785, 09,785, 1,25 1,254,785, 1,599,785, 1,944,785,

(b) 937,385, 37,385 5, (c)

2,584,395, 2,584,395 584,395,, 2,909,99 2,909,995, 3,235,595,

(d)

(e) 47,385 47,385,, (f)

, 656,785, 516,485, 376,185,

, 3,886,795,

, 47 478,145, 393,945, 309,745, ,

, 141,345

, 240,885, 305,385, 369,885

, 355,890, 291,090, 226,290, 161,490,

Hands On

Place a counter on the start square.

Roll the dice and move your counter forward the number of spaces shown on your dice. The space ce you land on is your number pattern rule.

Each take a turn in continuing the number mberr pattern following the rule. Each person must answer we correctly before you can move forward. ward. d.

Repeat steps 3 to 4 with the original ginal number till til you reach the finish.

du ca tio n

Work in groups of 4-5. As a group, write a 7-digit number in your notebook that is between 5 million and 6 million.

At Home Fill in the blanks.

Re ga le du ca tio n

(a)

Millions

Hundred Thousands

Ten Thousands

Thousands

Hundreds

325,000 less

Tens

Ones

325,000 25,000 more

(b)

Millions

Hundred Thousands

Ten Thousands

Thousands usands

1,250,000 0 less

Hundreds Hund

Tens

1,250,000 more

Fill in the blanks.

(a)

200,00 less 200,000

(b)

1,500,000 1,500,0 less le

(c)

1,000,500 1,000 000 less

(d) (d

700,000 less

(e)

2,250,000 less

375,304

2,385,032

1,064,053 8,356,158 7,620,147

200,000 more

1,500,000 more

1,000,500 more

700,000 more

2,250,000 more

Ones

Fill in the blanks.

Re ga le du ca tio n

(a) 8,374,294

7,374,294

6,374,294

5,374,294

Look at the digits in millions place.

The millions digit decreases by

in each eac step.

in each ac step.

The numbers decrease by –

The next number in the pattern tern is

(b)

1,384,103

2,984,103 3

4,584,103 ,58

The numbers rs increase ncrea by +

6,184,103

in each step.

The nextt number in the pattern is

(c)

5,440,250 ,440,250

4,940,250

4,440,250

numbers decrease by The num numbe –

3,940,250

in each step.

The next number in the pattern is

. 53

Fill in the missing numbers. .

Re ga le du ca tio n

(a) 150,000 more than 495,494 is (b) 230,000 less than 853,594 is (c)

1,400,000 more than 693,304 is

(d) 21,000 less than 1,442,494 is

(e) 2,350,000 more than 3,493,200 is

(f)

3,700,000 less than 8,384,101 is

(g) 200,500 more than 3,492,303 is

(h) 4,000,500 less than 5,492,202 is

(i)

125,400 more than 942,495 is

(j)

5,000,220 more than 2,405,304 05,304 5,304 is

Find the missing numbers number pattern. ers in n the numbe

(a) 842,394,

, 356,394, 194,394, 32,394

(b) 4,294,204, 4,815,234, 815,234, 5,23 5,336,264, 6,26

(c)

(d) 4,385,204, 04,

, 6,378,324,

, 3,742,302, 4,9 4,942,302, 4 6,142,302, 7,342,302, , 2,9 2,935,204, 2,210,204, 1,485,204,

(e)

, 3,621,3 3,621,325, 3,986,325, 4,351,325,

(f)

, 9,208 9,208,325, 9,293,525, 9,378,725, 9,463,925, 9,208,3

, 5,081,325

Rounding and Estimation

Re ga le du ca tio n

Let’s Learn

Round off 325,800 to the nearest thousand.

When round rounding, remember 5 or more – round roun up!

When rounding, remember 4 or less – round down!

325,800 325,8

325,500

325,000

326,000

When rounding to the nearest st thousand, thousand we look at the digit in the hundreds place. The digit in the hundreds reds ds place plac is 8, so we round up. 325,800 rounded off ff to o the nearest neares neare thousand is 326,000. Round 374,800 to the e nearest ten t thousand. t 374,800 374,8 3

370,000

375,000

380,000

When rounding to tthe nearest ten thousand, we look at the digit in the place. he thousands tho p The digit it in the tthousands place is 4, so we round down. 374,800 rounded und off to the nearest ten thousand is 370,000.

The population of Norway is 5,312,300. Round the population of Norway to the e nearest hundred thousand. The digit in the ten thousands place is 1. So, we round the hundred thousands down.

du c

5,312,300 ≈ 5,300,000 The population of Norway is approximately ately 5,300,000 rounded to the nearest hundred dred thousand.

Re g

First prize at a tennis tournament is $2,501,120. $2,501,12 Round the prize money to the nearest arest est million dollars. dolla doll

In 2,501,120 01,120 the digit in the hundred thousands place is 5. So, we round the millions millio up. m 2,501,120 ,501,120 ≈ 3,000,000 3,000,00 First prize is approximately $3,000,000 rounded to the nearest million appro dollars.

Use the table to answer the following questions.

Re ga le du ca tio n

Land Area (km2)

Australia

7,692,024

Mexico

1,972,550

France

643,801

U.S.A.

9,147,590

Round the land area of Australia to the nearest rest thousand. thousa thousan

sand, we look at a the digit in the When rounding to the nearest thousand, undreds eds place is 0, so we round down. hundreds place. The digit in the hundreds 7,692,024 ≈ 7,692,000 The land area of Australia is approximately proximately 7,692,000 km2.

ne Round the land area of Mexico to the nearest ten thousand.

ce. The dig d Look at the thousands place. digit in the thousands place is 2, so we round down. 1,972,550 ≈ 1,970,000 0,000 The land area approximately 1,970,000 km2. a of Mexico is appr a

e land d area of Franc F Round the France to the nearest hundred thousand.

igit in the tten en n thou thousa The digit thousands place is 4, so we round down.

43,8011 ≈ 600,000 643,801 The land area area o of Fra France is approximately 600,000 km2.

4..

Round und the la land area of the United States to the nearest million.

9,147,590 147,590 ≈ 9, 147,59 9,000,000 The land area of the United States is approximately 9,000,000 km2. and a

Let’s Practice Fill in the missing numbers.

Re ga le du ca tio n

(a)

14,600

14,500

14,000

15,000 15 15,0

rounded off to the nearest st thousand ousand is

≈

(b)

111,000

115,000

110,000

120,000

rounded ed off to o the nearest nea ten thousand is ≈

380,000

(c)

350,000

300,000 0,000 0

rounded ound off to the nearest

hundred undred thousand is ≈

400,000

An average car weighs 1,857,007 grams. Round the weight to the nearest hundred thousand grams. grams

Re ga le du ca tio n

≈

The average car weighs about

grams.

The population of Luxembourg is 613,894. Round d the population to the nearest ten thousand people. ≈

There are about

people in Luxembourg. mbourg.

A large house is for sale for $3,501,001. price to the nearest 001. Round the p hundred thousand dollars. ≈

The house costs about $

A charity is holding a large in Los Angeles. The number of arge e rock concert conce con people that attended the was 1,392,929. Round the number of e concert w people that attended ded to the nearest neare hundred thousand. ≈

There were about ut

people p

people at the concert.

A newspaper prints 8,640,212 newspapers every year. Round spaper er compan company pr the number printed every year to the nearest million. umber of newspapers newspap newspa ≈

The company company prin prints about

newspapers

newspapers every year.

Round the numbers to the nearest hundred. (b) 4,302,453 ≈

Re ga le du ca tio n

(a) 2,485,934 ≈ (c)

374,204 ≈

(d) 5,350,223 ≈

Round the numbers to the nearest thousand.

(a) 692,592 ≈

(b) 5,295,210 5,210 ≈

(c)

(d) 482,402 82,402 02 ≈

1,603,267 ≈

Round the numbers to the nearest ten en thousand. ousand.

(a) 497,926 ≈

(b) ( 9 9,285,394 ,285, ,285,39 ≈

(c)

(d) 259,493 2594 259 94 ≈

1,640,203 ≈

10. Round the numbers to the nearest hun hundred thousand.

11.

(a) 2,783,305 ≈

(b) 593,402 ≈

(c)

(d) 9,538,503 ≈

520,402 ≈

Round the numbers nearest million. mbers to the th nea

(a) 5,492,594 492,594 94 ≈

(b) 874,964 ≈

(c)

(d) 3,603,496 ≈

3,594,023 94,023 ≈

At Home Fill in the missing numbers.

Re ga le du ca tio n

(a)

1,239,021

1,250,000

1,200,000

1,300,000 1,30 1,300

rounded off to the nearest st

hundred thousand is

≈

6,611,341

(b)

6,500,000

6,000,000

7,000,000

rounded ded off to the nearest ne n

million is

≈

Round the numbers mbers ers to different differ place values.

(a)

5,204,532 04,53

≈ when rounded to the nearest ten thousand.

≈ when rounded to the nearest hundred thousand.

≈ when rounded to the nearest million.

≈ when rounded to the nearest hundred thousand. sand.

Re ga le du ca tio n

(b)

9,324,294

≈ when rounded ded to the nearest ten thousand. usand. nd.

≈ when rounded round to the nearest million. on

Round the numbers to the nearest thousand. sand.

(a) 582,593 ≈

(b) 1,394,022 1,394,02 ≈

(c)

(d) d) 856,00 856,0 856,009 ≈

5,495,201 ≈

Round the numbers to the nearest rest ten thousand. thou tho

(a) 7,396,083 ≈

(b) 749,592 ≈ (b

(c)

(d) 2,495,021 ≈

8,184,952 ≈

Round the numbers mbers ers to the nearest nea ne hundred thousand.

(a) 8,285,307 307 ≈

(b) 964,194 ≈

(c)

(d) 1,483,945 ≈

9,472,009 72,009 09 ≈

Round ound the numbers num to the nearest million.

(a) (a 7,295,206 7,295,2 ≈

(b) 9,499,999 ≈

(c)

(d) 7,281,592 ≈

1,492,493 ≈

Looking Back Write the numbers.

Re ga le du ca tio n

rteen. en. (a) Three hundred twenty thousand, six hundred fourteen.

(b) Seven million, eighty-three thousand, one hundred undred five.

Write in words.

(a) 710,509

(b) 3,245,081

Count on in 10,000s. s s.

(a) 3,900,

(b) 294,708,

5..

(a) 1,884,121, 4,121,

(b) b) 165,552, 5,552,

Count on in 100,000s. 100,000s

1,000,000s. Count ount on in 1,00

(a) a) 26,037, 26

(b) 4,825,910, 825

Write the number in its expanded form.

Re ga le du ca tio n

(a) 213,967

(b) 1,030,507

(c)

6,500,283

(d) 8,009,140

Write in exponent form in numbers mbers bers and in words. wo (a) 10 x 10

Exponent form:

W Word ord form form:

(b) 10 x 10 x 10 x 10 x 10 x 10 0 Exponent form: m:

Write the number. umber. er.

(a) 105 =

(b) 103 =

10 00 =

(d) 101 =

(c)

W Write rite the num number. (a) 5 x 101 = (c))

Wor Word form:

12 x 103 =

(b) 2 x 103 =

(d) 40 x 102 =

10. Use the symbols >, < and = to fill in the blanks. 6,987

(b) 73,122

73,122 22

Re ga le du ca tio n

(a) 50,765 (c)

11.

84,640

84,708

(d) 333,000

Arrange the numbers from the greatest to the smallest. malle mallest.

(a) 19,654

19,361

10,788

(b) 902,006

, 1,400, 2,400, 00, 3,400, 4,400, 4,400

(b) 306,500, (c)

, 305,500, 05,500, 305 305,000, 304,500,

50,155, 75,155, 100,155, 155,

(d)

14.

425,221 221

Find the missing numbers in the pattern. e number patte

(a)

13.

425,121 ,

12.

333,010 3,010

, 150,155,

, 320,001, 320 320,0 240,001, 40 001 160,001, 40,001

Round the numbers nearest ten thousand. umbers bers to the near

(a) 6,885 5≈

(b) 84,750 ≈

(c)

(d) 973,440 ≈

327,100 0≈

Round numbers to the nearest hundred thousand. R ound the num number

(a) 109 109,700 9 700 ≈

(b) 252,550 ≈

(c))

(d) 865,022 ≈

248,060 ≈ 24

Operations on Whole Numbers

Addition and Subtraction Anchor Task

$1,295,000 Verdichio Waterss

$98 $988,000 6 2

Andrea Point 2

$1,155,000 4

$1,105,000 6 2

Albatross Beach 4

Gentian Springs 4

Let’s Learn

4,937,782

914,110

Ireland

Re ga le du ca

Singapore

ion

The population of Ireland is 4,937,782. The population of Singapore pore e is 914,110 more than Ireland. Find the population of Singapore.

To find the population of Singapore, we add. dd.

We can regroup 18 hundred thousands into 1 million and 8 hundred thousands.

Hundred Thousands

Millions

We can regroup 11 thousands into 1 ten thousand and 1 thousand.

Ten Thousands Th

Thousands Thousa

Hundreds

Tens

Ones

4,937,782 ,937,782 + 914,110 = 5,851,892

The population of Singapore is 5,851,892. ula ulation

Re ga le du ca to n

Mr. Sanchez bought a house and a car for $1,024,795. The car costs $116,143. Find the cost of the house.

$1,024,795

house

car

$116,143 43

To find the cost of the house, we subtract. btract. Millions

Hundred Thousands

Ten Thousands

Thousands ousands

Hundreds H

Hundred Thousands Thousand

Ten Te Thousands Thou

1,024,795 5 – 116,143 116,14 = 908,652 The house costs cos $908,652.

Ones

Regroup 1 ten thousand into 10 thousands. Then subtract.

to Regroup 1 million into ds 10 hundred thousands. ct. Then subtract.

Millions

Tens

Thousands

Hundreds

Tens

Ones

Let’s Practice Add.

