Let's Do Mathematics 5 – Worktext A by Regal Education

Workt ext

for learners 10 - 11 years old

Aligned to the US Common Core State Standards

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Workt ext

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for learners 10 - 11 years old

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

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First edition 2021 This edition is published by Regal Education Inc. ISBN 978-1-953591-10-4

This book or parts thereof may not be reproduced in any form, stored in any retrieval system, or transmitted in any form by any means – electronic, mechanical, photocopy, recording, or otherwise – without prior written permission of the copyright owner.

Let’s Do Mathematics

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

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Central to the USCCSS is the promotion of problem-solving skills and reasoning. Let’s Do Mathematics achieves this by teaching and presenting concepts through a problem-solving based pedagogy and using the concrete-pictorial-abstract (CPA) approach. Learners acquire knowledge and understanding of concepts through a guided progression beginning with concrete examples and experiences which then flow into pictorial representations and finally mastery at the abstract and symbolic level. This approach ensures that learners develop a fundamental understanding of concepts rather than answering questions by learned procedures and algorithms. Key features of the series include:

Anchor Task

Angles of Triangles Anchor Task

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

$0.75 each

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$5.25 per pack

$1.45 each

Multiplying

Let’s Learn

Concepts are presented in a clear and colorful manner. Worked problems provide learners with guided step-by-step progression through examples. Series mascots provide guidance through helpful comments and observations when new concepts are introduced.

Operations on Decima ls

Anchor Task

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 kilogram cost? . 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 represents the . cost of 1 kg of pista chio . nuts.

Multiply the

chio nuts costs

3 x 0.3 = 0.9

tenths.

1 . 3

Tens

Multiply the

Tens

Ones

3 . 9

6.83 x 4 = 27.32

3x1=3

ones.

2 1 . 3 x

. .

Tenths

4 . 4

4 using the

od.

6 . 18 3

Tenths

$63.90.

7 27 . 4

77.4 x 6 = 464.4

Tenths

. .

Step 2

column meth

. 4

Find 6.83 x

Ones

. 9

6 using the

7 27 . 4

Ones .

21.3 x 3 = 63.9 So, 3 kg of pista

$21.30 Step 1

Tens

3 6 3 . 9

Find 77.4 x

Multiply the

tens.

2 1 . 3 x

7 27 . 4

6 4 6 4 . 4

column meth

od.

6 . 18 3 4 . 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.

(a)

Let’s Practice

Ones

Tens

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)

increases by The ten thousands digit The numbers increase

Tens

Hundreds

Ones

in each step. 125,000 more

125,000 less

in each step.

The next number in

the pattern is

(b)

2,824,575

1,574,575

The numbers increase

(c)

Millions

4,074,575

Ten Thousands Thousands

Hundreds

Ones

Tens

1,500,000 more

1,500,000 less

in each step.

(d)

+ The next number in

Hundred Thousands

324,575

Hundred Thousands

Millions

Ten Thousands Thousands

Hundred Thousands

Millions

the pattern is

Ten Thousands Thousands

Hundreds

Ones

Tens

10,000 more

10,000 less

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At Home

Classify each triangle .

(a)

Classify each triangle . Choose one classific ation per triangle . (b)

(a)

Right-angled

At Home

Scalene

Isosceles

(b)

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.

Right-angled

(c)

Scalene

(d)

Isosceles

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(c)

Right-angled

Scalene

Isosceles

(e)

(f)

(d)

Right-angled

Scalene

Isosceles

Hands On

ps of 4-5. in your it number Work in grou n. write a 7-dig n and 6 millio As a group, een 5 millio that is betw notebook square. on the start a counter the 2. Place ter forward e your coun dice and mov n on your dice. 3. Roll the spaces show number of the number t complete mus p in the grou 4. Everyone order to move forward. pattern in till nal number with the origi steps 3 to 4 5. Repeat the finish. you reach

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

Solve It!

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

P 20º

R S

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

38º

47º

(c)

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

56º H

m J

44º

120

2. Use the ordered pairs to plot the points

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

Looking Back

Consolidated practice where learners demonstrate their understanding on a range of concepts taught within a unit.

118º

Activities that require learners to apply logical reasoning and problem-solving. Problems are often posed which do not have a routine strategy for solving them. Learners are encouraged to think creatively and apply a range of problem-solving heuristics.

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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? (b)

1 How many students ran further than

(c)

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

6 1 miles? 2

the students who ran 4

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

3 the students who ran 1 4 miles

3 2 1 0

239 238

Contents 2 4 15 26 30 42 55

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

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2 Operations on Whole Numbers Addition and Subtraction Multiplying by 10s, 100s and 1,000s Multiplying by 1 and 2-digit Numbers Dividing by 10s, 100s and 1,000s Dividing by 1 and 2-digit Numbers Order of Operations Word Problems

66 6666 75 89 101 111 120 128 146 148 168 180 197 208

4 Decimals Tenths, Hundredths and Thousandths Comparing and Ordering Decimals Rounding and Estimation 6

224 224 242 256

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3 Fractions Adding Fractions Subtracting Fractions Multiplying Fractions Fractions and Division Word Problems

Whole Numbers

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Anchor Task

Diameter (km)

Mercury

4,879

Venus

12,104

Earth

12,742

Mars

6,779

Jupiter

139,820

Saturn

116,460

Uranus

50,724

Neptune

49,244

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Planet

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Diameter of Planets

Numbers Beyond 1,000,000 Let’s Learn

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

1 ten

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10 ones

100

10 tens

100

1 hundred

100

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100

10 hundreds

1,000

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1,000 1,000

1,000

1,000 1,000

1,000

1 thousand

1,000

10,000

1,000

10 thousands

1 ten thousand

10,000 10,000 10,000 10,000 10,000 100,000

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

10 ten thousands

1 hundred thousand

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

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

1 million

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One million is a one followed by 6 zeros.

10 hundred thousands

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

Ten Thousands

Thousands

Hundreds

Tens

Ones

Hundred Thousands

Ten Thousands

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(b)

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We say: Thirty thousand, five hundred forty. We write: 30,540. Thousands

Hundreds

Tens

Ones

We say: Five hundred forty thousand, nine hundred one. We write: 540,901. (c)

Hundred Thousands

Ten Thousands

Thousands

Hundreds

Tens

Ones

We say: Three hundred fifty-one thousand, four hundred four. We write: 351,404. 5

Millions

Hundred Thousands

Ten Thousands

Thousands

Hundreds

Millions

Hundred Thousands

Ten Thousands

Thousands

Hundreds

Tens

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(e)

Ones

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

Tens

(d)

Ones

We say: Five million, five thousand, four hundred eighty-nine. We write: 5,005,489. (f)

Hundred Thousands

Ten Thousands

Thousands

Hundreds

Tens

Ones

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Millions

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

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(g)

Millions

Hundred Thousands

Ten Thousands

Thousands

Hundreds

Tens

Ones

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

Count on in hundreds. +100

23,098

23,198 +100 159,087

Count on in thousands. (a)

+1,000 14,890

159,187

15,890

23,498 +100

159,287

+1,000

16,890

+1,000

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23,398 +100

+1,000

+100

159,387

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158,987

(b)

23,298

+100

(b)

+100

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(a)

167,213

+1,000

17,890

+1,000

168,213

18,890

+1,000

169,213

170,213

Count on in ten thousands. +10,000

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(a)

46,986

(b)

56,986

+10,000

587,563

+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.

187,620

+100,000

(b)

785,562

Count on in millions. (a)

1,085,562

1,185,562

2,564,236

3,564,236

4,564,236

5,564,236

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7,264,123

8,264,123

9,264,123

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1,000,022

2,000,022

3,000,022

4,000,022

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

2,425,352

+100,000

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

(d)

487,620

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

5,264,123

(c)

387,620

+100,000

985,562

+100,000

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

1,564,236 (b)

287,620

+100,000

885,562

+100,000

87,620

+100,000

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+100,000

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(a)

3,425,352

4,425,352

5,425,352

6,425,352

Let’s Practice 1. Write as numerals and words. Ten Thousands

Hundred Thousands

Ten Thousands

Thousands

Hundreds

Tens

Ones

Hundred Thousands

Thousands

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(b)

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(a)

(c)

Hundred Thousands

Ten Thousands

Tens

Ones

Thousands

Hundreds

Tens

Ones

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Millions

Hundreds

2. Write the numbers. (a) One hundred thousand, fifty-six.

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

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

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

(f) Eight million, six hundred forty-five thousand, eight hundred eleven.

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3. Write in words. (a) 1,758,284

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(b) 4,576,264

4. Count on in 1,000s. ,

(b) 254,

563,573,

, ,

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(d)

5. Count on in 10,000s. (a) 98,546, (c) 8,345,

(d) 265,925,

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(b) 89,354,

(a) 5,856,

6. Count on in 100,000s.

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(a) 530,

(b) 640,240,

(d) 1,542,155,

, ,

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7. Count on in 1,000,000s. (a) 1,754,899, (b) 5,983,085, (c) 879,690,

(d) 3,958,684,

, ,

Hands On

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

Millions

Hundred Thousands

Ten Thousands

Thousands

Hundreds

Tens

Ones

At Home

1. Match.

230,400

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seven hundred ninety thousand, thirty eight

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two hundred thirty thousand, four hundred

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eight million, four hundred forty-four thousand, eighty

8,444,080

650,366

nine million, two hundred thousand, six hundred two

790,038

six hundred fifty thousand, three hundred sixty-six

9,200,602

2. Write as numerals and words. Hundred Thousands

Ten Thousands

Millions

Hundred Thousands

Thousands

Hundreds

Tens

Ones

Ten Thousands

Thousands

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(b)

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(a)

Hundreds

Tens

3. Count on in 10,000s. (a) 98,546, (b) 89,354,

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4. Count on in 100,000s. (a) 54,570,

(b) 2,316,546,

5. Count on in 1,000,000s. (a) 24,641,

(b) 4,234,231,

, ,

Ones

Place Value Find the value of each digit in the numbers shown.

Hundred Thousands

Ten Thousands

Thousands

Hundreds

Tens

Ones

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Millions

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(a)

Let’s Learn

The digit in the millions place is 3. It represents 3,000,000. The digit in the hundred thousands place is 1. It represents 100,000. The digit in the ten thousands place is 2. It represents 20,000. The digit in the thousands place is 4. It represents 4,000. The digit in the hundreds place is 6. It represents 600. The digit in the tens place is 8. It represents 80. The digit in the ones place is 7. It represents 7.

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3,000,000 + 100,000 + 20,000 + 4,000 + 600 + 80 + 7 = 3,124,687

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

The digit in the millions place is 4. It represents 4,000,000. The digit in the hundred thousands place is 6. It represents 600,000. The digit in the ten thousands place is 3. It represents 30,000. The digit in the thousands place is 1. It represents 1,000. The digit in the hundreds place is 2. It represents 200. The digit in the tens place is 5. It represents 50. The digit in the ones place is 1. It represents 1.