Re ga le du ca tio n

(a)

(c)

(e)

(g)

((i)

(b)

(d)

(f)

(h)

(j)

Subtract. (a)

(b)

Re ga le du ca tio n

3 –

(c)

–

(e)

–

(g)

–

(i)

–

(d)

–

( (f)

–

(h)

–

(j)

–

0 0 0 0 0 0 1

Use the column method to add or subtract. (b) 135,401 – 124,022 2=

Re ga le du ca tio n

(a) 53,405 + 25,205 =

(c)

358,403 + 646,046 =

(e) 395,302 302 + 3,495,035 =

(d) 9,485,395 9,485,3 485 3 – 353,304 =

(f)

3,592,024 – 1,034,032 =

Solve It!

Re ga le du ca tio n

The sum of the numbers vertically and horizontally in the magic gic square quare are ar all 10,000. Can you find the missing numbers? (a)

4,218

3,000

5,718

(b)

3,840 40

6,040

2,260

(b) Home At Add.

Re ga le du ca tio n

(a)

(c)

(b)

(d)

(e) 9,745 + 54,905 =

(f) f)

395,045 395, 395,0 + 495,045 =

85,014 14 + 27,052 = (g) 2,385,014

(h) 5,042,080 + 1,304,953 =

Subtract. (a)

(b)

Re ga le du ca tio n

–

(c)

–

(d)

–

(e) 843,592 – 53,503 =

(f)

395,024 – 214,042 =

(g) 4,683,053 53 – 294,035 =

(h) 2,945,035 – 303,053 =

Multiplying by 10s, 100s and 1,000s

Millions

ga le du ca tio n

Anchor Task Hundred Thousands

(a) 12

Ten Thousands

Thousands

(b) 306

(c)

Hundreds

1,047

Tens ns

Ones O

(d) 4,560

12 x 10

306 x 10

1,047 x 10

4,560 x 10

12 x 100

306 x 100

1,047 x 100

4,560 x 100

12 x 1,000 10

306 x 1,000

1,047 x 1,000

4,560 x 1,000

Let’s Learn

Re ga le du ca tio n

Let’s use place value disks to help multiply numbers by 10. Find 124 x 10. 100

x 10

1,000 100 100

124

10 0

1,240

124 x 10 = 1,240

Find 4,265 x 10.

1,000 1,000 1,000 1,000 100 100

1 ,00 10 10,00 00 0 110,000 0,00 110,000 10,000 0,00 1 10,000 1,000 1,000

x 10

100 00 0 100 100 100 100 100 10

4,265

42,650

4,265 x 10 = 42,650

Let’s use place value disks 1,230 by 30. isks tto help multiply mu Method 1

10,000 1,000 1,000

100 100 100

1,000 100 100 0

x 10

1,230

110,000 0 1,000 1,000

100 100 100

10,000 1,000 1,000

100 100 100

12,300

10,000 1,000 1,000

1,230 x 30 = 1,230 x 10 x 3 = 12,300 12,3 x 3 = 36,900

100 100 100 36,900

Method 2 1,000 100 100

100 0 100 1 0 100

Re ga le du ca tio n

10,000 00 0 0 1, 11,000 1,000

1,000 100 100

x 10

110,000 0,00 0,00 00 0 11,000 ,000 11,000 ,0

100 0 10 100 100

1,230

1,000 100 100

110,000 0,0 0, 1,000 1,000

100 100 100

3,690

36,900

1,230 x 30 = 1,230 x 3 x 10 = 3,690 x 10 = 36,900 Multiply.

(a) 2,300 x 40 = 23 x 100 x 4 x 10 = 92 x 1,000 = 92,000

(b) 15,600 x 30 = 156 56 x 100 x 3 x 10 1 = 468 8 x 1,000 = 468,000

(c)

7,400 0 x 50 0 = 74 x 100 x 5 x 10 = 370 x 1,000 1,00 370 = 370,000

(d) d) 3,800 x 80 = 38 x 100 x 8 x 10 = 304 x 1,000 = 304,000

3 4

Let’s use a place value chart to help multiply numbers by 100.

Re ga le du ca tio n

Find 726 x 100. Ten Thousands

Thousands

Hundreds

Tens

Ones

726

72,600

726 x 100 = 72,600 Find 1,574 x 100. Hundred Thousands

Ten Thousands

Thousands

Hundreds ds

Tens

Ones

1,574

157,400

1,574 x 100 = 157,400 Multiply.

(a) 83 x 600 = 83 x 6 x 100 = 498 8 x 100 = 49,800 9,800

3 6

(b) 2,350 ,350 x 400 = 235 23 x 10 x 4 x 100 = 940 9 x 1,000 = 940,000 940

Let’s use a place value chart to help multiply numbers by 1,000.

Re ga le du ca tio n

Find 406 x 1,000. Hundred Thousands

Ten Thousands

Thousands

Hundreds

Tens

Ones

406 40

406,000

406 x 1,000 = 406,000 Find 1,308 x 1,000. Millions

Hundred Thousands

Ten Thousands

Thousands ds

Hundreds undre

Tens

Ones

1,308 x 1,000 = 1,308,000 0 Multiply.

(a) 46 x 3,000 = 46 x 3 x 1,000 = 138 38 x 1,000 = 138,000

(b) 290 90 x 6,000 = 29 2 x 6 x 10,000 = 174 1 x 10,000 = 1,740,000 1,74

Estimate the products by rounding off then multiplying.

ed uc ati on

(a) Estimate 435 x 52. Round off 435 to the nearest hundred. 435 ≈ 400 Round off 52 to the nearest 10. 52 ≈ 50

Multiply the rounded numbers. 400 x 50 = 4 x 100 x 5 x 10 = 20 x 100 x 10 = 20 x 1,000 = 20,000 435 x 52 ≈ 20,000

Can you find the estim estimate mentally? menta

(b) Estimate 3,730 x 227.

Round off 3,730 to the nearest rest thousand. thousan 3,730 ≈ 4,000 Round off 227 to the 100. he nearest n 100 227 ≈ 200 Multiply the rounded ounded ded numbers. numbe 4,000 x 200 0 = 4 x 1,000 x 2 x 100 10 = 8 x 1,000 x 100 = 8 x 100,000 100,0 = 800,000 3,730 ,730 x 227 ≈ 800,000 80

4x2=8 8 x 100,000 = 800,000

Let’s Practice Multiply by 10, 100 and 1,000.

Re ga le du ca tio n

(a) 3 x 10 =

(c)

3 x 100 =

56 x 100 =

3 x 1,000 =

56 x 1,000 00 =

72 x 10 =

(d) 295 95 x 10 =

72 x 100 =

295 5 x 100 =

72 x 1,000 =

295 95 x 1,000 1,00 =

(e) 664 x 10 =

(f)

890 0 x 10 =

664 x 100 =

890 89 x 100 =

664 x 1,000 =

890 x 1,000 =

(g) 1,052 x 10 =

(i)

(b) 56 x 10 =

(h) 2,368 x 10 =

1,052 x 100 =

2,368 x 100 =

1,052 x 1,000 ,000 0=

2,368 x 1,000 =

000 x 10 = 5,000

(j)

4,200 x 10 =

5,000 000 x 100 =

4,200 x 100 =

5,000 x 1,000 1,00 =

4,200 x 1,000 =

Find the products. (b) 4 x 8 =

Re ga le du ca tio n

(a) 6 x 2 =

(c)

6 x 20 =

4 x 80 =

6 x 200 =

4 x 800 =

6 x 2,000 =

4 x 8,000 0=

7x3=

7 x 30 =

9 x 50 0=

7 x 300 =

9 x 500 =

7 x 3,000 =

9 x 5,000 =

(e) 10 x 2 =

(f)

9x8=

10 x 20 =

9 x 80 =

10 x 200 =

9 x 800 =

10 x 2,000 =

9 x 8,000 =

(g) 7 x 7 =

(d) 9 x 5 =

(h) 6 x 9 =

7 x 70 =

6 x 90 =

7 x 700 =

6 x 900 =

7 x 7,000 000 =

6 x 7,000 =

Multiply. (b) 345 x 100 =

Re ga le du ca tio n

(a) 542 x 10 =

(c)

253 x 1,000 =

(d) d) 2,485 85 x 1,000 =

(e) 60 x 5 =

(f)

20 x 200 =

(g) 300 0 x 2,000 =

(h) 4,000 x 3,000 =

Estimate the products by rounding each number before multiplying. (b) 352 x 2 ≈

Re ga le du ca tio n

(a) 353 x 7 ≈

(c)

43 x 53 ≈

(d)) 858 8 x 53 ≈

(e) 994 x 535 ≈

(f)

1,493 x 212 ≈

(g) 332 x 2,900 2,900 ≈

(h) 1,295 x 551 ≈

Solve It!

Re ga le du ca tio n

Ethan and his friends are discussing their allowance. My allowance is $10 per week.

Dominic

My allowance is $52 per month.

Ethan

My allowance is ay. $1.50 per day.

W Wyatt

My allowance allowan is $12 pe per week.

Jordan

much mone mon (a) Assuming it is not a leap year, how mu money does each person receive in the month of February? ary? Dominic:

Ethan:

Wyatt:

Jordan:

ot a leap year, ye h (b) Assuming itt is not how much money does each person ar? receive in 1 year? ic: Dominic:

Ethan: an:

Wyatt: Wyat

Jordan:

(b) Home At Fill in the blanks.

Re ga le du ca tio n

(a)

100

12 x

(b)

100

1,000

10 0

1,000

101 x

(c)

100

1,000 11,000

100 10

11,000 1, 0

100 10

1,000

100 10

(d)

10 0

100

1,000

100 10

1,000

100 10

1,000

100 10

1,000

100 10

Multiply by 10, 100 and 1,000. (b) 18 x 10 =

Re ga le du ca tio n

(a) 1 x 10 =

(c)

1 x 100 =

18 x 100 =

1 x 1,000 =

18 x 1,000 =

321 x 10 =

(d) 285 x 10 =

321 x 100 =

285 x 100 =

321 x 1,000 =

285 5 x 1,000 =

Multiply.

(a) 946 x 10 =

(b) 463 x 100 =

(c)

(d) 24 x 1,000 =

5 x 1,000 0=

Find the products. (b) 2 x 9 =

Re ga le du ca tio n

(a) 5 x 8 =

(c)

5 x 80 =

2 x 90 =

5 x 800 =

2 x 900 =

5 x 8,000 =

2 x 9,000 000 0=

4x7=

(d) 6 x 3 =

4 x 70 =

6 x 30 =

4 x 700 =

6 x 300 =

4 x 7,000 =

6 x 3,00 3,000 =

Estimate the products by rounding ing each number n before multiplying. (a) 394 x 2 ≈

(b) ( 936 x 4 ≈

(c)

(d) 583 x 1,200 ≈

3,543 x 10 ≈

Multiplying by 1 and 2-digit Numbers be

Re ga le du ca tio n

Let’s Learn

Find 2,305 x 4 using the column method.

2 3 20 5

2 0

2 3 0 5

2 2 0

2 3 0 5

9 2 2 0

2,305 x 4 = 9,220

Find 32,045 x 3 using the column method. od. 1

3 2 0 4 5 x 3 5

3 2 0 4 5 x 3 3 5

3 2 10 4 5 x 3 1 3 5

3 2 0 4 5 x 3 6 1 3 5

3 2 0 4 5 x 3 9 6 1 3 5

32,045 x 3 = 96,135

Find 12,493 x 2 using g the column colum method. m 1 2 4 9 3 x 2 6

1 2 4 9 3 x 2 8 6

1 2 14 9 3 x 2 9 8 6

1 2 4 9 3 x 2 4 9 8 6

1 2 4 9 3 x 2 2 4 9 8 6

12,493 x 2 = 24,986 24,9

Re ga le du ca tio n

Multiply 25 and 37. We can regroup these numbers into tens and ones, then place them in a table and multiply each column and row.

600

150

140

Now, add the products together!

produc prod Add the products. 16

0 0

4 0

1 5 0

3 5

9 2 5

So, 25 multiplied by 37 is 925.

Multiply 423 and 21. We can regroup these numbers into nto hundreds, tens te and ones, then place ch column olumn and row. them in a table and multiply each

400 8,000

400

20 0

Can you add the products mentally?

Add the products. 8 0 0 0 4 0 0

4 0 0

2 0

6 0

8 8 8 3

23 multiplied by 21 is 8,883. So, 423

Find 1,221 x 12 using the column method. ducts. Add the products.

Multiply by 10.

Re ga le du ca tio n

Multiply by 2.

1 2 2 1 1 2 2 4 4 2

1 2 2 x 1 2 4 4 1 2 2 1

1 2 2 0

1 2 2 x 1 2 4 4 1 2 2 1 1 4 6 5

1 2 2 0 2

1,221 x 12 = 14,652

Find 953 x 2,403 using the column method. od.

Multiply y by 50.

Multiply by 3. x

2 4 0 3 9 5 3 7 2 0 9

Multiply by 900. 2 4 x 9 7 2 1 2 0 1 2 1 6 2 7

2 4 9 7 2 1 2 0 1

0 5 0 5

3 3 9 0

Add the products.

0 5 0 5 0

3 3 9 0 0

2 4 x 9 7 2 1 2 0 1 2 1 6 2 7 2 2 9 0 0

0 5 0 5 0 5

3 3 9 0 0 9

953 3 x 2,403 = 2,290,059 2,290,05 2,29

Let’s Practice Multiply.

Re ga le du ca tio n

(a)

(b)

(c)

(e)

(d)

(f)

Multiply using the column method. (b) 135 x 63 =

Re ga le du ca tio n

(a) 64 x 53 =

(c)

635 x 46 =

(d)) 625 5 x 39 =

(e) 1,396 x 25 =

(f)

2,494 x 64 =

(g) 532 x 290 =

(h) 1,295 x 433 =

Work out the following by multiplying rows and columns in a table. Then add the products.

Re ga le du ca tio n

(a) 46 x 64 = x

60 4

(b) 53 x 86 = x

(c)

346 x 93 3= x

Multiply using the column method. (a)

(b)

Re ga le du ca tio n

(c)

(d)

(e)

(f)

Solve It!

Re ga le du ca tio

Sophie's pens leaked ink onto her Math homework. Help her find the missing numbers to complete the multiplication.

10 0

1100 00

50 5 0

30 0 1,500 1,50 00 0

210 2 10 0

200

4 40 0

24 000 0 4 4,800 ,80 800 600 60 00 224,000

80 80 3,200 33,2 ,200 ,2 6

240 2 40 40

640 640 48 4 8

At Home Multiply.

Re ga le du ca tio n

(a)

(b)

(c)

2 2

(e)

(d)

(f)

Multiply using the column method. (b) 352 x 96 =

Re ga le du ca tio n

(a) 53 x 53 =

(c)

462 x 42 =

(d)) 2,294 94 x 33 =

Work out the following by multiplying multiplyin rows and columns in a table. Then add the products. uc

863 x 53 = x

Multiply using the column method. (a)

(b)

Re ga le du ca tio n

(c)

(d)

(e)

(f)

Hands On

Re ga le du ca tio n

Work in pairs. Use the number cards to form multiplication equations quations ons of a 4-digit number by a 2-digit number to complete the tasks.

(a) Write an equation with the greatest est product. oduct.

(b) Write an equation with w the smallest smalles product.

(c)

100

Write e 2 equations quations that have ha a 6 in the ones place.

Dividing by 10s, 100s and 1,000s

Re ga le du ca tio n

Let’s Learn

Let’s use place value disks to help divide numbers by 10. Find 420 ÷ 10.

100 100 100 100 10

÷ 10

10 0

420

10 0

42 2

420 ÷ 10 = 42

Find 3,600 ÷ 10.

100 100 100 10

1,000 1,000 1,000 0 100 100 100

÷ 10

100 100 100

360

3,600

3,600 ÷ 10 = 360

Divide 156,100 by y 10.

10,000 0 1,000 1,000 1,000 1,000 1,000

100,000 0 10,000 0 10,000 ,000 00 0 110,000 0,00 0,000 0 110,000 0,00 ,00 00 0 110,000 0,00 00

÷ 10

1,000 1,000 0 11,000 ,00 00 1,000 1,00 ,000 1,000 1,00 ,000 1,0 11,000 ,00

100 100 100 100 100 100 10

100

156,100 100

15,610

156,100 56,100 ÷ 10 = 15,610

1 01

Find 3,300 ÷ 30. ÷ 10

100 100 100

÷3

100

Re ga le du ca tio n

1,000 1,000 1,000

100 100 100

3,300

0 10

330

110

3,300 ÷ 30 = 110.

Divide 48,000 by 40. 10,000 10,000 0 10,000

÷ 10

1,000 1,000 1,000 0

10,000 1,000 1,000

1,000 100 100 0

1,000 1,000 1,000

100 100 00 0 100 00 0

1,000 1,000 1,000

100 0 100 00 0 100 0

48,000

4,800

÷4

11,000 100 100

1,200

48,000 ÷ 40 = 1,200.

Divide 244,200 by 20. 100,000 0 100,000 0 10,000 0

÷ 10

110,000 0,00 00 0 110,000 0 1,000

10,000 0 10,000 0 10,000 0,00 00

11,000 ,0 1,000 1,000

1,000 1,000 00 1,000 1,000

100 100 100

1,000 0 100 0 100 00 0

100

244,2 244,200

244,200 0 ÷ 20 2 = 12,210. 12

1 02

24,420

÷2

10,000 0 1,000

1,000

100 100

12,210

Let’s use a place value chart to help divide numbers by 100.

Re ga le du ca tio n

Find 72,700 ÷ 100. Ten Thousands

Thousands

Hundreds

Tens

Ones

72,700

7 727

72,700 ÷ 100 = 727

Find 143,300 ÷ 100. Hundred Thousands

Ten Thousands

Thousands

Hundreds ds

Tens

Ones

143,300

1,433

143,300 ÷ 100 = 1,433 Divide.

00 ÷ 100 ÷ 3 (a) 5,700 ÷ 300 = 5,700 = 57 ÷ 3 = 19

3 2

5,700 ÷ 100 = 57

400 ÷ 400 = 6,400 6, ÷ 100 ÷ 4 (b) 6,400 6 ÷4 = 64 = 16

4 2

6,400 ÷ 100 = 64

1 03

Let’s use a place value chart to help divide numbers by 1,000.

Re ga le du ca tio n

Find 52,000 ÷ 1,000. Ten Thousands

Thousands

Hundreds

Tens

Ones

52,000

5 52

52,000 ÷ 1,000 = 52

Find 273,000 ÷ 1,000. Hundred Thousands

Ten Thousands

Thousands

Hundreds ds

Tens

Ones

273,000

273

273,000 ÷ 1,000 = 273 Divide.

000== 136,000 ÷ 1,000 1 (a) 136,000 ÷ 8,000 ÷8 = 136 ÷ 8 = 17

6,000 0 ÷ 9,000 9,000 = 126,000 126,0 26 (b) 126,000 ÷ 1,000 ÷ 9 12 ÷ 9 = 126 = 14

104

Estimate the quotient by rounding off and dividing mentally.

ed uc ati on

(a) Estimate 35,032 ÷ 52. Round off 35,032 to the nearest thousand. 35,032 ≈ 35,000 Round off 52 to the nearest ten. 52 ≈ 50 Divide the rounded numbers. 35,000 ÷ 50 = 35,000 ÷ 10 ÷ 5 = 3,500 ÷ 5 = 700 35,032 ÷ 52 ≈ 700

Dividing by 50 is the sam same as dividing by b 10, then dividing by 5. divid

(b) Estimate 121,002 ÷ 6,011.

Round off 121,002 to the e nearest earest ten thousand. th 121,002 ≈ 120,000 Round off 6,011 to thousand. o the nearest nea ne ho 6,011 ≈ 6,000 Divide the rounded ounded ed numbers. numbe 120,000 ÷ 6,000 00 = 120,000 120,0 ÷ 1,000 ÷ 6 = 120 12 ÷ 6 = 20

Dividing by 6,000 is the same as dividing by 1,000, then dividing by 6.

121,002 21,002 2 ÷ 6,011 ≈ 20

1 05

Let’s Practice Fill in the blanks.

Re ga le du ca tio n

(a)

1,000

100

11,100 ÷

(b)

1,000

10,000

1,000

100

1,000

2,020 ÷

(c)

100

100 0

100,000

100

100 0

100,000

100 00 0

100 100

110,000 0,00 00 00 10,000 10 0,00 00 0

10,000

11,000 ,000

1,000 1,000

100 100

110,000 0,00 0,00 00

11,000 ,000 11,000 ,0

1,000

100

110,000 0,00 00

11,000 ,00

1,000

100

106

100,000

(d))

100

Divide by 10, 100 and 1,000. (b) 120,000 ÷ 10 =

Re ga le du ca tio n

(a) 72,000 ÷ 10 =

(c)

72,000 ÷ 100 =

120,000 ÷ 100 0=

72,000 ÷ 1,000 =

120,000 ÷ 1,000 00 =

320,000 ÷ 10 =

(d) 29,000 000 0 ÷ 10 =

320,000 ÷ 100 =

29,000 000 ÷ 100 =

320,000 ÷ 1,000 =

29,000 9,000 ÷ 1,000 1,00 =

Find the quotient.

(a) 60,000 ÷ 5 =

(c)

(b) ( 49,000 49,0 49 9,0 ÷ 7 =

60,000 ÷ 50 =

49,000 4 ÷ 70 =

60,000 ÷ 500 =

49,000 ÷ 700 =

60,000 ÷ 5,000 =

49,000 ÷ 7,000 =

210,000 ÷ 3 =

(d) 450,000 ÷ 9 =

210,000 ÷ 30 =

450,000 ÷ 90 =

210,000 00 ÷ 300 =

450,000 ÷ 900 =

210,000 0,000 0 ÷ 3,000 =

450,000 ÷ 9,000 =

1 07

Estimate the quotient by rounding each number before dividing. (b) 2,005 ÷ 22 ≈

Re ga le du ca tio n

(a) 353 ÷ 71 ≈

(c)

108

15,020 ÷ 53 ≈

(d)) 27,032 032 ÷ 91 ≈

(e) 120,101 ÷ 61 ≈

(f)

140,021 ÷ 71 ≈

(g) 361,00 361,001 0011 ÷ 99 ≈

(h) 63,025 ÷ 7,195 ≈

At Home Fill in the blanks.

Re ga le du ca tio n

(a)

100,000

10,000

100,000

10,000

100

(b)

100,000 10,000

1,000

10,000 ,00 00

1,00 ,000 1,000

100 0 1100

100,000

1,000 1,000

10,000 10,00 10, 00 0

100 100

10,000

1,000

11,000 ,000

100 100

1,000

100

Divide by 10, 100 and nd 1,0 11,000. (a) 85,000 ÷ 10 0=

(c)

(b) 32,000 ÷ 10 =

85,000 ÷ 100 0=

32,000 ÷ 100 =

85,000 000 ÷ 1,000 =

32,000 ÷ 1,000 =

930,000 0,000 ÷ 10 =

(d) 121,000 ÷ 10 =

930,000 ÷ 100 =

121,000 ÷ 100 =

= 930,000 ÷ 1,000 1,

121,000 ÷ 1,000 =

1 09

Find the quotient. (b) 64,000 ÷ 8 =

Re ga le du ca tio n

(a) 108,000 ÷ 9 =

108,000 ÷ 90 =

64,000 ÷ 80 =

108,000 ÷ 900 =

64,000 ÷ 800 00 =

108,000 ÷ 9,000 =

64,000 ÷ 8,000 ,000 =

mber er before div Estimate the quotient by rounding each number dividing.

(a) 421 ÷ 83 ≈

(b) b) 3,005 ÷ 52 ≈

(c)

(d) 32,032 ÷ 84 ≈

7,020 ÷ 73 ≈

(e) 1,420 20 ÷ 72 ≈

110

(f)

210,121 ÷ 3,001 ≈

Dividing by 1 and 2-digit Numbers rs

Re ga le du ca ti n

Let’s Learn

A bakery produces 2,334 donuts. They are packed into boxes of 6 donuts per box. Find the total number of boxes needed to pack all of the donuts. Step 1

3 6 2 3 3 4 1 8 5

Divide 2 thousands by 6. Regroup 2 thousands into o 20 hundreds. d divide. vide. Add the 3 hundreds and undreds reds remainder remain rema 23 hundreds ÷ 6 = 3 hundreds 5 hundreds. 23 hundreds – 18 hundreds undreds reds = 5 hundreds. hun

Step 2

3 6 2 3 1 8 5 4

8 3 4 3 8 5

Bring down the he e 3 tens. Now there are 53 tens.

53 tens ÷ 6 = 8 tens remainder 5 tens. rem 53 tenss – 48 tens = 5 tens.

Step 3

3 6 2 3 1 8 5 4

8 9 3 4

3 8 5 4 5 4 0

Bring down the 4 ones. Now there ther are ar 54 ones. 54 4÷6=9 54 – 54 = 0

2,334 ÷ 6 = 389 3 A total of 389 boxes are needed to pack all of the donuts.

111

Find 51,106 ÷ 4. Step 2

1 4 5 1 4 1

1 2 4 5 1 1 0 6 4 1 1 8 3

Re ga le du ca tio n

Step 1

1 0 6

5÷4=1R1

Step 3

1 2 4 5 1 4 1 1 8 3 2

11 ÷ 4 = 2 R 3

Step 4

7 1 0 6

1 8 3

31 ÷ 4 = 7 R 3

1 2 4 5 1 4 1 1 8 3 2

7 7 1 0 6

1 8 3 0 2 8 2

30 ÷ 4 = 7 R 2

Step 5

1 2 4 5 1 4 1 1 8 3 2

112

7 7 6 1 0 6

1 8 3 0 2 8 2 6 2 4 2

51,106 divided by 4 is 12,776 with 2 remainder.

26 ÷ 4 = 6 R 2

51,106 ÷ 4 = 12,776 R 2

Riley finds a bag full of 1-cent coins in her drawer. She counts the coins and finds there are 384 coins in total. (a) She wants to divide these coins equally among her 3 siblings. How much money does each sibling receive?

Re ga le du ca t

1 2 8 3 3 8 4 3 0 8 6 2 4 2 4 0

3÷3=1r0

8÷3=2r2

24 ÷ 3 = 8 r 0

Each sibling receives 128 1-cent coins coins. So, each sibling receivess $1.28. .28.

(b) There are 24 pupils in Riley's y'ss class. If she divided the coins equally among her classmates, mate how much mates, muc would each pupil receive? We need to divide number by a 2-digit number. We can do ivide e a 3-digit n num this using repeated peated ed subtraction. subtrac Step 1

Find a multiple ple of of 24 that th is close to the total number of coins. The multiple than the total but not greater than the total. tiple e can be less tha An easy easy multipl multiple to start with is 10. 10 x 24 = 240

This less than 382. So, let's subtract. his is le ss th

1 13

Step 2

Re ga le du ca tio n

24 3 8 4 – 2 4 0 1 0 1 4 4

Subtract the multiple of 24. d side. Write the factor on the right hand

Step 3

24 3 8 – 2 4 1 4 – 1 2 2

4 0 1 0 4 0 5 4

ultiple of 24 Now, find anotherr multiple n 144. 4. Let's try 5. that is less than 24 x 5 = 120.

Step 4

24 3 8 – 2 4 1 4 – 1 2 2 – 2

4 0 1 0 4 0 5 4 1 4 0

We e can see that th only 24 remains. So,, the final ffactor is 1.

Step 5

Finally, ly, we add the ffactors on the right side to find the quotient. 10 0 + 5 + 1 = 16

So, 384 ÷ 24 = 16

Each pupil would receive 16 cents.

114

Let’s Practice Divide.

eg al ed uc ati on

(a)

(b)

(c)

(d)

(e) (e

1 15

Complete the following. (b)

Re ga le du ca tio n

(a) 3

5 7 5

(c)

2 3 1

6 4 9 1

4 9 7 2 1

(d) d)

6 3 2 1

(e)

(f)

116

2 8 5 0 1

Estimate the quotient by rounding. Then divide.

Re ga le du ca tio n

(a) Find 244 ÷ 61. Estimate

61 ≈

61 2 4 4

244 ≈

244 ÷ 61 ≈

(b) Find 1,425 ÷ 75. Estimate

75 ≈

75 1 4 2 5

1,425 ≈

1,425 ÷ 75 ≈

(c)

Find 3,249 ÷ 57. Estimate

57 ≈

57 3 2 4 9

3,249 ≈

3,249 ÷ 57 ≈

(d) Find 3,827 ÷ 43. Estimate stimat

43 ≈

43 3 8 2 7

3,827 3 827 ≈

3,827 ÷ 43 ≈

1 17

At Home Divide.