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HTh TTh

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(b)

R eg

4,000,000 + 600,000 + 30,000 + 1,000 + 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. 2

1 9 6 0 4 0 0 2 0 0 0 0 0 0 0

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(b)

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 9

4 0

0 0 0 0 0 0 0

The value of the digit 1 is 1,000,000. The value of the digit 4 is 400,000. The value of the digit 6 is 60,000. The value of the digit 3 is 3,000. The value of the digit 2 is 200. The value of the digit 9 is 90. The value of the digit 0 is 0. 1,000,000 + 400,000 + 60,000 + 3,000 + 200 + 90 = 1,463,290

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9 2 0 3 0 0 6 0 0 0 0 0 0 0 0 0 0 0

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1 0 0 0 0 0

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(a)

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(d)

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 + 40 + 3 = 6,782,143 6

6 0 0 0 0 0

2 0 0 0 0 0 0

The value of the digit 8 is 8,000,000. The value of the digit 1 is 100,000. The value of the digit 4 is 40,000. The value of the digit 9 is 9,000. The value of the digit 7 is 700. The value of the digit 6 is 60. The value of the digit 2 is 2. 8,000,000 + 100,000 + 40,000 + 9,000 + 700 + 60 + 2 = 8,149,762

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7 9 0 4 0 0 1 0 0 0 0 0 0 0

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1 2 0 8 0 0 7 0 0 0 0 0 0 0

4 0 0 0 0 0

3 0 0 0 0 0 0

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(c)

Let’s Practice 1. Write the numbers shown in the place value abacus.

HTh TTh

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(a) (b)

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HTh TTh

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(e) (f)

HTh TTh

2. Write the number in its expanded form. (a) 546,540

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(b) 5,265,640

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(e) 6,289,365

3. Write the value of the digit.

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(a) (b)

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

(b)

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(a)

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Solve It!

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

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• The price has 7 digits. • The price is greater than 2 million and less than 3 million. • The price is an even number. • The sum of the digits in the hundreds, tens and ones place is 8. • The digit in the ten thousands place is 5 . • No digit is equal to 4. • All digits are less than 8 and no 2 digits are the same.

House price $ 22

At Home 1. Match the numbers in two ways.

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five hundred sixty-three thousand, eight hundred fifty-nine

3,000,000 + 700,000 + 40,000 + 8,000 + 100 + 60 + 7

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563,859

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

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3,748,167

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5,178,193

569,194

5,000,000 + 100,000 + 70,000 + 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 500,000 + 60,000 + 3,000 + 800 + 50 + 9

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

2. Write the numbers shown in the place value abacus.

HTh TTh

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(a) (b)

HTh TTh

(a)

du ca

3. Write the numbers represented by the place value disks. 100

100

1,000

100

10,000 10,000 1,000

100

1,000

100

1,000

100

1,000,000

100,000 100,000 10,000 10,000

1,000

1,000,000

100,000 100,000 10,000 10,000 100,000

10,000

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100,000

10,000

100,000

1,000

(b)

100

1,000

100

1,000

100

100,000

1,000

1,000,000

100,000

1,000

100

1,000,000

100,000

1,000

1,000,000

100,000

R eg 24

1,000

100

1,000,000

100

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

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(a)

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5. Add the place values.

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

(b) 100,000 + 60,000 + 1,000 + 7 =

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

(e) 3,000,000 + 20,000 + 800 + 4 = (f) 400,000 + 70,000 + 400 + 30 + 2 = (g) 7,000,000 + 600,000 + 10,000 + 8,000 + 800 + 20 + 2 = (h) 4,000,000 + 500,000 + 40,000 + 7,000 + 500 + 60 + 6 =

Powers of 10 and Exponents We can show repeated addition using multiplication.

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10 + 10 + 10 + 10 = 40 4 x 10 = 40

Let’s Learn

x 10

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

x 10

100

x 10

1,000

10 x 10 = 100

10 x 10 x 10 = 1,000

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1 x 10 = 10

1,000 x 10

10 x 10 x 10 x 10 = 10,000

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10,000

exponent.

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

The base is the number that is repeatedly multiplied. The exponent tells how many times the base is multiplied. We write: 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. 1 100 = 1 102 = 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

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1 x 10 x 10 x 10 x 10 x 10 x 10 106 = 1,000,000

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1 x 10 x 10

1 x 10 101 = 10

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

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

So, the distance from Earth to the moon is about 400,000 km.

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Blue whales can reach a mass of 150,000 kg. Find the mass as a whole number multiplied by a power of 10. 150,000 = 15 x 10,000 = 15 x 104

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

Let’s Practice 1. Write in exponent form in numbers and in words. (a) 10 x 10 x 10

(b) 10 x 10 Exponent form:

Word form:

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Exponent form:

Word form:

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Exponent form:

(d) 10 x 10 x 10 x 10 x 10 x 10 Exponent form: 2. Write the number.

(b) 102 =

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(a) 101 =

Word form:

(d) 104 =

(e) 103 =

(f) 106 =

(g) 100 =

(h) 107 =

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3. Write the number. (a) 2 x 102 =

(b) 3 x 101 =

(d) 25 x 103 =

(e) 9 x 105 =

(g) 99 x 102 =

(f) 3 x 106 = (h) 10 x 104 =

At Home Match the numbers in two ways.

tio

1,000

du ca

102

10 x 10 x 10

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104

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101

103

10,000

1 x 10

100

10 x 10 x 10 x 10

10 x 10

Comparing and Ordering Numbers Let’s Learn

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

Ten Thousands

Thousands

Hundreds

Tens

Ones

du ca

tio

Millions

First, compare the values in the millions place. The values in the millions place are the same. Compare the values in the next place – hundred thousands. The values in the hundred thousands place are also the same. Compare the values in the ten thousands place. 3 ten thousands is greater than 2 ten thousands.

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So, 1,432,523 is greater than 1,422,645.

(b) Compare the numbers 3,619,381 and 3,619,728. Hundred Thousands

Ten Thousands

Thousands

Hundreds

Tens

Ones

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Millions

The values in the millions, hundred thousands, ten thousands and thousands are the same. Compare the values in the hundreds place. 3 hundreds is smaller than 7 hundreds. 3,619,381 < 3,619,728 3,619,728 > 3,619,381

Ten Thousands

Thousands

Hundreds

Tens

Ones

du ca

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Millions

First, compare the values in the millions place. 540,571 does not have any digits in the millions place. So, it is the smallest number. The remaining numbers both have 5 millions. Compare the values in the hundred thousands place. The remaining numbers both have 3 hundred thousands. Compare the values in the ten thousands. 3 ten thousands is greater than 1 ten thousand. So, it is the greatest number. 5,315,763

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5,334,627

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greatest

540,571

smallest

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

(d) Compare the numbers using a bar model. What number is 500,000 greater than 367,194?

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500,000

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367,194

0 0 0 0 0

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

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

5,234,285

1,000,000

0 0 0 0 0 0

4 4

2 2

8 8

5 5

4,234,285 is 1,000,000 less than 5,234,285. 32

Let’s Practice

(a) 1,000

1,000,000 1,000,000

10,000 1,000

1,000

100

1,000

du ca

1,000

100,000 10,000

tio

100,000 100,000 100,000

1. Write the number represented by the base ten disks. Check the smaller number.

(b)

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

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

100,000 10,000 10,000 10,000

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

al E

1,000,000 1,000,000 1,000,000 1,000,000

1,000

100

R eg

1,000

2. Write the numbers in the place value chart and compare. (a) Compare 275,195 and 2,275,195. Hundred Ten Thousands Thousands Thousands

Hundreds

Tens

Ones

du ca

tio

Millions

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

Hundred Ten Thousands Thousands Thousands

Hundreds

Tens

Ones

al E

Millions

R eg

3. Use the symbols >, < and = to fill in the blanks. (a) 376,296

496,285 (b) 274,294

3,658,496 (d) 4,295,275

3,195,304 3,496,251

(e) 8,385,295

4,834,029 (f) 5,933,275

4,583,840

(g) 9,758,291

3,958,382 (h) 3,593,183

4,393,285

275,194

485,295

(b)

1,383,294

449,294

(c)

1,589,302

1,594,391

(d)

4,294,024

4,194,284

(e)

3,833,203

5,374,294

(f)

4,352,205

5,194,394

du ca

al E

5. Fill in the blanks.

tio

(a)

4. Check the smaller number.

145,600

100,000

R eg

(b)

is 100,000 more than 145,600. 1,520,080

200,000

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

2,222,500

500,000

(d)

tio

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

4,000,000

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

al E

du ca

6,720,500

(c)

5. Check the greatest number, cross the smallest number.

264,294

478,294

284,294

(b)

4,289,192

272,292

349,391

R eg

(a)

(c)

4,193,193

453,294

5,395,291

(d)

5,384,123

5,393,102

5,393,100

(e)

2,693,391

284,933

2,942,203

(f)

5,293,291

355,203

5,100,100

6. Arrange the numbers from the greatest to the smallest. (a) 109,558 105,558 110,598

du ca

(d) 29,158 19,414 9,455

tio

(b) 753,186 119,060 401,306

7. Use numbers to fill in the blanks. (a)

is 10,000 greater than 859,294.

(b) 583,495 is 100,000 less than

al E

(d) 5,339,495 is 1,000,000 more than (e) 2,530,395 is 300,000 less than

. .

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

(g)

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

(h)

is 300 more than 5,495,221.

(i)

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

(j)

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

R eg

(f)

At Home 1. Write the number represented by the place value abacus. Check the greater number.

HTh TTh

du ca

tio

(a)

al E

(b)

HTh TTh

R eg

(c)

HTh TTh

2. Write the numbers in the place value chart and compare. (a) Compare 1,316,200 and 475,950. Hundred Ten Thousands Thousands Thousands

Hundreds

Tens

Ones

tio

Millions

du ca

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

Hundred Ten Thousands Thousands Thousands

Hundreds

Tens

Ones

al E

Millions

3. Fill in the blank.

R eg

145,600

100,000

is 100,000 more than 145,600.

4. Check the numbers greater than 4,365,385.

5,275,293

7,296,395

2,352,183

4,365,384

4,365,387

4,654,292

5,385,184

4,234,580

tio

3,743,575

(a) 3,583,395 (b) 5,284,305 (c) 4,691,911 (d) 6,375,395

4,275,285 6,253,194

202,113

6,375,385

563,385

al E

(e) 1,295,294

du ca

5. Use the words is greater than, is smaller than and is equal to to fill in the blanks.

(f) 7,964,860

3,704,406

6. Arrange the numbers from the greatest to the smallest. (a) 4,203,529 4,284,495 7,285,395

R eg

(b) 7,595,395 8,190,641 7,645,120

(d) 6,512,481 6,516,384 6,512,484 40

Solve It! Read the table and answer the following questions.

1,146

New Orleans

San Francisco

4,130

Miami

Los Angeles

3,937

Boston

1,169

tio

Chicago

Distance from New York City (kilometers)

1,757 306

du ca

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

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

R eg

al E

Number Patterns Let’s Learn

What is the next number in the pattern?

125,800

126,800

Let's look at the thousands place!

tio

(a) 127,800

128,800

du ca

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

al E 5

R eg

The thousand digit increases by 1 each step.

+1,000

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

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

(b) 432,594

732,594

1,032,594

1,332,594

tio

Look at the hundred thousands place.

du ca

The hundred thousand digit increases by 3 each 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. (c) 5,385,395

5,635,395

5,885,395

6,135,395

(d)

al E

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

3,684,229

3,671,729

3,659,229

3,646,729

R eg

The numbers decrease by 12,500 each step. 3,646,729 - 12,500 = 3,634,229 The next number in the pattern is 3,634,229. (e)

7,562,595

7,529,595

7,496,595

7,463,595

The numbers decrease by 33,000 each step. 7,463,595 – 33,000 = 7,430,595 The next number in the pattern is 7,430,595. 43

What is the missing number?

tio

? , 1,573,489 , 1,073,489 (a) 3,573,489 , 3,073,489 , 2,573,489 , 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.

du ca

? , 98,700 , 94,200 , 89,700 , 85,200 , 80,700 (b) The numbers decrease by 4,500 each step. 98,700 + 4,500 = 103,200 The missing number is 103,200.

al E

? , 853,275 , 1,053,275 (c) 53,275 , 253,275 , 453,275 , The hundred thousand digit increases by 2 in each step. The numbers increase by 200,000 each step. 453,275 + 200,000 = 653,275 The missing number is 653,275.