Re ga le du ca tio n

(a)

(b)

(d)

(e) (e

118

(c)

Complete the following. (b)

Re ga le du ca tio n

(a) 6

5 3 8

(c)

2 5 1

6 2 0 4

(d) d)

6 4 4 8

Estimate the quotient Then divide. otient nt by rounding. rou ro Find 728 ÷ 91. Estimate

91 ≈

91 7 2 8

728 ≈

728 ÷ 91 ≈

1 19

Order of Operations

Anchor Task

21 – 16 + 4 16 6 + 4 = 20 21 – 20 = 1

21 – 16 = 5 5+4=9

2+7x9 2+7=9 9 x 9 = 81

120

7 x 9 = 63 2 + 63 = 65

Let’s Learn

Order of Operations Step 1

ed uc ati on

When a numerical expression uses more than one operation, we must follow some rules in order to get the correct answer.

Step 2

Do the operations in parenthesis.

( )

Step tep 3

Multiply and / or divide from left to right.

Add and / or o subtract from om left to right.

x ÷

+ –

Re g

Sue the florist has 400 roses. She he arranges ranges the roses into bunches of 12 roses. She makes a total of 30 0 such bunches. bunches How many roses are left?

400 – 12 x 30

Start with multiplication!

400 – 360 40 4

Sue has 40 roses left.

121

Re ga le du ca tio n

Riley has 30 liters of water and 12 liters of fruit juice. She mixes the liquids together and makes 7 jugs of juice mix. Each jug holds 4 liters. How many m liters of juice mix are left over? Add the number numbers n parenthesis parenthe in first!

(30 + 12) – 7 x 4 42

– 28

Riley had 14 liters of juice mix left over. (a) Find 3 + (7 x 4) ÷ 2.

(b) b) Find 6 x 8 ÷ (9 ( + 3).

3 + (7 x 4) ÷ 2

6 x 8 ÷ ((9 + 3)

3 + 28 ÷ 2

48 ÷

3 + 14

(c)

17 Find 9 x 2 + 3 x 3.

(d) Find 12 + 4 x (12 ÷ 6).

9x2+3x3 18 +

12 + 4 x (12 ÷ 6)

= 12 + 4 x 2

= 12 + 8

= 20

(e) Find 8.. nd 8 ÷ (6 – 2) x 8

8 ÷ (6 – 2) x 8 = 8 ÷ 4 x 8

122

(f)

Find 14 – 3 x (9 ÷ 3).

14 – 3 x (9 ÷ 3) = 14 – 3 x 3

=2x8

= 14 – 9

= 16

Let’s Practice

Re ga le du ca tio n

1. Fill in the blanks.

st (a) Ethan has 12 toy cars. He gives 5 cars to his youngest om his brother, Peter. He then receives 8 more toy cars from father. How many cars does Ethan have left?

Number of toy cars = 12 – = =

Ethan has

cars left. eft.

(b) There are 25 balloons att a party. 18 of the balloons burst. p and blow b p 13 1 more balloons. How many The guests help up balloons are at the e party part now? n

Number balloons = 25 – Numb mber er of ba balloon = =

So,, there th are

balloons at the party now.

123

Wyatt has 27 baseball cards. He shares his cards equally among himself and his two brothers. His mother then gives Wyatt tt four more w? packs of two cards. How many cards does Wyatt have now?

Re ga le du ca tio n

(c)

Number of cards = 27 ÷ = = =

So, Wyatt has

cards now. w.

(d) Jordan is helping his Dad the d paint th house. They use 20 literss of paint on he ho hou d 40 4 liters the outside of the house and of paint on the he inside de of the th house. They then paintt the shed usin using 3 tins u of 2-liter paint. How much muc paint pa did Jordan and his Dad use? us

Amount 20 + Amoun ount of paint = 2 = = =

So, they used

1 24

liters of paint.

Find the values. (b) 96 – 3 + 7

Re ga le du ca tio n

(a) 96 – (3 + 7)

(c)

96 + 3 – 7

(d) 96 + (77 – 3)

Which of the following is correct? your working. orrect? ct? Show y yo (a) 12 + 2 x (4 + 4) ÷ 2 = 14 4 x (4 + 4) ÷ 2 = 14 x 8 ÷ 2 = 112 ÷ 2 = 56 5

(b) 12 + 2 x (4 + 4) ÷ 2 = 12 2+2x8÷2 = 12 + 16 ÷ 2 = 28 ÷ 2 = 14 (c)

12 + 2 x (4 + 4) ÷ 2 = 12 + 2 x 8 ÷ 2 = 12 + 16 ÷ 2 = 12 + 8 = 20

125

At Home

Re ga le du ca to n

1. Fill in the blanks.

(a) Halle has 17 pots. She breaks 11 of them. She buys 4 more pots. Halle then shares her pots equally among herself and three friends. How many pots does she have left now? Number of pots = 17 – = = =

So, there are

pots left. ft.

ke ride. de. She rides (b) Keira is going on a bike e to the park and an 7 km from her home he mall. She Sh S then then a further 3 km to the rides to her friend's at a pace of nd'ss house nd h p 5 minutes per km. her 20 minutes to get to her friend's m. It takes take ta house from the mall. How fa far did Keira ride in total?

Distance nce rode = = =

So, sh So, she rode

1 26

km in total.

Find the values. (b) 54 – (4 – 3)

Re ga le du ca tio n

(a) 54 – (4 + 3)

(c)

54 + (4 – 3)

(d) 54 + 4 + 3

ct? Show your y Which of the following is correct? working. 6 x (9 + 12) ÷ 3 (a) 42 – 6 x (9 + 12) ÷ 3 = 36 = 36 6 x 21 ÷ 3 = 36 x 7 = 252 2 25

(b) 42 – 6 x (9 + 12) ÷ 3 = 42 – 6 x 21 ÷ 3 = 42 4 – 126 1 ÷3 = 42 – 42 =0 (c)

42 – 6 x (9 + 12) ÷ 3 = 42 – 6 x 3 + 12 = 42 – 18 + 12 = 24 + 12 = 36

127

Word Problems

tio n

Let’s Learn

Re ga le d

Mr. Langston owns a flower store. He buys 212 bouquets off roses ses and 4 boxes of tulips. Each box of tulips contains 82 bouquets. s. How w many bouquets did Mr. Langston buy in all?.

Step 1 First, let’s find the total numberr of bouquets of tulips. bouqu 82

tulips

To find the total of tulips, we multiply. otal number of o bouquets bou

8 2 4 x 3 2 8

82 x 4 = 328 3 The total al number nu numbe of bouquets of tulips is 328.

1 28

Step 2 Let's find the total number of bouquets.

roses

328

ed uc ati on

212

tulips

To find the total number of bouquets, we add.

2 11 2 3 2 8 5 4 0

212 + 328 = 540 The total number of bouquets iss 540. 0.

Check Let’s use rounding and estimation mation ion to check chec che that the answer is reasonable. Tulip bouquets = 328 ≈ 330 0 Rose bouquets = 212 ≈ 210 330 + 210 = 540 540 is equal So, the answer is reasonable. ual to o our answer. So

129

A jewelry store is making necklaces. The store has 338 beads. Each necklace uses 26 beads.

Re ga le du ca tio

(a) Find the total number of necklaces that can be made with the beads. Check that your answer is reasonable.

Let’s use a model to help find the answer. 26 beads

necklaces

26 3 3 8 2 6 0 1 0 7 8 7 8 3 0

338 ÷ 26 = 13 The jewelry store ore can make 13 necklaces.

Check Let’s check ck that hat the answer answ is reasonable. 300 ÷ 30 ≈ 10 0

10 0 is close clo ose to 13, so our ou answer is reasonable.

130

Re ga le du ca tio n

(b) The necklaces are sold for $1,428 each. How much money does the store receive if all of the necklaces are sold? Check that your is ur answer ans reasonable. $1,428

1 necklace

1 necklace 1 shirt

To find the total amount of money, we multiply. ply. 1 4 2 x 1 4 2 8 1 4 2 8 1 8 5 6

8 3 4 0 4

The store will receive $18,564. 4.

Check Let’s use rounding and estimation that the answer is mation to check c reasonable. 1428 ≈ 1,400 and 13 ≈ 10 10 x 1,400 = 14,000 000

14,000 is close ose to 18,564, so our answer is reasonable.

1 31

Re ga le du ca tio

Miner Co. mined 3,237 kg of coal from amines. Another mining company, Mineplex, mined 934 times the amount of coal as Miner Co. The 2 companies came together to sell bags of coal to the public. If each bag holds 5 kg of coal, how many bags of coal can be made?

Step 1 ed First, we need to find the total amount of coal mined. Multiply 3,237 by 934 to find the amount of coal mined ned by Mineplex. M

1 9 + 2 9 1 3 0 2

3 2 9 2 9 7 1 3 3 3 3

3 3 4 1 0 5

7 4 8 0 0 8

Mineplex mined 3,023,358 kg off coal. coal Check 3,237 ≈ 3,000 934 ≈ 900 3,000 x 900 = 2,700,000 700,000 00 2,700,000 ≈ 3,000,000 000,000 ,000

3,000,000 is close se to 3,023,358, 3,023, 3,023,358 so the answer er is reasonable. reasonable

132

Both factors were rounded down. So, we expect our estimate to be lower than our actual answer.

Now add to find the total amount of coal

Re ga le du ca tio n

3 0 2 3 3 5 8 + 3 2 3 7 3 0 2 6 5 9 5

3,026,595 kg of coal was mined in total.

Check 3,026,595 ≈ 3,000,000 3,237 ≈ 3,000 3,000,000 + 3,000 = 3,003,000

3,003,000 is close to 3,026,595, so the answer nswer is reasonable. reasona reason Step 2 Divide to find the number of bags. 6 0 5 5 3 0 2 6 3 0 0 2 6 2 5 1 1

3 1 9 5 9 5

5 5 0 9 5 4 5 4 5 0

A total al of 605,319 bags ba can c be made. Check he heck 3,026,595 3,000,000 026,595 ≈ 3,000,0 3,000,000 600,000 0,000 ÷ 5 = 6

600,000 is close to 605,319, so the answer is reasonable.

1 33

Let’s Practice

A nursery is buying some new plants. It buys 17 gum treess and d 3 times as many wattle bushes as gum trees. How many plantss did the nursery buy in total? Check that your answer is reasonable.

Re ga le d

Step 1 Find the number of wattle tle bushes bought. bo b

gum trees

wattless

The wattle bushes bought is e number numbe of w

1 34

ed uc ati on

Check

Step 2 Find the total number of plants bought.

gums

wattles

Re ga

The total number er of plants b bought is Check

1 35

Halle is traveling on a road trip for three days. On the first day, she travels 425 km. On the second day, she travels 3 times as far ar as tthe first. On the third day, she travels 5 times less than on the first day. How far fa does she travel? Check that your answer is reasonable.

Re ga le du ca tio n

1 36

Mrs. Krum buys 1,152 shrimps for her seafood company. She sells a pack of 32 shrimps for $21. Mrs. Krum also buys 5,405 pieces es of fish. fi Each piece of fish sells for $3. How much money will Mrs. Krum m make if she sells all of her stock? Check that your answer is reasonable. sonable. able.

Re ga le du ca tio n

1 37

At Home

tio n

om the he At a farming festival, 125 guests each pick 24 peaches from y between ween orchard. The peaches are collected and shared equally 4 different restaurants. How many peaches does each h restaurant estaurant receive? Check that your answer is reasonable.

Re ga le du

Step 1 Find the total number of peaches es picked. 24

125 25 peopl people peo

A total off

Check ck

1 38

peaches peache pea were picked.

Re ga le du ca tio n

Step 2 Find the number of peaches each restaurant received.

restaurants

Each restaurant received

peaches. ches.

Check

1 39

A bakery bakes 2,593 sausage rolls. A large supermarket bakes 123 times as many sausage rolls. How many sausage rolls were hat your baked by both the bakery and the supermarket? Check that answer is reasonable.

Re ga le du ca tio n

140

Looking Back Add or subtract.

Re ga le du ca tio n

(a)

(c)

(b)

–

(d)

–

(e) 4,864 + 74,046 =

(f) f)

804,405 804, 804,4 – 353,024 =

(g) 6,035,343 035,343 43 + 54,035 54,03 =

(h) 5,038,034 – 1,464,752 =

1 41

Multiply. (a)

(b)

Re ga le du ca tio n

(c)

(e)

142

(d)

(f)

Multiply using the column method. (b) 546 x 66 =

Re ga le du ca tio n

(a) 67 x 34 =

(c)

682 x 27 =

(d)) 3,964 64 x 83 =

Work out the following by multiplying multiplyin rows and columns in a table. Then add the products. uc 604 x 83 = x

1 43

Complete the following. (b)

Re ga le du ca tio n

(a) 4

5 8

(c)

4 9 3

5 6 2 7

6 4 8 7 2

(d) d)

5 9 2 0

(e)

(f)

1 44

6 5 2 7 8

A surfing competition has 234 participants. Each participant pays an entry fee of $56 to participate. Half of the participants paid triple aid trip petition. on. the entry fee to have their board waxed before the competition. eck that How much money did the surf competition receive? Check your answer is reasonable.

Re ga le du ca tio n

A fruit store is stocking up for or the summer summ season ahead. The store buys 694 mangoes. also buy 583 bananas. Each angoes. oes. They al banana sells for $2 and each ch mango mang sells for $3. How much money will the store make e if the th entire re stock sto is sold? Check that your answer is reasonable nable le

1 45

Anchor Task

146

Fractions

1 47

Adding Fractions

Re ga le du ca tio n

Let’s Learn

Sophie draws a circle with 9 equal parts. 2 of the circle blue. 9 5 Riley colors of the circle green. 9

She colors

Find the total fraction of the circle they colored.

5 9

2 9

Add the n numerators and keep the denominators unchanged.

7 9

2 5 7 + = 9 9 9 7 Sophie and Riley ey colored olored of the t c circle. 9 5 1 m of and 12 . Find the sum 12

sim Write the answer in its simplest form. 1 5 6 + = 12 2 12 12 1 =2

148

Divide the numerator and the denominator by 6 to simplify.

3 1 Find the sum of 4 and 8 .

Re ga le du ca tio n

To add unlike fractions, make the denominators all the same!

3 4

6 8

1 8

6 1 3 1 + = + 4 8 8 8 7 = 8

Find the sum of

1 7 and . 3 12

1 3

4 12

7 4 7 1 + = + 3 12 12 12 11 = 12

1 49

1 1 and 3 4. To make the denominators equal, we need to find the lowest common mmon multiple of the two denominators. Let's find the lowest common mon multiple mult of 3 and 4.

Re ga le du ca tio n

Find the sum of

Multiples of 3 Multiples of 4

3 4

6 8

9 12

12 16

15 20

18 24

21 28 8

24 32

27 36 3

30 3 40

The lowest common multiple is 12. Multiply each the h fraction action to make ma m denominators 12. x4

1 3

4 12

1 4

4 12 2

3 12

Now we can add.

4 12

4 3 1 1 + = 3 4 12 + 12 1 7 = 12

150

3 12

3 12 1

7 12

2 1 Find the sum of 7 and 5 5 7

10 14

15 21

20 28

25 35

30 42

2 1 10 7 + 7 5 = 35 + 35 17 = 35 Jordan folds two pieces of paper, each into 8 equal parts.

35 49

40 56 6

45 63

50 0 70

tio n

Multiples of 5 Multiples of 7

7 8 of the first piece blue. 1 nge. He colors 4 of the second piece orange.

Re ga le du c

He colors

Find the total fraction of paper Jordan colored.

7 1 7 2 + = + 8 4 8 8 9 = 8 1 =18

1 Jordan colored olored 1 8 of the pieces of paper in total. olo

1 51

Keira and Riley each have similar shaped pancakes for breakfast. 1 pancakes. 2 3 Riley eats 2 pancakes. 4

Re ga le du ca tio n

Keira eats 1

Find the total number of pancakes that Keira and Riley ate.

1 2 Add the whole numbers. 1

3 4

Add the fractions. +

1 2

3 4

3 1 1 3 +2 =3+ + 4 2 2 4 2 3 =3+ + 4 4 5 =3+ 4 1 =3+1+ 4 1 =4 4

Keira and Riley ate 4

152

2 4

3 4

1 4

Or we can add the d whole numbers and y. fractions separately.

1 pancakes in total. 4

3 5 and 3 . 4 6

Re ga le du ca tio n

Find the sum of 1

Add the whole numbers.

1+3=4

Add the fractions.

7 12

9 10 3 5 +3 =1 +3 12 12 4 6 7 =1 +4 12 7 =5 12

153

Let’s Practice Write the fractions and add. Write the answer in its simplest est form. orm.

Re ga le du ca tio n

(a)

(b)

(c)

(d)

154

Write the fractions and add. Write the answer in its simplest form.

Re ga le du ca tio n

(a) +

(b)

(c)

Complete the table and find d the lowest common multiple of each number set.

(a) 2, 3

Multiples of 2

Multiples off 3

(b) 3, 4, 6

Multiples ultiples of 3 Multip Multiples of 4

Multiples of 6

155

Find the equivalent fractions

(a)

2 = 8 4

(b)

4 = 8 7

(c)

4 = 10 5

(d)

5 = 7 14

(e)

3 = 4

(f)

5 = 10 9

(g)

2 = 6 3

(h)

5 = 10 8

(i)

4 = 12 5

(j)

1 = 3 9

(k)

7 = 14 9

(l)

4 = 6 12

(n) n)

7 = 21 8

(o)

6 = 10 5

(q) (q

2 = 10 5

(r)

1 = 9 18

(t (t)

3 = 16 8

(u)

11 = 24 12

(x)

13 = 14 28

Re ga le du ca tio n

(m) 1 = 2

156

(p)

1 = 11 22

(s)

2 = 12

(v)

3 = 9 3

(w)

1 = 6 10

(y)

3 = 6 2

(z)

1 = 4

Find the equivalent fraction and add. 1 1 1 + = + 2 4 4 4

Re ga le du ca tio n

(a)

(b)

2 3 + = 4 8

3 8

(c)

3 1 3 + = + 9 3 9 9 =

(d)

2 1 1 + = + 3 6 6 6 =

(e)

4 4 4 + = + 7 14 14 1 14 =

157

Find the equivalent fraction and add. Use the space to show your working. Write the answer in its simplest form.

Re ga le du ca tio n

1 58

(a)

1 1 + = 5 4

(b)

1 1 + = 2 6

(c)

3 2 + = 6 3

(d)

1 2 + = 3 7

(e)

4 3 + = 5 4

(f)

3 1 + = 11 2

(g)

6 5 + = 7 12 2

(h)

2 9 + = 3 10

(i)

6 5 + = 8 9

Fill in the blanks. Write the answer in its simplest form. (a)

3 1 + 4 3

(b)

4 5 + 7 6

Re ga le du ca tio n

(c)

1 = 3

5 = 6

2 2 + 9 5

(d)

3 1 +1 8 12

2 = 5

1 = 12

159

Find the equivalent fraction and add. Use the space to show your working. Write the answer in its simplest form.

Re ga le du ca tio n

(a) 1

1 8 + = 4 9

(b) 2

(c)

160

6 3 + = 8 5

2 1 +1 = 7 3

(d) 3

1 2 + = 7 4

(e) 4

3 3 +2 = 5 4

(f)

3 1 +5 = 12 4

(g) 2

6 3 +1 = 9 11

(h)

4 2 +6 = 7 3

(i)

7 2 +6 = 8 3

Solve It!

Re g

tio n

Jordan is baking a cake. He uses the recipe shown below. Jordan rdan adds all of the ingredients into a bowl and decides to add some ome more ingredients. He adds another quarter ounce of cocoa powder, wder, r, two and a third ounces of flour and three-eighths of an ounce nce off sugar. How much does the uncooked cake mixture weigh in ounces?

The cake mixture weighs

ounces.

1 61

At Home Write the fractions and add. Write the answer in its simplest est form. orm.

Re ga le du ca tio n

(a)

(b)

(c)

(d) d))

1 62

Find the first two equivalent fractions. (a)

(b)

(c)

5 = 6

(e)

2 = 7

(g)

7 9

3 = 4

(d)

7 = 11

(f)

3 = 5

(h))

1 = 3

(i)

8 = 13

(j)

6 = 9

(k)

2 = 7

(l)

11 = 12

(m) 10 = 9

(n)

13 = 12

(o)

(p)

1 = 14

(r)

6 = 7

Re ga le du ca tio n

1 2

(q)

3 = 10

1 1

1 63

Find the equivalent fraction and add. Write the answer in its simplest form.

Re ga le du ca tio n

(a)

1 1 3 + = + 3 2 6 6

(b)

(c)

2 1 1 + = 4 8

1 8

(d)

(e)

5 2 5 + = + 5 10 10

1 7 1 + = + 7 11 77 777

(f)

4 1 4 + = + 2 18 18

1 64

+ 5 8

9 8 3 + = + 6 14 42

(h)

(i)

3 + 5 = 4 8

(g)

2 1 1 + = + 7 21 21 21

4 2 + = + 2 12 3 3 3 =

(j)

1 3 + = 2 18

Find the equivalent fraction and add. Use the space to show y your working. Write the answer in its simplest form.

Re ga le du ca tio n

(a)

8 1 + = 9 3

(b)

9 3 + = 12 4

(c)

9 1 + = 18 2

(d)

1 2 + = 5 10

(e)

4 9 + = 6 27

(f)

5 8 + = 11 10

(g)

6 1 + = 10 12 2

(h)

2 11 + = 5 15

(i)

5 2 + = 27 3

1 65

Fill in the blanks. 1 5 + 3 6

(b)

8 2 + 9 12

Re ga le du ca tio n

(a)

+ 5 =

(c)

3 2 + 7 10

(d)

1 66

2 1 +1 4 11

Find the equivalent fraction and add. Use the space to show your working. Write the answer in its simplest form.

Re ga le du ca tio n

1 8 + 7 11

(a) 1

(b) 2

6 3 + = 8 5

5 2 +1 8 3

(d) 1

8 1 + 9 4

(e) 7

1 3 +1 = 3 9

(f)

3 1 +6 = 11 12

(c)

(g) 1

6 2 +1 = 10 11

(h)

3 2 +5 = 7 3

(i)

3 2 +6 = 8 7

1 67

Subtracting Fractions

Re ga le du ca tio n

Let’s Learn

Ethan and Wyatt are playing with a rope. The rope is Ethan cuts

9 of a meter long. 10

3 1 of a meter off the rope. Wyatt cuts off a meter off the th rope. 10 10

How long is the remaining rope? 9 10

3 10

1 10

9 1 3 5 – – = 10 10 10 10 1 = 2

When subtracting like fractions, the numerators and leave the ns,, we subtract subt denominator unchanged. ed.

Find the difference ce between etween 4 9

2 9

4 – 2 = 2 9 9 9

168

4 2 and . 9 9

2 1 and . 3 6

Re ga le du ca tio n

Find the difference between

2 3

–

1 6

4 6

–

1 6

4 6

2 – 1 = 4 – 1 6 6 6 3 = 3 6 = 1 2

Express the answer in its simplest form.

Find the difference between n

3 6

1 2

3 3 and . 4 8

3 – 3 = 6 – 3 8 8 4 8 = 3 8

Find the difference ence e between Multiples of 6 Multiples off 8

6 8

12 16

5 3 and . an 6 8 18 24

24 32

30 40

36 48

42 56

48 64

54 72

60 80

owest common multiple mu The lowest is 24. Multiply each fraction to make the nominators 24. Then T denominators subtract. 5 – 3 = 20 – 9 8 24 6 24 2 11 = 11 24

1 69

Dominic buys a 4-liter carton of orange juice. He drinks

2 liters off orange or 3

Re ga le du ca tio n

n in the he carton? carton juice from the carton. How many liters of orange juice remain

4–

2 3 2 =3 – 3 3 3 1 =3 3

Find the difference between n 5 and 5–

2 5 2 =4 – 5 5 5 3 =4 5

Find the difference ce between 1 and 1–

170

2 . 5

2 1 1 = – 2 2 2 1 = 2

1 . 2

3 1 . and 2 . 4 8

Re ga le du ca tio n

Find the difference between 5

1 3 1 3 –2 =3 – 8 4 8 4 6 1 =3 – 8 8 5 =3 8

1 71

Let’s Practice Label the fraction model and complete the subtraction. Write the answer in its simplest form.

Re ga le du ca tio n

(a)

7 10 –

–

(b)

(c)

–

(d)

172

Find the equivalent fraction and subtract. Write the answer in its simplest form.

Re ga le du ca tio n

(a)

5 – 1 = 6 12

–

(b)

3 – 1 = 2 4

–

(c)

4 – 2 = 5 15

–

(d)

7 – 1 = 8 3 18

–

(e)

19 – 3 = 20 4

–

((f)

2 – 7 = 3 12

–

(g) g)

4 5 – = 7 21

–

(h)

17 – 1 = 32 8

–

1 73

Fill in the blanks to find equivalent fractions. Then subtract. Write the answer in its simplest form. (a) Multiples of 4: 4, 8,

Re ga le du ca tio n

Multiples of 6: 6, 12,

3 4

1 6

3– 1 = 4 6

–

(b) Multiples of 8:

Multiples of 10:

7 8

174

3 10

7 – 3 = 8 10

–

Multiples of 10:

Multiples of 12:

Re ga le du ca tio n

(c)

3 10

1 12

3 – 1 = 10 12

–

(d) Multiples of 9:

Multiples of 6:

8 9

5 6

8– 5 = 9 6

–

1 75

Subtract. Write the answer in its simplest form. –

(b) 7 – 4 = 6 9

–

Re ga le du ca tio n

(a) 4 – 2 = 3 5 =

(c)

5–12 =3 7 =

–

(d) 6 – 4 3 = 3 4

–

Subtract. Use the space provided working. ovided ed to show your y Write the answer in its simplest mplest form. for

(a) 6 1 – 2 2 = 3 2

(b) 3 3 – 1 2 = 5 4

5 1 –33 = 8 4

(d) 7 8 – 6 7 = 12 9

(c)

176

Solve It!

Re ga le du ca tio n

Halle and Sophie are carrying bags of soil to their vegetable patch. h.

ns 2 5 kg of so soil. Halle's bag contains 4 7 kg of soil and Sophie's bag contains 8 8 (a) Find the combined mass of soil in their bags. (b) Halle gets tired as her bag of soil is too heavy. Sophie phie suggests she takes some of Halle's soil so that they each have weight. ave an equal we How much soil does Sophie need to take from om Halle? Draw a model to help find the answer. Show w your working. work

1 77

At Home Find the equivalent fraction and subtract. Write the answer in its simplest form.

Re ga le du ca tio n

(a)

3 – 3 = 8 4

–

1 – 5 = 9 2

(b)

(c)

–

5 – 1 = 6 12

–

7 – 1 = 15 3

(d)

–

Fill in the blanks to find equivalent uivalent fr frac fractions. Then subtract. Write the answer in its simplest mplest plest form. form Multiples of 9:

Multiples of 12::

7 9

7 – 5 = 9 12

178

5 12

–

Subtract. Use the space provided to show your working. Write the answer in its simplest form.

Re ga le du ca tio n

(a) 2 1 – 1 2 = 5 2

(c)

33 –3 1 = 5 4

(b) 3 3 – 3 1 = 5 4

(d) 10 2 – 4 1 = 8 7

(e) 7 2 – 4 5 = 12 9

(f)

2 1 –1 5 = 24 4

(g)) 8 7 – 2 1 = 4 16 6

(h) 5 8 – 1 2 = 3 15

1 79

Multiplying Fractions

Re ga le du ca tio n

Let’s Learn

Halle is baking cakes for the school fair. The recipe requires a

2 cup of sugar per cake. 3

She plans on making 5 cakes.

How much sugar will she need in total?

1 3 1 3

1 3 1 3 1 3

1 3

10 = 3 1 3 3

Multiply ply the or by the numerator hole number. whole hen simpli Then simplify.