R eg

? , 3,564,590 , 3,564,290 , 3,563,990 , 3,563,690 , 3,563,390 (d) The hundred digit decreases by 3 each step. The numbers decrease by 300 each step. 3,564,590 + 300 = 3,564,890 The missing number is 3,564,890.

? , 5,450,404 , 6,700,404 (e) 450,404 , 1,700,404 , 2,950,404 , The numbers increase by 1,250,000 each step. 2,950,404 + 1,250,000 = 4,200,404 The missing number is 4,200,404.

What are the missing numbers? (a)

, 1,282,293,

, 2,582,293, 3,232,293, 3,882,293 Subtract 650,000 from and add 650,000 to 1,282,293.

du ca

tio

The numbers increase by 650,000 in each step.

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

The missing numbers are 632,293 and 1,932,293. ?

al E

(b)

, 658,165, 888,165, 1,118 ,165,

, 1,578,165

R eg

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 = 428,165 1,118,165 + 230,000 = 1,348,165 The missing numbers are 428,165 and 1,348,165. 45

Let’s Practice 1. Fill in the blanks. (a) 556,795

Look at the ten thousands place

The ten thousands digit increases by The numbers increase by

du ca

576,795

536,795

tio

516,795

in each step.

al E

The next number in the pattern is

(b)

324,575

1,574,575

2,824,575

The numbers increase by

R eg

in each step.

The next number in the pattern is

4,074,575

2. Fill in the blanks. Hundred Thousands

Ten Thousands

Thousands

100,000 less

Millions

Hundred Thousands

Ten Thousands

Thousands

Hundred Thousands

Ten Thousands

Thousands

R eg

1,500,000 less

(d)

Millions

Hundreds

Tens

Hundred Thousands

Ten Thousands

10,000 less

Ones

125,000 more

al E

Millions

Ones

100,000 more

125,000 less

(c)

Tens

du ca

(b)

Hundreds

Millions

tio

(a)

Thousands

Hundreds

Tens

Ones

1,500,000 more

Hundreds

Tens

Ones

10,000 more

3. Fill in the blanks.

3,000 less

(c)

325,000 less

(d)

1,200,000 less

(e)

250,000 less

(f)

100,500 less

220,000 more

485,830

3,000 more

325,002

325,000 more

(b)

3,019,392

tio

220,000 less

1,249,102

1,200,000 more

du ca

(a)

5,140,001

250,000 more

583,293

100, 500 more

al E

4. Find the number that comes next in the pattern. (a) 462,395

439,395

416,395

393,395

(b) 4,298,358

4,423,358

4,548,358

4,673,358

1,728,491

3,178,491

4,628,491

7,372,020

5,272,020

3,172,020

245,053

490,053

735,053

677,465

565,465

453,465

278,491

R eg

(c)

(d) 9,472,020 (e)

(f) 789,465

5. Write the rule for the number pattern. The first one has been done for you. (a)

254,500,

+6,200

260,700,

(b)

(c)

34,

365,294,

2,444,482, 2,024,482

2,100,034, 4,200,034, 6,300,034

al E

(d)

266,900

du ca

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

248,300,

+6,200

tio

+6,200

317,794,

270,294,

222,794

6. Find the missing numbers in the number pattern.

R eg

(a)

, 909,785, 1,254,785, 1,599,785, 1,944,785,

(b) 937,385,

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

(d)

(e) 47,385, (f)

, 3,886,795,

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

, 141,345

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

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

Hands On

1. 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.

tio

2. Place a counter on the start square. 3. Roll the dice and move your counter forward the number of spaces shown on your dice. The space you land on is your number pattern rule.

du ca

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

R eg

al E

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

R eg

tio

du ca

al E

At Home 1. Fill in the blanks. Hundred Thousands

Ten Thousands

Thousands

Millions

Tens

Hundred Thousands

Ten Thousands

Thousands

Hundreds

Tens

1,250,000 more

al E

1,250,000 less

2. Fill in the blanks.

200,000 less

375,304

200,000 more

(b)

1,500,000 less

2,385,032

1,500,000 more

1,064,053

1,000,500 more

8,356,158

700,000 more

7,620,147

2,250,000 more

R eg

(a)

(c)

1,000,500 less

(d)

700,000 less

(e)

2,250,000 less

Ones

325,000 more

du ca

325,000 less

(b)

Hundreds

Millions

tio

(a)

Ones

3. Fill in the blanks. (a) 7,374,294

6,374,294

5,374,294

8,374,294

The millions digit decreases by

tio

Look at the digits in millions place.

The numbers decrease by

in each step.

–

al E 1,384,103

2,984,103

4,584,103

The numbers increase by

6,184,103

in each step.

The next number in the pattern is

R eg

in each step.

The next number in the pattern is (b)

du ca

(c)

5,440,250

4,940,250

4,440,250

The numbers decrease by

–

3,940,250

in each step. =

The next number in the pattern is

. 53

4. Fill in the missing numbers. (a) 150,000 more than 495,494 is

(b) 230,000 less than 853,594 is

(e) 2,350,000 more than 3,493,200 is (f) 3,700,000 less than 8,384,101 is

du ca

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

tio

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

al E

5. Find the missing numbers in the number pattern. (a) 842,394,

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

(b) 4,294,204, 4,815,234, 5,336,264, (c)

(d) 4,385,204,

, 6,378,324,

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

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

(f)

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

R eg

(e)

, 5,081,325

Rounding and Estimation Let’s Learn

Round off 325,800 to the nearest thousand.

When rounding, remember 5 or more – round up!

du ca

tio

When rounding, remember 4 or less – round down!

325,800

325,500

326,000

al E

325,000

When rounding to the nearest thousand, we look at the digit in the hundreds place. The digit in the hundreds place is 8, so we round up. 325,800 rounded off to the nearest thousand is 326,000.

R eg

Round 374,800 to the nearest ten thousand.

370,000

374,800

375,000

380,000

When rounding to the nearest ten thousand, we look at the digit in the thousands place. The digit in the thousands place is 4, so we round down. 374,800 rounded off to the nearest ten thousand is 370,000. 55

The population of Norway is 5,312,300. Round the population of Norway to the nearest hundred thousand.

tio

du ca

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

The digit in the ten thousands place is 1. So, we round the hundred thousands down.

R eg

al E

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

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

Use the table to answer the following questions.

7,692,024

Mexico

1,972,550

France

643,801

U.S.A.

9,147,590

tio

Australia

Land Area (km2)

du ca

1. Round the land area of Australia to the nearest thousand.

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

al E

2. Round the land area of Mexico to the nearest ten thousand. Look at the thousands place. The digit in the thousands place is 2, so we round down. 1,972,550 ≈ 1,970,000 The land area of Mexico is approximately 1,970,000 km2.

R eg

3. Round the land area of France to the nearest hundred thousand. The digit in the ten thousands place is 4, so we round down. 643,801 ≈ 600,000 The land area of France is approximately 600,000 km2. 4. Round the land area of the United States to the nearest million.

9,147,590 ≈ 9,000,000 The land area of the United States is approximately 9,000,000 km2. 57

Let’s Practice 1. Fill in the missing numbers. (a)

15,000

tio

14,500

14,000

14,600

rounded off to the nearest thousand is

≈

(b)

111,000

115,000

110,000

du ca

120,000

rounded off to the nearest ten thousand is

≈

al E

(c)

350,000

R eg

300,000

rounded off to the nearest

hundred thousand is

380,000

≈

400,000

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

≈

grams grams.

The average car weighs about

tio

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

people in Luxembourg.

du ca

There are about

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

≈

The house costs about $

al E

5. A charity is holding a large rock concert in Los Angeles. The number of people that attended the concert was 1,392,929. Round the number of people that attended to the nearest hundred thousand. ≈

R eg

There were about

people people at the concert.

6. A newspaper company prints 8,640,212 newspapers every year. Round the number of newspapers printed every year to the nearest million.

≈

The company prints about

newspapers newspapers every year.

7. Round the numbers to the nearest hundred.

(b) 4,302,453 ≈

(d) 5,350,223 ≈

tio

8. Round the numbers to the nearest thousand.

(a) 2,485,934 ≈

(b) 5,295,210 ≈

(d) 482,402 ≈

du ca

(a) 692,592 ≈

9. Round the numbers to the nearest ten thousand. (a) 497,926 ≈ (c) 1,640,203 ≈

(b) 9,285,394 ≈ (d) 259,493 ≈

al E

10. Round the numbers to the nearest hundred thousand. (a) 2,783,305 ≈ (c) 520,402 ≈

(b) 593,402 ≈

(d) 9,538,503 ≈

R eg

11. Round the numbers to the nearest million. (a) 5,492,594 ≈

(b) 874,964 ≈

(d) 3,603,496 ≈

At Home 1. Fill in the missing numbers. (a)

1,300,000

tio

1,250,000

1,200,000

1,239,021

rounded off to the nearest

≈

(b)

du ca

hundred thousand is

6,611,341

6,500,000

6,000,000

rounded off to the nearest

al E

7,000,000

million is

≈

2. Round the numbers to different place values.

R eg

(a)

5,204,532

≈ when rounded to the nearest ten thousand. ≈ when rounded to the nearest hundred thousand. ≈ when rounded to the nearest million.

9,324,294

≈ when rounded to the nearest hundred thousand. ≈ when rounded to the nearest ten thousand.

(b)

tio

≈ when rounded to the nearest million.

(a) 582,593 ≈ (c) 5,495,201 ≈

du ca

3. Round the numbers to the nearest thousand.

(b) 1,394,022 ≈ (d) 856,009 ≈

4. Round the numbers to the nearest ten thousand.

(b) 749,592 ≈

al E

(a) 7,396,083 ≈ (c) 8,184,952 ≈

(d) 2,495,021 ≈

5. Round the numbers to the nearest hundred thousand.

R eg

(a) 8,285,307 ≈ (c) 9,472,009 ≈

(b) 964,194 ≈

(d) 1,483,945 ≈

6. Round the numbers to the nearest million. (a) 7,295,206 ≈

(b) 9,499,999 ≈

(d) 7,281,592 ≈

Looking Back 1. Write the numbers. (a) Three hundred twenty thousand, six hundred fourteen.