5x 2 = 5x2 3 3 = 10 = 3 1 3 3

When hen m multiplying a fraction by a whole number, we multiply the numerator by the who number. Then simplify if possible. whole num Halle needs 3

180

1 cups of sugar in total. 3

Multiply

5 by 4. 6 Remember to write the fraction in its simplest form.

Re ga le du ca tio n

5 4x5 = 4x 6 6 20 = 6 1 2 =3 =3 3 6

When multiplying a proper fraction by a whole number, is less mber, the product pro than the whole number. A brick has a mass of 3

3 kg. Find the mass ass off 4 such bricks. b br 4

3 4

4x3

3 15 =4x 4 4 4 x 15 = 4 = 15 5

12 = 3 4

3 3 4 is a mixed number. So we expect the product to be greater than 4!

When multiplyin multiplying a m mixed number by a whole number, we convert the mixed xed nu number into an improper fraction. Then we multiply and simplify. When multiplying an improper fraction or mixed number by a whole ult ultiplyi number, the product is greater than the whole number.

1 81

6x2

5 21 =6x 8 8 6 x 21 = 8 126 = 8 6 3 = 15 = 15 8 4 5 3 = 15 8 4

ed uc ati on

5 Find 6 x 2 . 8

1 8 1 2 8 4 4

5 6

5 16 + 5 211 28 = = 8 8

6 0 6

Mr. Lovato is building a gate. He e usess wood planks plan pla that each have a

2 in. A total of 14 such h planks are used and there are no gaps 5 between the planks. Find the total otal width of the gate. width of 8

182

2 by 14 to find the total width of the gate. 5 588 ÷ 5 is 117 17 R 3. 2 40 + 2 3 x 14 8 x 14 = The productt is 117 . 5 5 5 42 4 2 1 1 7 = x 14 x 1 4 5 5 5 8 8 588 1 6 8 5 = 4 2 0 0 8 5 5 8 8 5 3 = 117 3 8 5

Re ga le du ca tio n

Let's multiply 8

3 5 3

The gate has a width of 117 Jordan brought

3 in. 5

4 of a banana cake 5

to school to share with his friends. They ate

2 of the cake Jordan brought. ght. 3

ana What fraction of the whole banana cake did Jordan and his friends endss eat? 4 of whole 5

When both factors are proper fractions, the product is less than both factors.

4 2 of 5 3

4 2 4x2 x = 5 3 5x3 8 = 15

When a fraction by a fraction, multiply the numerators and the en multiplying mu denominators. simplify if possible. inators. Then inato T Jordan and his friends ate

8 of the whole banana cake. 15

1 83

Find

3 3 of . 4 4

Re ga le du ca tio n

3 3 3x3 x = 4 4 4x4 9 = 16

3 4

3 9 3 of is . 4 16 4

3 3 of 4 4

Find the product of 2 3 2x3 x = 3 8 3x8 6 = 24 1 = 4

3 2 and . 8 3

2x3 3 2 3x8 = 3 x 8 2 =1x 8

3 8

3 2 of 8 3

The product of

2 3 1 and is . 3 8 4

Find the product oductt of o

8 3 and . 5 4

3 8 3x8 x = 4 5 4x5 24 2 = 2 20 1 =1 5

The product ct of o

184

8 5 is an improper fraction.

3 8 1 and is 1 . 4 5 5

Let’s Practice Complete the following. Show your working and write your ur answer nswer in its simplest form.

Re ga le du ca tio n

(a)

4 x3 5

(b) 6 x

(c)

2 x4 3

(d)) (d

2 x8 7

3 4

(f)

5 x 10 12

(e)) 9 x

3 8

1 85

Multiply the fractions. Show your working and write your answer in its simplest form. 1 3

(b)

6 x3 7

Re ga le du ca tio n

(a) 10 x

(d) 5 x

3 4

7 x6 12

((f)

2 5

7 18 1

(h)

4 x 10 15

(c)

(e)

(g) 3 x

186

4 9

Multiply the mixed numbers. Show your working and write your answer in its simplest form. (a) 2

1 x4 2

Re ga le du ca tio n

(b) 3 x 3

(c)

3 4

7 x6 8

1 87

Multiply the mixed numbers. Show your working and write your answer in its simplest form. 2 x2 7

(b) 2

2 x5 3

Re ga le du ca tio n

(a) 5

(c)

4x1

(e) 5

5 6

2 x 10 5

(g) 20 x 8

188

(d) 9 x 2

1 3

(f) (

1 2

7 x4 10

(h) 12 x 3

4 5

Color squares in the rectangle to show the product of the fractions. Write the product in its simplest form. (a)

2 1 x 2 3

(b)

3 1 x 3 4

(c)

2 2 x 3 3

(d) (d

1 4 x 5 2

(e)

5 2 x 8 3

(f)

4 5 x 5 6

Re ga le du ca tio n

1 89

Multiply the fractions. Show your working and write your answer in its simplest form. (a)

1 1 x 2 4

(b)

1 3 x 5 2

(c)

3 3 x 4 4

(d)

5 2 x 3 5

(e)

7 3 x 2 4

(f) (

7 2 x 9 3

(g)

4 3 x 5 111

(h)

5 8 x 6 3

Re ga le du ca tio n

190

Hands On

Re ga le du ca tio n

Work in pairs.

(a) Use the grid below to draw a rectangle. Lightly shade rectangle blue. Color

1 off the 2

1 of the shaded part green. Write the fraction fractio of fract 3

the rectangle that is colored green.

w to draw d recta (b) Use the grid below a rectangle. Lightly shade w. Color olor rectangle yellow.

1 of the 4

2 of tthe shaded part red. Write the fraction of o 3

le that at is colored colore red the rectangle red.

1 91

(c)

Use the grid below to draw a rectangle. Lightly shade

2 of the shaded part blue. Write the fraction raction of o 3

Re ga le du ca tio n

rectangle yellow. Color

3 of the he 4

the rectangle that is colored blue.

(d) Use the grid below to draw w a rectangle. recta rectangle Lightly shade rectangle red. Colorr

1 of the he shaded shade part green. Write the fraction of 4

at is colored color green. the rectangle that

192

5 of the 6

At Home Complete the following. Show your working and write your ur answer nswer in its simplest form.

Re ga le du ca tio n

(a)

4 x3 7

(b) 6 x

2 3

(c)

5 x6 8

(d) (d d) 8 x

5 6

(e) 6 x

3 4

(f)

7 x3 9

1 93

Multiply the mixed numbers. Show your working and write your answer in its simplest form. 4 x4 5

Re ga le du ca tio n

(a) 4

(b) 2 x 3

5 8

(c)

2 3

4x2

(e) (e 12 x 4

1 94

1 8

(d) 7 x 3

3 5

(f)

3 12

8x5

Color squares in the rectangle to show the product of the fractions. Write the product in its simplest form. (a)

3 2 x 4 3

(b)

1 4 x 5 2

(c)

1 2 x 7 4

(d)

5 3 x 8 4

Re ga le du ca tio n

Multiply the e fractions. actions. Show Sho your yo working and write your answer in its simplest est form.

(a)

3 3 x 4 5

(b)

15 2 x 4 5

1 95

Solve It!

tio

Help the rabbit return to its burrow by multiplying the numbers rs and d fractions. fractio

1 x4 2

1 2

1 3

1 2

2 3 x

1 2

5 12 12

196

1 5

3 8

Fractions and Division

Re ga le du ca tio n

Let’s Learn

Keira and her 3 friends share 3 cakes equally. Find the fraction ction n of cake e ea each person receives.

You can think of a fraction as tthe merator divided d numerator by he denominator! denom the

3 ÷ 4 = 1 of 3 4 = 3 4

Each person receives es

3 of a cak cake. c 4

ipe requires 12 liters lit A fruit punch recipe of pineapple juice to make 8 jugs of punch. Find juice in each jug. d the volume of pineapple pine 1 off 12 1 8 12 = 8 1 3 = =1 2 2

12 ÷ 8 =

Each jug contains 1 nt

Here we have an improper fraction. Simplify if possible.

1 liters of pineapple juice. 2

1 97

Ethan has

2 meters of string. He cuts the 3

Re ga le du ca tio n

string into 4 pieces of equal length. Find the length of each piece of string. 2 m 3

2 1 of m 3 4

2 1 2 ÷ 4 = of 3 4 3 2 1 = x 4 3 1 2 = = 12 6

Dividing ividing by 4 is thee same as 1 multiplying by 4 !

Each piece of string has a length ength th of

Find

3 ÷ 5. 4

3 1 3 ÷ 5 = of 4 5 4 3 1 = x 5 4 3 = 20

3 3 ÷5= 20 4

1 98

3 4

3 1 of 4 5

1 meters. m me 6

Blake is baking raspberry tarts. Each tart requires

2 cup of raspberries. Blake has a 3

Re ga le du ca ti

total of 4 cups of raspberries. How many tarts can he make?

2 3

raspberries

1 cup

4÷

1 cup

2 3 =4x 3 2 4x3 = 2 12 = 2

1 cup

2 Dividing by 3 is the same 3 as multiplying m by 2 !

Blake can make 6 raspberry aspberry erry tarts. ta tart

Find 8 divided by

8÷

3 . 5

5 3 =8x 3 5 40 = 3 1 = 13 3 3

8 divided d by

3 1 = 13 5 3

1 99

Let’s Practice Complete the following. Show your working and write your ur answer nswer in its simplest form.

Re ga le du ca tio n

(a) 10 bags of flour are used to make 12 cakes. How w many any bags of flour are used in 1 cake?

(b) 14 pizzas are ordered to feed 8 guestss at a pa party. party Each guest received an equal amount of pizza. much pizza does each a. How muc guest receive?

(c)

6÷4

(e) 8 ÷ 20

20 0

(d) 10 ÷ 4

(f)

9 ÷ 27

Use the model to help divide the fractions. Write the answer in its simplest form 1 ÷5 2

(b)

7 ÷4 8

Re ga le du ca tio n

(a)

Complete the following. Show your ur working rking and write w your answer in its simplest form.

(a)

1 ÷ 10 2

(b) (b)

4 ÷6 5

(c)

8 ÷2 3

(d)

11 ÷8 5

(e) (e)

4 ÷6 7

(f)

2 ÷ 10 3

2 01

Use the model to help divide whole numbers by fractions. Write the answer in its simplest form (a) 3 ÷

2 5

(b) 4 ÷

2 9

Re ga le du ca tio n

20 2

Complete the following. win Show ow your working and write your answer in its simplest form.

(a) 10 ÷

1 2

(b) 8 ÷

3 4

(c)) (c

2 5

(d) 8 ÷

2 7

12 ÷

Solve It!

Help the clown fish return to its home by dividing the fractions. s.

÷ 1 6

÷ 5 8

1 2

÷4 ÷ 3 10

÷ 1 4

÷6

Re g

÷ 10

÷ 5 12

÷ 3 5

÷ 1 9

÷ 16

2 03

At Home

(a) 3 ÷ 9

(c)

5 ÷ 20

Re ga l

(e) 12 ÷ 8

ed uc ati on

Complete the following. Show your working and write your answer nswer er in its simplest form. (b) 10 ÷ 6

(d) 6 ÷ 10

(f)) (f

2 ÷ 18

(g)

2 ÷3 3

(h) (

6 ÷8 7

(i)

5 ÷ 10 2

(j)

8 ÷4 3

20 4

5 ÷6 4

(l)

3 ÷6 10

Re ga le du ca tio n

(k)

(m)

14 ÷7 3

(n)

4 ÷ 12 9

(o) 3 ÷

4 7

(p) 6 ÷

2 3

(q) 12 ÷

5 3

((r)) (r

8÷

3 4

(s)

7 3

(t)

10 ÷

16 7

9÷

2 05

Let’s Learn Jordan is making an apple pie. He uses 1

3 1 kg green apples and 2 kg red apples. 4 2

Word Problems

Re ga le du ca t

Find the total mass of apples used.

3 1 3 1 +2 =3+ + 4 2 4 2 2 3 =3+ + 4 4 5 =3+ 4 1 =3+1 4 1 =4 4

Jordan uses 4 Sophie has

She uses

1 kg of apples. es. 4

5 kg of diced iced ced tomato. tom to 6

2 of the tomato mato to make ma e 3

ow much diced pizza sauce. How tomato did she he use?

5 2 5 2 of = x 6 3 6 3 10 = 18 5 = 9

Sophie used

206

5 kg 6

5 kg of diced tomato. 9

5 2 of kg 6 3

Ms. Wardi took 192 mangoes to sell at a farmers' market. She sold d

1 of the 2

1 of them in the afternoon. 3

Re ga le du ca to n

mangoes in the morning and

1 2

1 3

(a) How many mangoes did Ms. Wardi ardi sell in a day? day 1 2 3 2 + = + 2 3 6 6 5 = 6

She sold

5 of her er mangoes. mangoes mango Let's find the number of mangoes sold. 6

5 5 x 192 2 of 192 = 6 6 960 60 = 6

1 9 2 x 5 9 6 0

= 160

1 6 9 6 3 3

6 0 6 0

6 6 0

mangoes. Ms. Wardi Wardi sold 1160 m

(b) mangoes did she have left? b) How w many m man 192 32 92 – 16 160 = 3

She had 32 mangoes left.

2 07

Riley had 240 stickers. She gave stickers to her sister. She gave

1 of the 4

1 of the 5

Re ga le du ca tio

y remaining stickers to her brother. How many stickers did she give to her brother? 240

given to sister

I gave my 1 3 brother of 5 4 of my stickers.

given to brother

3 1 3 1 of = x 4 5 4 5 3 = 20

Riley gave

3 of her stickers to her brother. brothe broth 20

3 x 240 3 of 240 = 20 20 3 x 24 = 2 72 = 2 = 36

10 3 x 240 3 x 24 = x 10 20 2 3 x 24 = x1 2 3 x 24 = 2

ey gave 36 stick stickers tto her brother. Riley

208

There is a common factor of 10. We can simplify!