2. Write in words. (a) 710,509 (b) 3,245,081

al E

du ca

tio

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

3. Count on in 10,000s. (a) 3,900,

(a) 1,884,121,

(b) 165,552,

R eg

(b) 294,708,

4. Count on in 100,000s.

5. Count on in 1,000,000s. (a) 26,037, (b) 4,825,910,

, ,

, 63

6. Write the number in its expanded form. (a) 213,967

(b) 1,030,507

tio

(d) 8,009,140

du ca

7. Write in exponent form in numbers and in words. (a) 10 x 10

Word form:

al E

Exponent form:

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

Word form:

8. Write the number.

(b) 103 =

(d) 101 =

R eg

(a) 105 =

9. Write the number. (a) 5 x 101 =

(b) 2 x 103 =

(d) 40 x 102 =

10. Use the symbols >, < and = to fill in the blanks. 6,987 (b) 73,122

84,708 (d) 333,000

73,122 333,010

(a) 19,654 19,361 10,788

du ca

(b) 902,006 425,121 425,221

tio

11. Arrange the numbers from the greatest to the smallest.

(a) 50,765

12. Find the missing numbers in the number pattern. (a) (b) 306,500,

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

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

al E

, 150,155,

, 320,001, 240,001, 160,001,

13. Round the numbers to the nearest ten thousand.

R eg

(a) 6,885 ≈

(b) 84,750 ≈ (d) 973,440 ≈

14. Round the numbers to the nearest hundred thousand. (a) 109,700 ≈

(b) 252,550 ≈

(d) 865,022 ≈

Operations on Whole Numbers

Addition and Subtraction

du ca

tio

Anchor Task

$1,295,000 Verdichio Waters 3

R eg

al E

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

tio

Ireland

4,937,782

Singapore

du ca

To find the population of Singapore, we add.

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

al E

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

R eg

Millions

Ten Thousands

Thousands

Hundreds

Tens

Ones

4,937,782 + 914,110 = 5,851,892 The population of Singapore is 5,851,892.

$1,024,795 car

du ca

house

tio

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

$116,143

To find the cost of the house, we subtract. Hundred Thousands

Ten Thousands

Thousands

Hundreds

al E

Millions

R eg Hundred Thousands

Ten Thousands

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

Thousands

Ones

Regroup 1 ten thousand into 10 thousands. Then subtract.

Regroup 1 million into 10 hundred thousands. Then subtract.

Millions

Tens

Hundreds

Tens

Ones

Let’s Practice 1. Add.

(e) (f) 1 5 3 8 4 6 3 9

al E

(g) (h) 2 7 5 3 7 1 2 4

R eg

4 +

(i) (j) 8 5 7 5 3 6 3 +

du ca

tio

(a) (b) 3 1 4 1 3

7 +

2. Subtract. (a) (b) 3 6 4 7 4 3

–

(e) (f) 8 1 3 9 2 4 4 2

al E

–

(g) (h) 4 2 6 2 4 1 8 1

R eg

–

6 –

(i) (j) 8 3 7 7 4 2 1 –

du ca

–

tio

–

4 –

0 0 0 0 0 0 1

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

du ca

tio

(a) 53,405 + 25,205 =

al E

R eg

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

(d) 9,485,395 – 353,304 =

(f) 3,592,024 – 1,034,032 =

Solve It!

4,218

du ca

3,000

tio

(a)

The sum of the numbers vertically and horizontally in the magic square are all 10,000. Can you find the missing numbers?

(b)

al E

5,718

R eg

3,840

6,040

2,260

(b) Home At 1. Add.

(f) 395,045 + 495,045 =

R eg

al E

(e) 9,745 + 54,905 =

du ca

tio

(a) (b) 5 6 7 1 0

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

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

2. Subtract. (a) (b) 7 4 2 6 4 3

–

du ca

–

tio

–

(f) 395,024 – 214,042 =

al E

(e) 843,592 – 53,503 =

R eg

(g) 4,683,053 – 294,035 =

(h) 2,945,035 – 303,053 =

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

Ten Thousands

Thousands

Hundreds

Tens

Ones

R eg

al E

du ca

tio

Millions

Anchor Task

(a) 12

(b) 306

(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

306 x 1,000

1,047 x 1,000 4,560 x 1,000

Let’s Learn Let’s use place value disks to help multiply numbers by 10.

x 10

1,000 100 100

124

1,240

Find 4,265 x 10.

du ca

124 x 10 = 1,240

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

x 10

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

100 100 100 100 100 100 10

42,650

al E

4,265

tio

100

Find 124 x 10.

4,265 x 10 = 42,650

Let’s use place value disks to help multiply 1,230 by 30.

R eg

Method 1

1,000 100 100

x 10

1,230

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

10,000 1,000 1,000

100 100 100

10,000 1,000 1,000

100 100 100 x3

10,000 1,000 1,000

100 100 100

12,300 10,000 1,000 1,000

100 100 100 36,900

1,000 100 100

1,230

100 100 100

1,000 100 100

x 10

100 100 100

1,000 100 100

10,000 1,000 1,000

100 100 100

du ca

3,690

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

al E

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

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

R eg

10,000 1,000 1,000

tio

1,000 100 100

10,000 1,000 1,000

Method 2

36,900

3 4

5 3

8 3

Let’s use a place value chart to help multiply numbers by 100. Find 726 x 100. Thousands

Hundreds

Tens

Ones

tio

726

Ten Thousands

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

Thousands

Hundreds

al E

Hundred Thousands

du ca

72,600

Tens

1,574 x 100 = 157,400 Multiply.

R eg

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

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

3 6

4 9

Ones

1,574

157,400

Let’s use a place value chart to help multiply numbers by 1,000. Find 406 x 1,000. Ten Thousands

Thousands

Hundreds

Tens

Ones

Hundred Thousands

tio

406

406 x 1,000 = 406,000 Find 1,308 x 1,000. Hundred Thousands

Ten Thousands

Thousands

al E

Millions

du ca

406,000

Hundreds

Tens

Ones

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

R eg

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

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

6 3

6 1

Estimate the products by rounding off then multiplying.

Round off 52 to the nearest 10. 52 ≈ 50

435 x 52 ≈ 20,000

du ca

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

Can you find the estimate mentally?

tio

Round off 435 to the nearest hundred. 435 ≈ 400

(a) Estimate 435 x 52.

(b) Estimate 3,730 x 227.

al E

Round off 3,730 to the nearest thousand. 3,730 ≈ 4,000 Round off 227 to the nearest 100. 227 ≈ 200

R eg

Multiply the rounded numbers. 4,000 x 200 = 4 x 1,000 x 2 x 100 = 8 x 1,000 x 100 = 8 x 100,000 = 800,000 3,730 x 227 ≈ 800,000

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

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

(d) 295 x 10 =

(g) 1,052 x 10 =

1,052 x 100 =

R eg

1,052 x 1,000 = (i) 5,000 x 10 = 5,000 x 100 =

5,000 x 1,000 =

295 x 100 =

295 x 1,000 =

(f) 890 x 10 =

890 x 100 =

890 x 1,000 =

al E

664 x 1,000 =

56 x 1,000 =

3 x 1,000 =

56 x 100 =

tio

3 x 100 =

(b) 56 x 10 =

du ca

(a) 3 x 10 =

(h) 2,368 x 10 =

2,368 x 100 =

2,368 x 1,000 =

(j) 4,200 x 10 = 4,200 x 100 = 4,200 x 1,000 =

2. Find the products.

6 x 2,000 = (c) 7 x 3 = 7 x 30 = 7 x 300 = 7 x 3,000 = (e) 10 x 2 = 10 x 20 =

4 x 8,000 = (d) 9 x 5 =

9 x 50 =

10 x 2,000 = (g) 7 x 7 =

7 x 70 =

R eg

7 x 700 =

7 x 7,000 =

9 x 500 =

9 x 5,000 =

(f) 9 x 8 =

9 x 80 =

9 x 800 =

al E

10 x 200 =

4 x 800 =

6 x 200 =

4 x 80 =

tio

6 x 20 =

(b) 4 x 8 =

du ca

(a) 6 x 2 =

9 x 8,000 =

(h) 6 x 9 = 6 x 90 = 6 x 900 = 6 x 7,000 =

Multiply. (b) 345 x 100 =

(f) 20 x 200 =

R eg

al E

(e) 60 x 5 =

(d) 2,485 x 1,000 =

du ca

tio

(a) 542 x 10 =

(g) 300 x 2,000 =

(h) 4,000 x 3,000 =

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

(d) 858 x 53 ≈

du ca (f) 1,493 x 212 ≈

R eg

al E

(e) 994 x 535 ≈

tio

(a) 353 x 7 ≈

(g) 332 x 2,900 ≈

(h) 1,295 x 551 ≈

Solve It! Ethan and his friends are discussing their allowance. My allowance is $1.50 per day.

My allowance is $12 per week.

My allowance is $52 per month.

Dominic

du ca

tio

My allowance is $10 per week.

Ethan

Wyatt

Jordan

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

al E

Ethan:

Wyatt:

Jordan:

R eg

(b) Assuming it is not a leap year, how much money does each person receive in 1 year?

Dominic:

Ethan:

Wyatt:

Jordan:

(b) Home At 1. Fill in the blanks. (a) 1

12 x

100

101 x (c)

1,000

al E

du ca

(b)

100

tio

1,000

100 10

1,000

100 10

1,000

100 10

R eg

(d)

100

1,000

100 10

1,000

100 10

1,000

10 100

1,000

100 10

2. Multiply by 10, 100 and 1,000.

Multiply.

18 x 1,000 = (d) 285 x 10 =

285 x 100 =

285 x 1,000 =

(b) 463 x 100 =

al E

(a) 946 x 10 =

18 x 100 =

1 x 1,000 =

tio

1 x 100 =

(b) 18 x 10 =

du ca

(a) 1 x 10 =

(d) 24 x 1,000 =

R eg

4. Find the products.

5 x 8,000 = (c) 4 x 7 = 4 x 70 = 4 x 700 = 4 x 7,000 =

2 x 900 = 2 x 9,000 =

5 x 800 =

2 x 90 =

tio

5 x 80 =

(b) 2 x 9 =

(d) 6 x 3 =

6 x 30 =

du ca

(a) 5 x 8 =

6 x 300 =

6 x 3,000 =

5. Estimate the products by rounding each number before multiplying. (b) 936 x 4 ≈

R eg

al E

(a) 394 x 2 ≈

(d) 583 x 1,200 ≈

Multiplying by 1 and 2-digit Numbers Let’s Learn

2 3 20 5 x

2 0

2 3 0 5 4

2 2 0

9 2 2 0

du ca

2,305 x 4 = 9,220

2 3 0 5

tio

2 3 20 5

Find 2,305 x 4 using the column method.

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

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

al E

3 2 0 4 5 x 3 5

32,045 x 3 = 96,135

R eg

Find 12,493 x 2 using the column method. 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

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. 5

600

150

140

0 0

4 0

Add the products.

tio

Now, add the products together!

1 5 0

3 5

du ca

9 2 5

So, 25 multiplied by 37 is 925.

Multiply 423 and 21. We can regroup these numbers into hundreds, tens and ones, then place them in a table and multiply each column and row. 20

400 8,000

400

al E

400

R eg

So, 423 multiplied by 21 is 8,883.

Can you add the products mentally?

Add the products. 8 0 0 0 4 0 0 4 0 0 2 0 6 0 +

3 8 8 8 3

Find 1,221 x 12 using the column method. Multiply by 2. Multiply by 10. Add the products. 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 2 2 x 1 2 4 4 1 2 2 1

tio

1 2 2 1 1 2 2 4 4 2

du ca

1,221 x 12 = 14,652 Find 953 x 2,403 using the column method.