12 x 2

18 4 = 12 x 7 7 12 x 18 = 7 216 = 7 6 = 30 7

1 x 1 9 1 2 2 1

2 8 6 0 6

4 kg. Find the mass of 12 such cans. ans. 7

du ca tio n

A can of lentils has a mass of 2

3 0 7 2 1 6 2 1 0 6

12 cans of lentils has a mass of 30

6 kg. 7

Michelle is pouring water from a cooler into cups. The cooler contains c 12 liters of water and each cup can hold

3 liters of w water. How many cups 8

Re ga

ater?? can she fill with the 12 liters of water?

We need to divide de 12 by

12 ÷

3 . 8

8 3 = 12 x 3 8 9 96 = 3 = 32

Michelle 32 cups of water. e ca can fill 3

2 09

A plank of wood has a length of

3 m. It is cut into 6 pieces of equal ual length. 4

Re ga le du ca tio n

Find the length of each piece of wood.

We need to divide

3 m by 6. 4

3 3 1 ÷ 6 = of 4 4 6 1 3 = x 6 4 1 3 = = 24 8

as a length le Each piece of wood has of

1 m. 8

24 loaves of bread equally d are e divided eq equa among 18 people. What fraction of a loaf does each h person son receive? receiv 24 18 8 4 = 3 1 =1 3

24 ÷ 18 =

Each receives 1 ch person per recei

210

1 loaves of bread. 3

Let’s Practice 3 of them are boys. s. 4 (a) How many girls are playing at the beach?

48 children are playing at the beach.

Re ga le du ca tio n

(b) How many more boys than girls are there?

1 Sophie made 120 muffins to selll at the fair. fai fair She sold of them on 3 5 Saturday and of the remaining maining muffins muff on Sunday. How many 8 muffins did she sell on Sunday? unday? day?

211

Mr. Hopper is tiling his bathroom floor which has a length of 4 m and a 3 m. 4

Re ga le du ca tio n

width of 2

(a) Find the area of Mr. Hopper's bathroom (b) The tiles cost $36 per square meter. How much will it cost to tile the bathroom?

212

4 min to com complete co a full rotation. How long does 9 it take to complete e 5 rotations? rrot s?? It takes a Ferris wheel 8

Halle spent

2 1 of her savings on a new guitar. She spent of the 3 2

Re ga le du ca tio n

remaining money on some new shoes. (a) What fraction of her money did she spend on the shoes? s? (b) She had $42 left over. How much did the guitar cost??

1 Keira picked some flowers garden. of the flowers were roses, wers in her gar ga 3 1 of them were tulips ulips and a the e rest res were daisies. If she picked 10 daisies, 4 how many flowers werss did she pick pic p in all?

213

At Home 2 Ethan has 140 toy cars. He gives his brother of the cars. s. How ow many 7 cars does he have left?

Re ga le du ca tio n

21 4

5 Wyatt is making a poster He colors of the er forr a school presentation. pr 9 1 poster blue and of the he remaining emaining part p green. What fraction of the 2 poster is green?

Mrs. Potter's patio is rectangular in shape with a length of 5 m and a 1 m. She buys new tiles to cover her patio. 3

Re ga le du ca tio n

breadth 3

(a) Find the area of Mrs. Potter's patio. (b) The tiles cost $24 per square meter. How much will it cost to tile the patio?

215

1 Riley bought some candy from the shop. of the candies were er lemon 2 1 buttons, of them were candy corns and the rest were gummy mmy bears. bear 8 If she bought 12 gummy bears, how many candies did d she e buy in all? a

Re ga le du ca tio n

21 6

Looking Back Find the equivalent fraction and add. Use the space to show how your working. Write the answer in its simplest form.

Re ga le du ca tio n

(a)

2 2 + = 7 9

(b) 2

1 3 + = 4 5

(c)

1 2 +1 = 2 3

(d) 4

3 1 +5 = 4 4

(e) 7

1 5 +1 = 3 12

(f)

5 1 +2 = 18 12 2

(g) 1

(h)

7 7 +1 = 8 12 2

3 2 +5 = 19 3

217

Subtract. Use the space provided to show your working. Write the answer in its simplest form.

Re ga le du ca tio n

(a) 2 – 2 = 5

(c)

21 8

3 1 –1 1 = 5 2

(b) 4 – 3 = 8

(d) 5 3 – 1 3 = 12 1 4

(e) 7 5 – 4 4 = 7 9

(f)

9 1 –1 5 = 24 4

(g) g) 8 7 – 2 1 = 4 6 16

(h) 5 8 – 1 2 = 3 15

Multiply. Show your working and write your answer in its simplest form. (a) 3

1 x2 2

(b) 2

3 x3 4

Re ga le du ca tio n

4 7

(d) 4 x 8

2 3

(c)

5x2

(e)

2 1 x 8 3

(f) (

5 4 x 2 9

(g)

1 4 x 3 8

(h)

6 5 x 7 9

219

Complete the following. Show your working and write your answer in its simplest form. (a) 2 ÷ 4

(b) 12 ÷ 18

(c)

(d) 6 ÷ 10

Re ga le du ca tio n

8 ÷ 32

(e) 17 ÷ 6

22 0

(f) (f)

4 ÷ 30

(g)

4 2 ÷ 7 7

(h) 4 ÷

(i)

3 ÷8 5

(j)

3 5

3 ÷4 8

2 of them are boys. 3 (a) How many girls are playing at the park? (b) How many more boys than girls are there?

60 children are playing at the park.

Re ga le du ca tio n

221

5 1 of them to his uncle and of the 6 2 remaining stickers to his aunt. How many stickers did his aunt receive?

Ethan has 72 stickers. He gave

Re ga le du ca tio n

222

3 min to c complete a full rotation. co 7 How long does it take to complete omplete 6 rotations?

It takes a merry-go-round und 1

7 504 people went to the beach on the weekend. of the people ople went 8 on Sunday.

Re ga le du ca tio n

(a) How many people went to the beach on Saturday? ? (b) How many more people went to the beach on Sunday unday ay than Saturday?

223

Decimals

Tenths, Hundredths and Thousandths sandths Anchor Task

224

Let’s Learn

Re ga le du ca tio n

The square is divided into 10 equal al parts.

1 of the square. square 10 0 We can also write this in n decimal form as 0.1. The colored part shows

We read this number er as 'zero point poin one'. Ones

Tenths Tent

decimal p point

There are 10 tenths in 1 whole. 0.1

0.1

01 0.1

0.1

0.1 .1

0. 0.1

0.1

Write and say the decimal by the place value disks. ecimal mal represented re repr

Ones

0.1

0. 0.1

0.1 0

0.1

Ones

0.1

. Tenths .

0.3 zero point three

0.7 zero point seven

225

The square is divided into 100 equal parts. 1 of the he square. quare. 100 mal form orm as 0.0 We can also write this in decimal 0.01.

Re ga le du ca tio n

The colored part shows

We read this number as 'zero ero point zero one'. o Ones

Tenths nths

Hundredths Hund

decimal mal point

There are 10 hundredths in 1 tenth. 0.01

0.01 0.1

00.1 0.01 0. 1 0

0.01 0.1 .11

0.01 0.1

0.01

0.011

0.01

0.1 1

Write and say the decimal ma represented esented by the place value disks.

0.1

0.11

0.011

Ones

Tenths

Hundredths

0 1 0.01

4.25 four point two five

0.01

22 6

0.01 011

0.01 0.01

Lets find the value of each digit in the number. 5 . 9

Re ga le du ca tio n

(a)

0 . 0

0 . 9 5

The value of the digit 5 is 5. The value of the digit 9 is 0.9. The value of the digit 2 is 0.02. 5 + 0.9 + 0.02 = 5.92

(b)

3 . 4

0 . 0

0 . 4 3

The value off the e digit 1 is 10. The value of the e digit 3 is 3. The value 0.4. ue off the digit 4 is 0.4 The value alue of the digit 7 is 0.07. 0 10 + 3 + 0.4 + 0.07 = 13.47 13.4

227

Re ga le du ca tio n The square is divided into 1000 equal parts.

4 of the e square. 1000 We can also write this in decimal al form rm as 0.00 0.004 0.004. The colored part shows

We read this number as 'zero o point oint zero zero four'. Ones

Tenths

Hund Hundredths

Thousandths

decimal mal point nt

There are 10 thousandths usandths in 1 hundredth. hu 0.00 0.001 00 01

0.001

0 0.001

0.001

0.011

22 8

Lets find the value of each digit in the number. 8 . 2

Re ga le du ca tio n

(a)

0 . 0

0 . 2 8

The value of the digit 8 is 8. The value of the digit 2 is 0.2. The value of the digit 4 is 0.04. The value of the digit 7 is 0.007 8 + 0.2 + 0.04 + 0.007 = 8.247

(b)

4 . 2

0 . 0

0 . 2 4

The value alue off the digit 6 is 60. 6 The value ue of the digit 4 is i 4. e value lue of the digit 2 is 0.2. The lue of the digit digi 1 is 0.01. The value value of the th digit d The value 9 is 0.009. 60 + 4 + 0.2 + 0.01 0.01 + 0.009 = 64.219

229

Let’s Practice Write the decimal number shown by the colored parts.

Re ga le du ca tio n

2 30

(a)

(b)

(c)

(d)

(e)

(f)

Write the decimal number shown by the colored parts.

Re ga le du ca tio n

(a)

Ones

Tenths

(b)

Ones

Tenths

Hundredths

Tenths

Hundredths

(c)

Ones On

. .

2 31

Write the decimal number shown by the place value disks. (a) 1

0.1

0.11

0.1

0.01

0.1

0.1 .1

0.11

0.1 0

0.01

0.01 0.01

0.1

0.01

0.01 011

0.011

0.01 0

0.001

0.1

0.00 01 0.001

0.0 0.001

0.001

Re ga le du ca tio n

(b)

(c)

(d)

0.01

(e)

23 2

0.01

Write the value of the digit. (b)

(a)

45.88 88

Re ga le du ca tio n

4.8

(c)

(d)

35.003

0.392

Read and write the numbers ers in the place place value chart. place. (a) The three is in the oness place. The eight is in the tenths hs place. he hundredths redths place. p The two is in the Ones

Te Tenths

Hundredths

he one e is in the ones one o (b) The place. The e zero zero is in the tte tenths place. The he two two is in the hundredths place. The six is in the thousandths place. Ones On

Tenths

Hundredths Thousandths

2 33

Write as words.

(b) 4.8 (c)

4.69

(d) 5.294 (e) 2.40 (f)

42.35

(g) 0.023

al ed uc ati on

(a) 0.6

(h) 53.093

Write as decimals.

(a) four thousandths ndths ths

(b) three and nd one ne tenths (c)

en and seven hund h seven hundredths

o hundred ninet (d) two ninety-one thousandths

2 34

(e) 3

4 10

(f)

(g) 5

74 100

(h) 9

5 63 100 56 1,000

Hands On

ati on

Work in pairs to build decimals to the thousandths place using g place ace value disks, number cards, base 10 blocks or any other materials available. able. Take turns in modeling the value of each digit.

Re ga

e chart below. Write down the numbers you create in the place value

Ones

Tenths ths

Hundredths Thousandths

. . . . .

2 35

At Home Match.

Re ga le du ca tio n

0.81

0.96

0.77

0.22

0.60

0.06

23 6

Match.

0.1

Re ga le du ca tio n

0.1

0.01

1 10.3 10.331

0.01

1.52

0.1

0.001 0.00 01 0

0.1

0.11

0.001 0.00 01

0.1

0.11

0.1

14.21

0.001

0.01

0.01 0.0 0

0 011 0.01

0.1 0

0.1 0.

0.1

0. 0.1

0.1

0.001

4.202

1.004

2.6

2 37

Write the value of each digit. Then add the values. 3 . 8

Re ga le du ca tio n

(a)

(b)

8 . 5

5 . 7

238

(c)

Fill in the blanks.

46.9

Re ga le du ca tio n

(a)

(b)

(c)

The 4 is in the

place. It has a value alue of

The 6 is in the

place. It has a value of

The 9 is in the

place. It has a value of

53.18

The 5 is in the

place. ace. It has a valu value of

The 3 is in the

place. It has a value of

The 1 is in the

place. It has ha a value of

The 8 is in the

plac place place. It has a value of

The 2 is in the he

place. It has a value of

The e 3 iss in the

place. It has a value of

The e 0 is in the

place. It has a value of

The 8 is in the

place. It has a value of

The 9 is in the

place. It has a value of

23.089 89 9

2 39

Write as words.

Re ga le du ca tio n

(a) 5.3 (b) 7.38 (c)

24.496

(d) 64.962 (e) 3.594 (f)

6.402

(g) 64.736 (h) 17.343

Write as decimals.

(a) five tenths

ndred d tenths (b) two hundred

(c)

eighty-one hty-one one hundre hundredths

(d) six thousandths

24 0

(e) 4

6 10

(f)

(g) 4

85 100

(h) 7

4 12 100

43 1000

Solve It!

Re ga le du ca tio n

Halle and Sophie are thinking of 4-digit decimals. Use the clues to find their numbers.

All of the digits are even and each digit git is used han 23 and le only once. The number is greater than less than 30. The sum of the digits in the whole numb number places is 6. The digit 6 has a valuee of 6 tenths.

ch digi Each digit is used only once. The number is greater han 40 and lless than 50. The sum of the digits in the than numb places is 6 and the sum of all of the whole number 1 The digit 1 has a value of 1 hundredth. digits is 12.

2 41

Comparing and Ordering Decimals als

eg al ed uc ati on

Let’s Learn

Compare 4.55 and 4.44. Which number is smaller?

Let's write the numbers in a place value chart. Ones

Tenths

Hundredths

Compare the values from left to right.t. The values in the ones place are the e same. Ones

Tenths

Hundredth Hundredths

Move on to compare e the digits in the tenths place. Ones

Tenths

Hundredths

4 tenths ths is smaller than th 5 tenths. So, 4.44 is smaller tthan 4.55. We e write: write

242

4.44 < 4.55

Re ga le du ca tio n

Compare 3.274 and 3.276. Which number is greater? Let's write the numbers in a place value chart. Ones

Tenths

Hundredths

Thousandths dth

ces are the same. The values in the ones, tenths and hundredthss places andths ths place. Move on to compare the digits in the thousandths Ones

Tenths

Hundredths dths

Thou Thousandths

6 thousandths is greater than an 4 thousandths. thousandths We write:

3.276 > 3.274

We can compare decimals on a number line too!