Multiply by 3. Multiply by 50. x

al E

2 4 0 3 9 5 3 7 2 0 9

2 4 9 7 2 1 2 0 1

0 5 0 5

3 3 9 0

Multiply by 900. Add the products. 0 5 0 5 0

3 3 9 0 0

R eg

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

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 x 2,403 = 2,290,059

Let’s Practice (a) (b) 1 4 3

du ca

tio

1. Multiply.

al E

(e) (f) 1 6 8 4

R eg

3 x

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

(f) 2,494 x 64 =

R eg

al E

(e) 1,396 x 25 =

(d) 625 x 39 =

du ca

tio

(a) 64 x 53 =

(g) 532 x 290 =

(h) 1,295 x 433 =

3. Work out the following by multiplying rows and columns in a table. Then add the products. (a) 46 x 64 =

(b) 53 x 86 =

al E

du ca

R eg

tio

4. Multiply using the column method. (a) (b)

du ca

al E

R eg

(e) (f)

tio

Solve It!

100

30 1,500

210

al E

tio

du ca

R eg

200

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

600 24,000 4,800 80 3,200 6

240

640 48

At Home 1. Multiply.

du ca

tio

(a) (b) 1 2

R eg

(e) (f) 6 6 8 1 x

al E

4 x

2. Multiply using the column method. (a) 53 x 53 =

tio

(b) 352 x 96 =

(d) 2,294 x 33 =

al E

du ca

3. Work out the following by multiplying rows and columns in a table. Then add the products. 863 x 53 =

R eg

4. Multiply using the column method. (a) (b)

du ca

al E

R eg

(e) (f)

tio

Hands On

du ca

tio

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

al E

(a) Write an equation with the greatest product.

R eg

(b) Write an equation with the smallest product.

100

Dividing by 10s, 100s and 1,000s Let’s Learn

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

÷ 10

100 100 100 100 10

420 ÷ 10 = 42

Find 3,600 ÷ 10.

du ca

420

tio

Find 420 ÷ 10.

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

al E

100 100 100

÷ 10

100 100 100 10 10

360

3,600

3,600 ÷ 10 = 360

R eg

Divide 156,100 by 10.

100,000 10,000 10,000 10,000 10,000 10,000

1,000 1,000 1,000 1,000 1,000 1,000

100

156,100

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

÷ 10

100 100 100 100 100 100 10 15,610

156,100 ÷ 10 = 15,610

1 01

Find 3,300 ÷ 30. ÷ 10

100 100 100

100 100 100 10

3,300

110

tio du ca

Divide 48,000 by 40. ÷ 10

100 10

330

3,300 ÷ 30 = 110.

10,000 10,000 10,000

÷3

1,000 1,000 1,000

÷4

1,000 100 100

10,000 1,000 1,000

100 100 100

1,000 1,000 1,000

100 100 100

1,000 1,000 1,000

4,800

1,200

al E

48,000

48,000 ÷ 40 = 1,200.

Divide 244,200 by 20.

÷ 10

R eg

100,000100,000 10,000

10,000 10,000 1,000

10,000 10,000 10,000

1,000 1,000 1,000

100 100 100

1,000 100 100

100

244,200

244,200 ÷ 20 = 12,210.

1 02

10 24,420

÷2

10,000 1,000

1,000

100 100

10 12,210

Let’s use a place value chart to help divide numbers by 100. Find 72,700 ÷ 100. Thousands

Hundreds

Tens

Ones

Ten Thousands

tio

72,700

72,700 ÷ 100 = 727 Find 143,300 ÷ 100. Ten Thousands

Thousands

Hundreds

al E

Hundred Thousands

du ca

727

Tens

Ones

143,300

1,433

143,300 ÷ 100 = 1,433 Divide.

R eg

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

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

3 2

5,700 ÷ 100 = 57

4 2

6,400 ÷ 100 = 64

103

Let’s use a place value chart to help divide numbers by 1,000. Find 52,000 ÷ 1,000. Thousands

Hundreds

Tens

Ones

Ten Thousands

tio

52,000

52,000 ÷ 1,000 = 52 Find 273,000 ÷ 1,000. Ten Thousands

Thousands

Hundreds

al E

Hundred Thousands

du ca

Tens

Ones

273,000 ÷ 1,000 = 273 Divide.

R eg

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

(b) 126,000 ÷ 9,000 = 126,000 ÷ 1,000 ÷ 9 = 126 ÷ 9 = 14

8 5

6 0

9 3

6 0

104

273,000

273

Estimate the quotient by rounding off and dividing mentally. (a) Estimate 35,032 ÷ 52.

35,032 ÷ 52 ≈ 700

du ca

Divide the rounded numbers. 35,000 ÷ 50 = 35,000 ÷ 10 ÷ 5 = 3,500 ÷ 5 = 700

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

tio

Round off 52 to the nearest ten. 52 ≈ 50

Round off 35,032 to the nearest thousand. 35,032 ≈ 35,000

(b) Estimate 121,002 ÷ 6,011.

al E

Round off 121,002 to the nearest ten thousand. 121,002 ≈ 120,000 Round off 6,011 to the nearest thousand. 6,011 ≈ 6,000

R eg

Divide the rounded numbers. 120,000 ÷ 6,000 = 120,000 ÷ 1,000 ÷ 6 = 120 ÷ 6 = 20

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

121,002 ÷ 6,011 ≈ 20

105

Let’s Practice 1. Fill in the blanks. (a) ÷

1,000

100

1,000

du ca

11,100 ÷

(b)

1,000

tio

10,000

100

al E

2,020 ÷

(c)

100,000

100

100,000

100

100,000

100

R eg

(d)

10,000 10,000

10,000

1,000

1,000 1,000

100 100

1,000 1,000

1,000

100

10,000

1,000

100

10,000

106

100

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

(a) 72,000 ÷ 10 = 72,000 ÷ 100 =

120,000 ÷ 100 = 120,000 ÷ 1,000 =

du ca (b) 49,000 ÷ 7 =

49,000 ÷ 70 =

49,000 ÷ 700 =

210,000 ÷ 30 =

R eg

210,000 ÷ 300 =

210,000 ÷ 3,000 =

(d) 450,000 ÷ 9 = 450,000 ÷ 90 = 450,000 ÷ 900 = 450,000 ÷ 9,000 =

49,000 ÷ 7,000 =

al E

60,000 ÷ 5,000 =

29,000 ÷ 1,000 =

320,000 ÷ 1,000 =

60,000 ÷ 500 =

29,000 ÷ 100 =

320,000 ÷ 100 =

60,000 ÷ 50 =

tio

(d) 29,000 ÷ 10 =

(a) 60,000 ÷ 5 =

72,000 ÷ 1,000 =

3. Find the quotient.

107

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

(f) 140,021 ÷ 71 ≈

R eg

al E

(e) 120,101 ÷ 61 ≈

(d) 27,032 ÷ 91 ≈

du ca

tio

(a) 353 ÷ 71 ≈

(g) 361,001 ÷ 99 ≈

108

(h) 63,025 ÷ 7,195 ≈

At Home 1. Fill in the blanks. (a) ÷

10,000

100

du ca

1,000

10,000

1,000

100 100

100,000

1,000 1,000

10,000

100

10,000

1,000

100

1,000

100

al E

100,000 10,000

tio

100,000

(b)

10,000

100,000

2. Divide by 10, 100 and 1,000. (a) 85,000 ÷ 10 =

85,000 ÷ 100 =

R eg

85,000 ÷ 1,000 = (c) 930,000 ÷ 10 =

930,000 ÷ 100 =

930,000 ÷ 1,000 =

(b) 32,000 ÷ 10 =

32,000 ÷ 100 =

32,000 ÷ 1,000 =

(d) 121,000 ÷ 10 = 121,000 ÷ 100 = 121,000 ÷ 1,000 =

109

3. Find the quotient. (b) 64,000 ÷ 8 =

(a) 108,000 ÷ 9 =

64,000 ÷ 80 =

108,000 ÷ 900 =

64,000 ÷ 800 =

64,000 ÷ 8,000 =

(a) 421 ÷ 83 ≈

(b) 3,005 ÷ 52 ≈

(d) 32,032 ÷ 84 ≈

R eg

al E

(e) 1,420 ÷ 72 ≈

110

Estimate the quotient by rounding each number before dividing.

du ca

tio

108,000 ÷ 9,000 =

108,000 ÷ 90 =

(f) 210,121 ÷ 3,001 ≈

Dividing by 1 and 2-digit Numbers

3 6 2 3 3 4 1 8 5 Step 2

8 3 4 3 8 5

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

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

al E

3 6 2 3 1 8 5 4

Divide 2 thousands by 6. Regroup 2 thousands into 20 hundreds. Add the 3 hundreds and divide. 23 hundreds ÷ 6 = 3 hundreds remainder 5 hundreds. 23 hundreds – 18 hundreds = 5 hundreds.

du ca

Step 1

tio

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.

Let’s Learn

Step 3

8 9 3 4

R eg

3 6 2 3 1 8 5 4

3 8 5 4 5 4 0

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

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

111

Step 2

1 4 5 1 4 1

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

1 0 6 5÷4=1R1

7 1 0 6

1 8 3

1 2 4 5 1 4 1 1 8 3 2

31 ÷ 4 = 7 R 3

al E

1 2 4 5 1 4 1 1 8 3 2

Step 4

Step 5

112

1 8 3 0 2 8 2

30 ÷ 4 = 7 R 2

7 7 6 1 0 6

R eg

1 2 4 5 1 4 1 1 8 3 2

7 7 1 0 6

du ca

Step 3

11 ÷ 4 = 2 R 3

tio

Step 1

Find 51,106 ÷ 4.

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

3÷3=1r0

du ca

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

tio

(a) She wants to divide these coins equally among her 3 siblings. How much money does each sibling receive?

Riley finds a bag full of 1-cent coins in her drawer. She counts the coins and finds there are 384 coins in total.

8÷3=2r2

24 ÷ 3 = 8 r 0

al E

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

(b) There are 24 pupils in Riley's class. If she divided the coins equally among her classmates, how much would each pupil receive? We need to divide a 3-digit number by a 2-digit number. We can do this using repeated subtraction.

R eg

Step 1

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

This is less than 382. So, let's subtract.

113

Step 3

4 0 1 0 4 0 5 4

Step 4

4 0 1 0 4 0 5 4 4 1 0

We can see that only 24 remains. So, the final factor is 1.

R eg

al E

24 3 8 – 2 4 1 4 – 1 2 2 – 2

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

du ca

24 3 8 – 2 4 1 4 – 1 2 2

24 3 8 4 – 2 4 0 1 0 1 4 4

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

tio

Step 2

Step 5

Finally, we add the factors on the right side to find the quotient.

10 + 5 + 1 = 16 So, 384 ÷ 24 = 16 Each pupil would receive 16 cents.

114

Let’s Practice 1. Divide.

du ca

tio

(a) (b) (c)

(d) (e) 8

R eg

al E

115

2. Complete the following. (a) (b) 3 5 7 5

du ca

tio

3 2 3 1

al E

9 6 3 2 1

5 6 4 9 1

(e) (f)

R eg

4 2 8 5 0 1

116

3 4 9 7 2 1

3. Estimate the quotient by rounding. Then divide. (a) Find 244 ÷ 61. Estimate

61 ≈

tio

244 ≈

61 2 4 4

244 ÷ 61 ≈

Estimate

75 ≈ 1,425 ≈ 1,425 ÷ 75 ≈

75 1 4 2 5

al E

du ca

(b) Find 1,425 ÷ 75.

Estimate

57 ≈

3,249 ≈

57 3 2 4 9

R eg

3,249 ÷ 57 ≈

(d) Find 3,827 ÷ 43. Estimate

43 ≈

3,827 ≈

43 3 8 2 7

3,827 ÷ 43 ≈

117

At Home 1. Divide.

du ca

tio

(a) (b) (c)

(d) (e) 9

R eg

al E

118

2. Complete the following. (a) (b) 6 5 3 8

du ca

tio

7 2 5 1

al E

8 6 4 4 8

3. Estimate the quotient by rounding. Then divide. Find 728 ÷ 91.

R eg

Estimate

91 ≈

728 ≈

91 7 2 8

728 ÷ 91 ≈

119

Order of Operations

tio

16 + 4 = 20 21 – 20 = 1

R eg

al E

21 – 16 = 5 5+4=9

du ca

21 – 16 + 4

Anchor Task

2+7x9

2+7=9 9 x 9 = 81

120

7 x 9 = 63 2 + 63 = 65

Let’s Learn

Order of Operations Step 2

( )

Multiply and / or divide from left to right.

Add and / or subtract from left to right.

tio

Do the operations in parenthesis.

Step 3

du ca

Step 1

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

x ÷

+ –

R eg

al E

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

400 – 12 x 30

Start with multiplication!

400 – 360 40

Sue has 40 roses left.

121

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 liters of juice mix are left over? Add the numbers in parenthesis first!

(30 + 12) – 7 x 4

du ca

Riley had 14 liters of juice mix left over.

tio

42 – 28

(a) Find 3 + (7 x 4) ÷ 2. (b) Find 6 x 8 ÷ (9 + 3). 3 + (7 x 4) ÷ 2 3 + 28 ÷ 2

48 ÷

al E

3 + 14

6 x 8 ÷ (9 + 3)

17 (c) Find 9 x 2 + 3 x 3. (d) Find 12 + 4 x (12 ÷ 6). 9x2+3x3 12 + 4 x (12 ÷ 6) = 12 + 4 x 2

R eg

= 12 + 8 18 + 9 = 20 27 (e) Find 8 ÷ (6 – 2) x 8. (f) Find 14 – 3 x (9 ÷ 3).

8 ÷ (6 – 2) x 8 = 8 ÷ 4 x 8 14 – 3 x (9 ÷ 3) = 14 – 3 x 3 = 2 x 8 = 14 – 9 = 16 = 5

1 22

Let’s Practice 1. Fill in the blanks.

du ca

tio

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

Number of toy cars = 12 – = =

cars left.

al E

Ethan has

R eg

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

Number of balloons = 25 – = = So, there are

balloons at the party now.

123

Number of cards = 27 ÷

du ca

= = =

cards now.

al E

So, Wyatt has

R eg

(d) Jordan is helping his Dad paint the house. They use 20 liters of paint on the outside of the house and 40 liters of paint on the inside of the house. They then paint the shed using 3 tins of 2-liter paint. How much paint did Jordan and his Dad use?

Amount of paint = 20 + = = = So, they used

124

tio

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

liters of paint.

2. Find the values.

tio

(a) 96 – (3 + 7) (b) 96 – 3 + 7

du ca

3. Which of the following is correct? Show your working.

R eg

al E

(a) 12 + 2 x (4 + 4) ÷ 2 = 14 x (4 + 4) ÷ 2 = 14 x 8 ÷ 2 = 112 ÷ 2 = 56 (b) 12 + 2 x (4 + 4) ÷ 2 = 12 + 2 x 8 ÷ 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

= = = So, there are

du ca

Number of pots = 17 –

tio

(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?

1. Fill in the blanks.

pots left.

R eg

al E

(b) Keira is going on a bike ride. She rides 7 km from her home to the park and then a further 3 km to the mall. She then rides to her friend's house at a pace of 5 minutes per km. It takes her 20 minutes to get to her friend's house from the mall. How far did Keira ride in total?

Distance rode = = =

= So, she rode

126

km in total.

2. Find the values.

tio

(a) 54 – (4 + 3) (b) 54 – (4 – 3)

du ca

3. Which of the following is correct? Show your working.

R eg

al E

(a) 42 – 6 x (9 + 12) ÷ 3 = 36 x (9 + 12) ÷ 3 = 36 x 21 ÷ 3 = 36 x 7 = 252 (b) 42 – 6 x (9 + 12) ÷ 3 = 42 – 6 x 21 ÷ 3 = 42 – 126 ÷ 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 Let’s Learn

du ca

tio

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

al E

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

tulips

R eg

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

8 2 x 4 3 2 8

82 x 4 = 328 The total number of bouquets of tulips is 328.

1 28

212

328

roses

tulips

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

2 11 2 3 2 8 5 4 0

du ca

To find the total number of bouquets, we add.

tio

212 + 328 = 540 The total number of bouquets is 540.

al E

Check Let’s use rounding and estimation to check that the answer is reasonable.

R eg

Tulip bouquets = 328 ≈ 330 Rose bouquets = 212 ≈ 210

330 + 210 = 540 540 is equal to our answer. So, the answer is reasonable.

129

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

necklaces

du ca

26 beads

al E

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

R eg

338 ÷ 26 = 13 The jewelry store can make 13 necklaces. Check Let’s check that the answer is reasonable. 300 ÷ 30 ≈ 10

10 is close to 13, so our answer is reasonable.

130

tio

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

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

(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 answer is reasonable.

tio

1 necklace 1 shirt

1 necklace

$1,428

To find the total amount of money, we multiply. 8 3 4 0 4

du ca

1 4 2 x 1 4 2 8 1 4 2 8 1 8 5 6

The store will receive $18,564.

al E

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

R eg

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

131

n 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?

x 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

du ca

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

al E

Mineplex mined 3,023,358 kg of coal.

R eg

Check 3,237 ≈ 3,000 934 ≈ 900 3,000 x 900 = 2,700,000 2,700,000 ≈ 3,000,000

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

1 32

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

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

du ca

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

tio

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

3,003,000 is close to 3,026,595, so the answer is reasonable. Step 2 Divide to find the number of bags. 3 1 9 5 9 5

al E

6 0 5 5 3 0 2 6 3 0 0 2 6 2 5 1 1

R eg

5 5 0 9 5 4 5 4 5 0

A total of 605,319 bags can be made. Check 3,026,595 ≈ 3,000,000 3,000,000 ÷ 5 = 600,000 600,000 is close to 605,319, so the answer is reasonable.

133

Let’s Practice

du ca

tio

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

al E

Step 1 Find the number of wattle bushes bought.

gum trees

R eg

wattles

The number of wattle bushes bought is

1 34

gums

du ca

Step 2 Find the total number of plants bought.

tio

Check

al E

wattles

The total number of plants bought is

R eg

Check

135

R eg

al E

du ca

tio

2. 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 as the first. On the third day, she travels 5 times less than on the first day. How far does she travel? Check that your answer is reasonable.

136

R eg

al E

du ca

tio

3. 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 of fish. Each piece of fish sells for $3. How much money will Mrs. Krum make if she sells all of her stock? Check that your answer is reasonable.

137

At Home

du ca

tio

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

Step 1 Find the total number of peaches picked.

al E

125 people

R eg

A total of Check

138

peaches were picked.

Step 2 Find the number of peaches each restaurant received.

R eg

al E

Check

peaches.

du ca

Each restaurant received

tio

restaurants

139

R eg

al E

du ca

tio

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

140

Looking Back 1. Add or subtract.

–

(f) 804,405 – 353,024 =

R eg

al E

(e) 4,864 + 74,046 =

du ca

tio

(a) (b) 7 7 4 2 6

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

(h) 5,038,034 – 1,464,752 =

1 41

2. Multiply. (a) (b) 1 4 2

tio

du ca 5

al E

(e) (f) 8 2 0 3

R eg

142

7 x

3. Multiply using the column method. (a) 67 x 34 =

tio

(b) 546 x 66 =

(d) 3,964 x 83 =

al E

du ca

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

R eg

143

5. Complete the following. (a) (b) 4 5 8

du ca

tio

5 4 9 3

al E

6 5 9 2 0

7 5 6 2 7

(e) (f)

R eg

8 6 5 2 7 8

144

9 6 4 8 7 2

du ca

tio

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

R eg

al E

7. A fruit store is stocking up for the summer season ahead. The store buys 694 mangoes. They also buy 583 bananas. Each banana sells for $2 and each mango sells for $3. How much money will the store make if the entire stock is sold? Check that your answer is reasonable

145

Fractions

R eg

al E

du ca

tio

Anchor Task

146

147

R eg

tio

du ca

al E

Adding Fractions Let’s Learn Sophie draws a circle with 9 equal parts.

5 9

al E

2 9

du ca

Find the total fraction of the circle they colored.

tio

2 of the circle blue. 9 5 Riley colors of the circle green. 9

She colors

Add the numerators and keep the denominators unchanged.

7 9

R eg

2 5 7 + = 9 9 9 7 Sophie and Riley colored of the circle. 9 5 1 Find the sum of 12 and 12 .

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

1 = 2

1 48

Divide the numerator and the denominator by 6 to simplify.

3 4

6 8 x2

6 8

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

1 7 and . 3 12

al E

Find the sum of

du ca

1 8

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

tio

3 1 Find the sum of 4 and 8 .

1 3

4 12

R eg

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

149

3 4

6 8

9 12

12 16

15 20

18 24

21 28

24 32

27 36

30 40

tio

Multiples of 3 Multiples of 4

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

du ca

The lowest common multiple is 12. Multiply each fraction to make the denominators 12. x4

1 3

4 12 x4

1 4

al E

Now we can add.

3 12

R eg 1 1 4 3 3 + 4 = 12 + 12 7 = 12

150

1 4

4 12

3 12

7 12

3 12

1 2 Find the sum of 7 and 5 5 7

10 14

15 21

20 28

30 42

35 49

40 56

45 63

50 70

2 1 10 7 7 + 5 = 35 + 35 17 = 35

25 35

du ca

Jordan folds two pieces of paper, each into 8 equal parts.

tio

Multiples of 5 Multiples of 7

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

R eg

al E

Find the total fraction of paper Jordan colored.

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

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

1 51

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

Keira eats 1

tio

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

1 2 Add the whole numbers. 1

3 4

al E

du ca

Add the fractions. +

1 2

3 4

R eg

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

2 4

3 4

1 4

Keira and Riley ate 4

152

Or we can add the whole numbers and fractions separately.

1 pancakes in total. 4

Find the sum of 1

3 5 and 3 . 4 6

+ 35 6

tio

Add the whole numbers.

al E

Add the fractions.

du ca

1+3=4

7 12

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

R eg

1 53

Let’s Practice 1. Write the fractions and add. Write the answer in its simplest form.