3.274

3.27 27

3.276

3.28

2 43

Let's compare decimals on a number line. (a) Compare 0.46 and 0.49. 49 0.49

Re ga le du ca tio n

0.46

0.4

0.45

0.5

0.49 > 0.46

0.46 < 0.49 0.4

0.49 is greater than 0.46

0.46 smaller than 0.49 46 is smalle

(b) Compare 1.224 and 1.214.

1.224

1.214

1.21

(c)

1.22

1.23

1.224 > 1.214 2

1.214 < 1.224

1.224 is greater than 11.214

1.214 is smaller than 1.224

Compare e 6.615 15 and 6.637. 6.637 6. 6.615

6.61 .61

6.637

6.62

6.637 > 6.615

6.637 is greater than 6.615

244

6.63

6.64

6.615 < 6.637

6.615 is smaller than 6.637

Compare the numbers in the place value chart. Order the numbers from the greatest to the smallest. .

Tenths

Hundredths

Thousandths

Re ga le du ca tio n

Ones

All the digits in the ones and tenths places are the same. redths is greater than Let's compare the hundredths place. 4 hundredths 2 hundredths. So, 3.841 is the largest number. undredths. redths. The remaining numbers both have 2 hundredths. hs place. ce Compare the values in the thousandths usandths usandths. 8 thousandths is smaller than 9 thousandths. So, 3.828 is the smallest number.

3.841

greatest

3.829

85,580 3.828

smallest

Alw Always start by co comparing the digits in the highest p place value.

2 45

Arrange the decimals from the smallest to the greatest.

Re ga le du ca tio n

(a) 0.99, 0.9 and 0.95 0.9

0.95

0.9

0.95

99 0.99

0.9 < 0.95 and 0.9 < 0.99 0.9 is the smallest. 0.9

0.99 9 > 0.95 and 0.99 0.9 > 0.9 0.99 iss the greatest. g greate rea

0.95

smallest

0.99 85,580

greatest

(b) 0.543, 0.548 and 0.546

0.546

0.543

0.54

0.545

0.543

0.546

smallest allestt

(c)

0.55

0.548 85,580

greatest

9.783, 9.781, 81, 9.788 .781 9.781

9.783 783

9.78 9 78

9.788

9.785

9.781

smallest sm

246

0.548

9.783

9.79

9.788 85,580

greatest

Let’s Practice Write the decimal represented by the place value disks. Check the greater number.

Re ga le du ca tio n

(a)

0.1

0.11

0.1

0.11

0. 0.1

0.01 0

0.1

0.001

(b)

1 10

0.1 0

0.01

(c)

0.001 001 011 0.001 0 01 0.001 0.00 0.00 01 0.00 0.001 0 0

0.01 0.01 0.001 0.001

((d)

0.01 0 011 0.0 0.01 0.01 0.01 0.001

0.1

0.01 0.01 0.01 0.001

2 47

Write the numbers in the place value chart and compare.

Re ga le du ca tio n

(a) Compare 3.783 and 3.793. Ones

Tenths

Hundredths

Thousandths sandt

Hundredths Hundr

Thousandths

Hundredths

Thousandths

. .

(b) Compare 6.494 and 6.944. Ones

Tenths

. .

(c)

Compare e 5.893 893 and 5.93. 5.93 Ones es

. . .

248

Tenths

Write the numbers on the number line and compare.

Re ga le du ca tio n

(a) Compare 0.546 and 0.548.

0.54

0.545

is greater than

0.55

(b) Compare 3.435 and 3.456.

3.43

3.44 .44

is smaller er than han

(c)

3.45

3.46

2.37

2.38

Compare 2.356 56 and 2.371. 2.37

2.35

2.36

is smaller s than

2 49

Check the smaller number.

7.948

17.948

(b)

13.853

13.875

(c)

1,204.39

1,204.387 387 87

Re ga le du ca tio n

(a)

Check the greatest number.

(a)

0.34

0.347 .347 47

1.34

(b)

12.033

0.33

12.33

(c)

0.002

0.00 0.005

5.001

Arrange the numbers from m the greatest great gre to the smallest.

(a) 3.673

3.574 3 3.5

(b) 0.385

0.384

(c)

21.475 1.475

0.38

21.478

(d) 9.999

21.476

2 50

4.768

9.9

Solve It!

ed uc ati on

What do you call an alligator in a vest?

To find the answer, arrange the numbers from the smallest greatest. st to o the great greates Write the matching letters in the boxes according to their ir order. de

o t i

v t

Re g

smallest st

0.004

0.044

3.952

1.06

2.03

3.97

3.963

5.118 8

2.401

11.006

1.26

5.109

2.3

5.4

greatest

2 51

At Home Add the place values and compare.

Re ga le du ca tio n

(a) 3 + 0.2 + 0.003 =

3 + 0.2 + 0.01 + 0.003 = >

(b) 20 + 3 + 0.1 + 0.06 + 0.003 = 20 + 3 + 0.1 + 0.06 + 0.004 = >

(c)

9 + 0.001 0.00 .0 1 = 400 + 40 + 3 + 0.3 + 0.09

09 + 0.00 0.0011 = 400 + 20 + 3 + 0.8 + 0.09 >

02 = (d) 0.1 + 0.002 20 + 0.2 =

(e) 300 + 0.9 + 0.0 0.002 =

0 + 0.09 + 0.002 = 300 + 1 + 0.2 >

25 2

Write the numbers in the place value chart and compare.

Re ga le du ca tio n

(a) Compare 4.395 and 4.935. Ones

Tenths

Hundredths

Thousandths sandt

Hundredths Hundr

Thousandths

Hundredths

Thousandths

. .

(b) Compare 9.873 and 9.812. Ones

Tenths

. .

(c)

Compare e 0.112 112 and 1.112. Ones es

Tenths

. .

253

Draw an arrow to show the position of the numbers on the number line. Fill in the blanks.

Re ga le du ca tio n

(a) Compare 2.483 and 2.502.

2.48

2.49

2.5 5

2.51

3.02

3.03

(b) Compare 3.001 and 3.024.

3.01 01

Arrange the numbers from to the smallest. om m the greatest grea gre

(a) 4.395

4.312 4.3

(b) 10.094

10.493

(c)

53.53 3

10.385

56.287 56. 56.2

(d) (d 35.309

53.533

0.039

254

4.295

39.305

Circle the numbers that are smaller than 0.85.

0.856

3.85

0.845

0.325 325

0.5

0.8

0.21

Re ga le du ca tio n

Write the fractions as decimals and compare. are.

(a)

121 = 100

145 = 100

(b)

88 = 10

88 = 100

(c)

130 = 100

40 = 100 00

(d)

570 = 1000

56 6 = 100 00

Use the symbolss >, < and = to fill in the blanks.

(a) 3.64 (c)

3 1.243

(e) 2.002 2 g) 8 (g)

(b) 89.95

89.75

1.254

(d) 15.376

13.563

2.002

8.0 8.001

(f)

35.01

(h) 24.99

1.35

25.003

255

Anchor Task

25 6

Rounding and Estimation

Let’s Learn

Re ga le du

tio n

Michelle weighs 32.46 kg. Round off her mass to the nearest whole e number. numbe

32.46

32.5

When rounding to the nearest whole number, we look at the digit nea nu in the tenths place. The digit in the tenths hs place ce is 4, 4 so s we round down. 32.46 rounded off to the he nearest whole who number is 32. Michelle weighs approximately roximately 32 kg. k o the he nearest whole w Round 18.62 to number. 18.62

18.5

When ro rounding to the nearest whole number, we look at the digit in the tenths place. plac The digit in n the tenths place is 6, so we round up. 18.62 rounded off to the nearest whole number is 19.

257

Round 4.75 to one decimal place.

Re ga le du ca tio n

4.75

4.7

4.75

4.8

he digit in the When rounding to one decimal place, we look at the hundredths place. und up. The digit in the hundredths place is 5, so we round 8. 4.75 rounded off to one decimal place is 4.8.

Halle's Math score was 57.893. Find Halle's score when rounded to two decimal places. pla pl The digit in the thousandths place e is 3, so we round roun down. Rounded off to two decimal places, Halle's sc score is 57.89. 57.893 ≈ 57.89

Find Halle's score rounded to onee decimal place.

2 58

We need to look at the digit in the hundredths place.

Let’s Practice Fill in the missing numbers.

Re ga le du ca tio n

(a)

7.698

7.5

rounded off to the nearest st

whole number is

≈

3.512

(b)

3.55 3.5

3.5

3.6

rounded ded off to

one decimal place pla is

≈

4.128

(c)

4.125

4.12

4.13

rounded off to rou

two decimal decim places is

≈

259

An average beaver weighs 20.5 kilograms. Round the weight to the nearest whole kilogram.

Re ga le du ca tio n

≈

The average beaver weighs about

kilograms. rams. ms.

Sophie runs 5 kilometers in 20.3 minutes. Round the time to the nearest whole minute. ≈

Sophie runs 5 kilometers in about

minutes minutes.

A new book costs $23.78. Round the place. e cost ost to one decimal de ≈

A new book costs about $

There are 365.24 days in n a year. Round the number of days in a year to one decimal place. ≈

There are aboutt

days in a year.

Wyatt is 143.893 tall. Round his height to two decimal places. 3.893 3 centimete centimeters ta ≈

Wyatt att is about

centimeters tall.

liters of water every year. A dam passes passes 123,495.913 123,4 Round the number numbe of liters to two decimal places. n ≈

The da dam p passes about

260

liters every year.

Round the numbers to the nearest whole number. (b) 2.5 ≈

Re ga le du ca tio n

(a) 4.63 ≈ (c)

11.458 ≈

(e) 4.593 ≈

(d) 9.53 ≈

(f)

1,305.5 ≈

Round the numbers to one decimal place.

(a) 6.496 ≈

(b) 11.111 111 ≈

(c)

(d) 3.01 3.0 01 ≈

5.037 ≈

(e) 3.953 ≈

(f)

1.493 493 ≈

10. Round the numbers to two decimal ecimal imal places. (a) 5.001 ≈

(b)) 2.485 2 ≈

(c)

(d) 8.483 ≈

9.940 ≈

(e) 3.507 ≈

(f)

2.690 ≈

2 61

At Home Fill in the missing numbers.

Re ga le du ca tio n

(a)

4.8

4.5

rounded off to the nearest st

whole number is

≈

3.53

(b)

3.55 5

3.5

3.6

rounded ded off to

one decimal place

≈

Round the numbers mbers ers to different differe place values.

(a)

2,697.386 97.386

≈ when rounded to the nearest whole number.

≈ when rounded to one decimal place.

≈ when rounded to two decimal place.

2 62

≈ when rounded to the nearest whole number.r.

Re ga le du ca tio n

(b)

154.396

≈ when rounded ded to one decimal place.

≈ when rounded round to two decimal al places. ces.

Round the numbers to the nearest whole ole number. number

(a) 2.64 ≈

(b) 1.9 ≈

(c)

(d) 6.93 6 93 ≈

4.682 ≈

(e) 7.5 ≈

17.205 ≈

Round the numbers rs to one decimal decima place.

(a) 1.23 ≈

(b) 4.76 ≈

(c)

(d) 77.765 ≈

7.35 ≈

(e) 4.115 ≈

(f))

(f)

9.997 ≈

Round und the numbers to two decimal places.

(a) 1.386 ≈

(b) 7.255 ≈

(c)

(d) 9.752 ≈

6.510 6.510 ≈

(e) e) 99.975 9 ≈

(f)

545.368 ≈

2 63

Looking Back Write as words.

Re ga le du ca tio n

(a) 0.9 (b) 2.5 (c)

8.38

(d) 13.47

(e) 1.493 (f)

0.003

(g) 86.535

(h) 34.351

Write as decimals. als.

(a) eight thousandths ousandths andths

o and d eight tenths tenth (b) two (c)

one e and three hun hundredths

(d) tw two o hundr hundred fforty-one thousandths

(e) 2

6 10

(g) 55

264

64 64 10

(f)

11 86 100

(h) 5

353 1000

Check the smaller number. (a)

2.582

(b)

1.395

13.95

(c)

145.395

145.359 59 9

Re ga le du ca tio n

2.583

Check the greatest number.

(a)

9.99

9.009

(b)

1.603

16.03

1.613

(c)

0.001

0.01

0.1

Arrange the numbers from m the greatest great gre to the smallest.

(a) 6.497

6.5 6

(b) 0.111

0.121

(c)

64.972

89.041 9.041

1.111

8.904 8.9

(d) 13.090

8.403

12.992

139.9

2 65

Circle the numbers that are smaller than 0.901.

0.9

0.325 325

0.344

0.91

0.921

0.899 0.89

Re ga le du ca tio n

Write the fractions as decimals and compare. are.

(a)

35 = 100

135 = 100

(b)

35 = 10

222 = 100

(c)

24 = 100

86 = 100 00

(d)

234 = 1000

23 3 = 100 00

Use the symbolss >, < and = to fill in the blanks.

(a) 5.385 (c)

(e) 4.593 3 (g) g) 9

266

53.8

1.254

4.193

9.0 9.001

(b) 1.021

1.021

(d) 15.376

13.563

(f)

11.23

11.203

(h) 32.406

32.451

Round the numbers to different places values.

Re ga le du ca tio n

when rounded unded d to ≈ the nearest whole number. mber.r

679.875

≈ when hen rounded to one decimal place. lace. ace.

≈ when ro rounded to rou two decimal cimal places.

10. Round the numbers to the nearestt whole number. ole number (a) 3.975 ≈

(b) 3.54 4≈

(c)

(d) 9.9 ≈

2.35 ≈

(e) 1.03 ≈

11.

18.995 ≈

Round the numbers ers rs to one o decimal ecim place.

(a) 5.963 ≈

(b) 2.466 ≈

(c)

(d) 24.395 ≈

3.504 ≈

(e) 2.564 4≈

12.

(f)

68.78 ≈

Round ound the numbers to two decimal places.

(a) 4.647 ≈

(b) 5.496 ≈

(c)

(d) 7.437 ≈

76.567 76.56 76 5677 ≈

(e)) 43.594 43 ≈

(f)

243.549 ≈

2 67

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