(a)

(b)

du ca

tio

al E

R eg

(c)

(d)

154

2. Write the fractions and add. Write the answer in its simplest form. (a) =

du ca

(b)

tio

(c)

al E

3. Complete the table and find the lowest common multiple of each number set. (a) 2, 3

Multiples of 2

R eg

Multiples of 3

(b) 3, 4, 6

Multiples of 3 Multiples of 4 Multiples of 6

155

4. Find the equivalent fractions 4 = 8 (b) 7

4 = (c) 10 5

5 = (d) 7 14

3 = (e) 4

5 = 10 (f) 9

2 = (g) 6 3

5 = 10 (h) 8

tio 4 = 12 (i) 5

du ca

2 = (a) 8 4

7 = 14 (k) 9

4 = (l) 6 12

7 = 21 (n) 8

6 = (o) 10 5

2 = (q) 10 5

1 = (r) 9 18

3 = (t) 8 16

11 = (u) 12 24

3 = (v) 9 3

1 = 6 (w) 10

13 = (x) 14 28

3 = (y) 6 2

1 = (z) 4

1 = (j) 3 9

al E

1 = (m) 2

1 = (p) 11 22

R eg

2 = (s) 12

156

5. Find the equivalent fraction and add. 1 1 1 (a) + = + 2 4 4 4 ?

2 3 (b) + = 4 8

3 8

al E

3 1 3 (c) + = + 9 3 9 9 =

2 1 1 + = + 3 6 6 6

R eg

(d)

tio

du ca

(e)

4 4 4 + = + 7 14 14 14

1 57

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

1 1 (a) + = 5 4

2 1 (d) + = 3 7

al E

4 3 (e) + = 5 4

du ca

3 2 (c) + = 6 3

tio

1 1 (b) + = 2 6

3 1 (f) + = 11 2

R eg

6 5 (g) + = 7 12 2 9 (h) + = 3 10 6 5 (i) + = 8 9

158

7. Fill in the blanks. Write the answer in its simplest form.

tio

1 = 3

5 = 6

du ca

4 5 3 1 (a) + (b) + 7 6 4 3

al E

2 2 3 1 (c) 2 + (d) + 1 9 5 8 12

2 = 5

1 + 1 = 12

R eg

159

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

1 8 (a) 1 + = 4 9

1 2 (d) 3 + = 7 4

al E

3 3 (e) 4 + 2 = 5 4

du ca

2 1 (c) +1 = 7 3

tio

6 3 (b) 2 + = 8 5

3 1 (f) 3 + 5 = 12 4

R eg

6 3 (g) 2 + 1 = 9 11 4 2 (h) + 6 = 7 3

7 2 (i) 5 + 6 = 8 3

160

Solve It!

R eg

al E

du ca

tio

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

The cake mixture weighs

ounces.

161

At Home 1. Write the fractions and add. Write the answer in its simplest form.

tio

(a)

(b)

du ca

al E

(c)

R eg

(d)

= 1 62

3 = 4

5 = (c) (d) = 6

7 = 11

(e) (f) 2 = = 7

3 = 5

tio

(a) (b) 1 = = 2

2. Find the first two equivalent fractions.

du ca

1 = 3

(i) (j) 8 = = 13

6 = 9

(k) (l) 2 = = 7

11 = 12

(m) (n) 10 = = 9

13 = 12

(o) (p) 3 = = 10

1 = 14

(q) (r) 1 = = 1

6 = 7

R eg

al E

(g) (h) 7 = = 9

163

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

2 1 1 (c) + = 4 8

tio

2 1 3 1 1 1 + (b) + = + (a) + = 7 21 6 21 3 2 6 21

+ 5 8

du ca

1 3 + 5 = (d) 8 4 8

al E

5 9 2 5 8 3 (e) + = + (f) + = + 5 10 6 14 10 42 =

R eg

1 4 2 1 7 (g) + = + (h) + = + 2 7 11 12 3 77 3 77 3 =

4 1 4 (i) + = + 2 18 18

164

1 3 (j) + = 2 18

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

8 1 (a) + = 9 3

1 2 (d) + = 5 10

al E

4 9 (e) + = 6 27

du ca

9 1 (c) + = 18 2

tio

9 3 (b) + = 12 4

5 8 (f) + = 11 10

R eg

6 1 (g) + = 10 12 2 11 (h) + = 5 15 5 2 (i) + = 27 3

165

5. Fill in the blanks.

+ 5 =

tio

du ca

8 2 1 5 + (a) + (b) 9 12 3 6

al E

1 3 2 2 (c) 1 + (d) + 1 11 7 10 4

R eg

= 166

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

1 8 (a) 1 + = 7 11

8 1 (d) 1 + = 9 4

al E

1 3 (e) 7 + 1 = 3 9

du ca

5 2 (c) + 1 = 8 3

tio

6 3 (b) 2 + = 8 5

3 1 (f) 4 + 6 = 11 12

R eg

6 2 (g) 1 + 1 = 10 11

2 3 (h) + 5 = 7 3 3 2 (i) 1 + 6 = 8 7

1 67

Subtracting Fractions Let’s Learn 3 1 of a meter off the rope. Wyatt cuts of a meter off the rope. 10 10

tio

Ethan cuts

9 of a meter long. 10

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

9 10

du ca

How long is the remaining rope?

7 7 7 7 3 10

al E

9 1 3 5 – – = 10 10 10 10 1 = 2

1 10

When subtracting like fractions, we subtract the numerators and leave the denominator unchanged. Find the difference between

R eg

4 9

2 9

4 – 2 = 2 9 9 9

168

4 2 and . 9 9

Find the difference between

–

4 6

–

1 6

4 6 1 6

3 6

du ca

tio

2 3

2 1 and . 3 6

2 – 1 = 4 – 1 6 6 6 3 = 3 6 = 1 2

Express the answer in its simplest form.

3 3 and . 4 8

al E

Find the difference between

1 2

3 – 3 = 6 – 3 8 8 8 4 = 3 8

R eg

Find the difference between Multiples of 6 Multiples of 8

6 8

12 16

5 3 and . 6 8 18 24

24 32

30 40

36 48

42 56

48 64

54 72

60 80

The lowest common multiple is 24. Multiply each fraction to make the denominators 24. Then subtract.

5 – 3 = 20 – 9 8 24 24 6 = 11 24

169

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

2 liters of orange 3

2 3 2 = 3 – 3 3 3 1 = 3 3

2 . 5

al E

4–

du ca

tio

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

Find the difference between 5 and 2 5 2 = 4 – 5 5 5 3 = 4 5

R eg

5–

Find the difference between 1 and

1 2 1 = – 2 2 2 1 = 2 1–

170

1 . 2

3 1 . and 2 . 4 8

R eg

al E

du ca

tio

Find the difference between 5

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

171

Let’s Practice 1. Label the fraction model and complete the subtraction. Write the answer in its simplest form.

(a)

tio

7 – 10

du ca

7 7 7 7 (b)

7 7 7

–

al E

(c)

R eg

–

(d)

7 7 7 7 7

172

2. Find the equivalent fraction and subtract. Write the answer in its simplest form. 3 – 1 = (b) 4 2

–

tio

–

du ca

4 – 2 = (c) 5 15

7 – 1 = (d) 18 3

–

al E

(e) 19 – 3 = 20 4

–

5 – 1 = (a) 6 12

–

(f) 2 – 7 = 3 12

–

R eg

4 5 (g) – = 7 21

–

17 – 1 = (h) 32 8

–

173

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

, ,

1 6

3 – 1 = 4 6

–

(b) Multiples of 8:

al E

Multiples of 10:

R eg

7 8

7 – 3 = 8 10

174

–

du ca

3 4

tio

Multiples of 6: 6, 12,

3 10

Multiples of 12:

1 12

3 – 1 = 10 12

–

(d) Multiples of 9:

al E

Multiples of 6:

8 9

R eg

8 – 5 = 9 6

tio

du ca

3 10

5 6

–

175

4. Subtract. Write the answer in its simplest form. (b) 7 – 4 = 6 9

–

(d) 6 – 4 3 = 3 4

–

du ca

–

tio

(a) 4 – 2 = 3 5

5. Subtract. Use the space provided to show your working. Write the answer in its simplest form. 3 –12 = (b) 3 5 4

R eg

al E

1 –2 2 = (a) 6 3 2

1 –33 = (c) 5 8 4

176

8 –67 = (d) 7 12 9

Solve It! Halle and Sophie are carrying bags of soil to their vegetable patch.

Halle's bag contains 4 7 kg of soil and Sophie's bag contains 2 5 kg of soil. 8 8 (a) Find the combined mass of soil in their bags.

tio

(b) Halle gets tired as her bag of soil is too heavy. Sophie suggests she takes some of Halle's soil so that they each have an equal weight. How much soil does Sophie need to take from Halle?

R eg

al E

du ca

Draw a model to help find the answer. Show your working.

177

At Home

3 – 3 = (a) 8 4

1 – 5 = (b) 9 2

–

7 – 1 = (d) 15 3

–

du ca

5 – 1 = (c) 6 12

–

tio

–

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

al E

2. Fill in the blanks to find equivalent fractions. Then subtract. Write the answer in its simplest form. ,

Multiples of 12:

R eg

Multiples of 9:

7 9

7 – 5 = 9 12

178

5 12

–

3. Subtract. Use the space provided to show your working. Write the answer in its simplest form. 3 –3 1 = (b) 3 5 4

(e) 7 2 – 4 5 = 12 9

R eg

(d) 10 2 – 4 1 = 8 7

du ca

al E

3 –3 1 = (c) 3 5 4

tio

1 –12 = (a) 2 5 2

7 –2 1 = (g) 8 4 16

1 –1 5 = (f) 2 24 4

8 –12 = (h) 5 3 15

179

Multiplying Fractions Let’s Learn Halle is baking cakes for the school fair. 2 cup of sugar per cake. 3

tio

She plans on making 5 cakes.

The recipe requires a

1 3 1 3

R eg

1 3 1 3

al E

du ca

How much sugar will she need in total?

Multiply the numerator by the whole number. Then simplify.

1 3 1 3 1 3

1 3

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

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

180

1 cups of sugar in total. 3

5 by 4. 6

Remember to write the fraction in its simplest form.

tio

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

Multiply

A brick has a mass of 3

du ca

When multiplying a proper fraction by a whole number, the product is less than the whole number. 3 kg. Find the mass of 4 such bricks. 4

3 4

al E

R eg

3 15 4x3 =4x 4 4 4 x 15 = 4 = 15

12 = 3 4 3 3 4 is a mixed number. So we expect the product to be greater than 4!

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

181

6x2

5 3 = 15 8 4

5 6 6 0 6

5 16 + 5 21 28 = 8 = 8

tio

1 8 1 2 8 4 4

du ca

21 5 6 x 2 = 6 x 8 8 6 x 21 = 8 126 = 8 6 3 = 15 = 15 8 4

5 Find 6 x 2 . 8

Mr. Lovato is building a gate. He uses wood planks that each have a 2 in. A total of 14 such planks are used and there are no gaps 5 between the planks. Find the total width of the gate.

R eg

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width of 8

182

2 by 14 to find the total width of the gate. 5 588 ÷ 5 is 117 R 3. 2 40 + 2 3 x 14 8 x 14 = The product 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

tio

Let's multiply 8

3 5 3

Jordan brought

3 in. 5

du ca

The gate has a width of 117

4 of a banana cake 5

to school to share with his friends. They ate

2 of the cake Jordan brought. 3

al E

What fraction of the whole banana cake did Jordan and his friends eat?

R eg

4 of whole 5

4 2 of 5 3

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

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

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

8 of the whole banana cake. 15

183

3 3 of . 4 4 3 4

3 9 3 of is . 4 16 4

3 3 of 4 4

2 3 and . 3 8

du ca

Find the product of

3 8

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

al E

2 3 2x3 x = 3x8 3 8 6 = 24 1 = 4

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

tio

Find

2 3 1 and is . 3 8 4 3 8 and . 4 5

R eg

The product of

3 2 of 8 3

Find the product of 3 8 3x8 x = 4 5 4x5 24 = 20 1 = 1 5

The product of

184

3 8 1 and is 1 . 4 5 5

8 5 is an improper fraction.

Let’s Practice

3 4 x 3 (b) 6 x 5 8

(c)

2 2 x 4 (d) x 8 3 7

R eg

al E

du ca

tio

(a)

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

(e) 9 x

3 5 (f) x 10 4 12

185

2. Multiply the fractions. Show your working and write your answer in its simplest form. 6 1 (b) x3 7 3

4 3 (d) 5 x 9 4

du ca

tio

(a) 10 x

al E

7 2 x 6 (f) 8 x 5 12

R eg

(e)

(g) 3 x

186

7 4 (h) x 10 18 15

3. Multiply the mixed numbers. Show your working and write your answer in its simplest form. 1 x4 2

3 4

al E

(b) 3 x 3

du ca

tio

(a) 2

7 x6 8

R eg

1 87

4. Multiply the mixed numbers. Show your working and write your answer in its simplest form. 2 2 x 2 (b) 2 x 5 3 7

5 1 (d) 9 x 2 6 2

du ca

tio

(a) 5

al E

2 7 x 10 (f) 3 x 4 5 10

R eg

(e) 5

1 4 (g) 20 x 8 (h) 12 x 3 3 5

1 88

5. Color squares in the rectangle to show the product of the fractions. Write the product in its simplest form. 2 3 1 1 x (b) x 3 4 2 3

(c)

1 2 2 4 x (d) x 3 3 5 2

al E

du ca

tio

(a)

5 2 x (f) 8 3

R eg

(e)

4 5 x 5 6

189

6. Multiply the fractions. Show your working and write your answer in its simplest form. 1 1 3 1 x (b) x 5 2 2 4

(c)

3 3 5 2 x (d) x 4 4 3 5

du ca

tio

(a)

al E

7 3 x (f) 2 4

R eg

(e)

(g)

190

7 2 x 9 3

4 3 5 8 x (h) x 5 11 6 3

Hands On Work in pairs. (a) Use the grid below to draw a rectangle. Lightly shade

al E

du ca

the rectangle that is colored green.

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

tio

rectangle blue. Color

1 of the 2

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

1 of the 4

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

R eg

the rectangle that is colored red.

191

3 of the 4

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

du ca

tio

the rectangle that is colored blue.

al E

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

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

R eg

the rectangle that is colored green.

192

5 of the 6

At Home

2 4 x 3 (b) 6 x 7 3

(c)

5 5 x 6 (d) 8 x 6 8

R eg

al E

du ca

tio

(a)

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

(e) 6 x

3 (f) 4

7 x3 9

193

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

5 8

al E

(b) 2 x 3

du ca

tio

(a) 4

R eg

2 3 (c) 4 x 2 (d) 7 x 3 3 5

1 3 (e) 12 x 4 (f) 8 x 5 8 12

194

3. Color squares in the rectangle to show the product of the fractions. Write the product in its simplest form. 1 4 3 2 x (b) x 5 2 4 3

(c)

1 2 5 3 x (d) x 7 4 8 4

al E

du ca

tio

(a)

R eg

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

(a)

3 3 15 2 x (b) x 4 5 4 5

195

Solve It!

1 2

tio x

2 3

al E

R eg

196

1 3

du ca

1 x4 2

1 2

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

1 2

5 12

x4 x

1 5

3 8

Fractions and Division Let’s Learn

du ca

tio

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

You can think of a fraction as the numerator divided by the denominator!

al E

3 ÷ 4 = 1 of 3 4 = 3 4

Each person receives

3 of a cake. 4

R eg

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

12 ÷ 8 =

Each jug contains 1

Here we have an improper fraction. Simplify if possible.

1 liters of pineapple juice. 2

197

Ethan has

2 meters of string. He cuts the 3

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

tio

2 m 3

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

du ca

2 1 of m 3 4

Dividing by 4 is the same as 1 multiplying by 4 !

Find

3 ÷ 5. 4

R eg

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

1 98

1 meters. 6

al E

Each piece of string has a length of

3 4 3 1 of 4 5

Blake is baking raspberry tarts. Each tart requires

2 cup of raspberries. Blake has a 3

2 3

raspberries

1 cup 2 3 =4x 3 2 4x3 = 2 12 = 2 4÷

2 3

du ca

2 3

tio

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

1 cup

2 3

1 cup

al E

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

= 6

Blake can make 6 raspberry tarts. 3 . 5

R eg

Find 8 divided by 5 3 = 8 x 3 5 40 = 3 1 = 13 3 8÷

8 divided by

3 1 = 13 5 3

199

Let’s Practice 1. Complete the following. Show your working and write your answer in its simplest form.

du ca

tio

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

al E

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

R eg

(e) 8 ÷ 20 (f) 9 ÷ 27

2 00

2. Use the model to help divide the fractions. Write the answer in its simplest form 7 1 ÷ 5 (b) ÷4 8 2

du ca

tio

(a)

3. Complete the following. Show your working and write your answer in its simplest form. 4 1 ÷ 10 (b) ÷ 6 5 2

al E

(a)

8 11 ÷ 2 (d) ÷ 8 3 5

R eg

(c)

(e)

4 ÷ 6 (f) 7

2 ÷ 10 3

2 01

4. Use the model to help divide whole numbers by fractions. Write the answer in its simplest form 2 5

(b) 4 ÷

2 9

al E

du ca

tio

(a) 3 ÷

5. Complete the following. Show your working and write your answer in its simplest form. 3 1 (b) 8 ÷ 4 2

R eg

(a) 10 ÷

202

2 2 (d) 8 ÷ 5 7

Solve It!

R eg

tio ÷4

÷6

al E

÷ 1 4

du ca

1 2

÷ 3 10

÷ 1 6

÷ 5 8

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

÷ 10

÷ 5 12

÷ 3 5

÷ 1 9

÷ 16

203

At Home

du ca

tio

(a) 3 ÷ 9 (b) 10 ÷ 6

omplete the following. Show your working and write your answer in C its simplest form.

2 6 ÷ 3 (h) ÷ 8 3 7

R eg

(g)

al E

(e) 12 ÷ 8 (f) 2 ÷ 18

(i)

2 04

5 8 ÷ 10 (j) ÷4 2 3

14 4 ÷ 7 (n) ÷ 12 3 9

4 2 (p) 6 ÷ 7 3

al E

(o) 3 ÷

(m)

tio

5 3 ÷ 6 (l) ÷ 6 4 10

du ca

(k)

5 3 (r) 8 ÷ 3 4

R eg

(q) 12 ÷

(s) 9 ÷

7 16 (t) 10 ÷ 3 7

205

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

Find the total mass of apples used. 1 3 1 3 +2 =3+ + 4 2 4 2 2 3 = 3 + + 4 4 5 = 3 + 4 1 = 3 + 1 4 1 = 4 4

1 kg of apples. 4

al E

Jordan uses 4

du ca

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

tio

Sophie has She uses

5 kg of diced tomato. 6

2 of the tomato to make 3

R eg

pizza sauce. How much diced tomato did she use?

2 5 2 5 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 1 of them in the afternoon. 3

1 3

du ca

1 2

tio

mangoes in the morning and

1 of the 2

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

al E

She sold

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

5 x 192 5 1 9 2 of 192 = x 5 6 6 9 6 0 960 = 6

R eg

= 160

1 6 9 6 3 3

6 0 6 0 6 6 0

Ms. Wardi sold 160 mangoes. (b) How many mangoes did she have left?

192 – 160 = 32 She had 32 mangoes left.

207

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

1 of the 4

1 of the 5

240 given to sister

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

du ca

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

given to brother

3 of her stickers to her brother. 20

al E

Riley gave

R eg

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

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

Riley gave 36 stickers to her brother.

208

tio

stickers did she give to her brother?

remaining stickers to her brother. How many

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

1 x 1 9 1 2 2 1

2 8 6 0 6

3 0 7 2 1 6 2 1 0 6

6 kg. 7

du ca

12 cans of lentils has a mass of 30

18 4 = 12 x 7 7 12 x 18 = 7 216 = 7 6 = 30 7 12 x 2

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

tio

A can of lentils has a mass of 2

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

3 liters of water. How many cups 8

al E

can she fill with the 12 liters of water?

R eg

We need to divide 12 by

3 . 8

8 3 = 12 x 3 8 96 = 3 12 ÷

= 32

Michelle can fill 32 cups of water.

209

A plank of wood has a length of

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

We need to divide

du ca

tio

Find the length of each piece of wood.

3 m by 6. 4

al E

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

Each piece of wood has a length of

1 m. 8

R eg

24 loaves of bread are divided equally among 18 people. What fraction of a loaf does each person receive? 24 18 4 = 3 1 =1 3

24 ÷ 18 =

Each person receives 1

21 0

1 loaves of bread. 3

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

du ca

tio

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

1. 48 children are playing at the beach.

R eg

al E

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

211

3. Mr. Hopper is tiling his bathroom floor which has a length of 4 m and a width of 2

3 m. 4

du ca

tio

(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?

al E

4 min to complete a full rotation. How long does 9 it take to complete 5 rotations?

R eg

4. It takes a Ferris wheel 8

212

5. Halle spent

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

remaining money on some new shoes.

du ca

tio

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

R eg

al E

1 6. Keira picked some flowers in her garden. of the flowers were roses, 3 1 of them were tulips and the rest were daisies. If she picked 10 daisies, 4 how many flowers did she pick in all?

213

At Home

du ca

tio

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

R eg

al E

5 2. Wyatt is making a poster for a school presentation. He colors of the 9 1 poster blue and of the remaining part green. What fraction of the 2 poster is green?

21 4

3. Mrs. Potter's patio is rectangular in shape with a length of 5 m and a breadth 3

1 m. She buys new tiles to cover her patio. 3

R eg

al E

du ca

tio

(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

R eg

al E

du ca

tio

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

21 6

Looking Back

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

tio

2 2 (a) + = 7 9

1 2 (c) 4 + 1 = 2 3 1 3 (d) 4 + 5 = 4 4

al E

5 1 (e) 7 + 1 = 12 3

du ca

1 3 (b) 2 + = 4 5

R eg

5 1 (f) 3 + 2 = 18 12 7 7 (g) 1 + 1 = 8 12 3 2 (h) + 5 = 3 19

217

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

(b) 4 – 3 = 8

(d) 5 3 – 1 3 = 12 4

du ca

(e) 7 5 – 4 4 = 7 9

1 –1 5 = (f) 9 24 4

R eg

al E

1 –1 1 = (c) 3 5 2

tio

(a) 2 – 2 = 5

8 –12 = (h) 5 3 15

7 –2 1 = (g) 8 4 16

218

3. Multiply. Show your working and write your answer in its simplest form. 3 1 x 2 (b) 2 x 3 4 2

4 2 (d) 4 x 8 7 3

du ca

tio

(a) 3

al E

2 1 x (f) 8 3

5 4 x 2 9

R eg

(e)

(g)

1 4 6 5 x (h) x 3 8 7 9

219

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

tio

(a) 2 ÷ 4 (b) 12 ÷ 18

du ca

al E

(e) 17 ÷ 6 (f) 4 ÷ 30

4 2 3 ÷ (h) 4 ÷ 5 7 7

R eg

(g)

(i)

22 0

3 3 ÷ 8 (j) ÷4 5 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?

R eg

al E

du ca

tio

5. 60 children are playing at the park.

221

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

du ca

tio

6. Ethan has 72 stickers. He gave

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

R eg

al E

7. It takes a merry-go-round 1

22 2

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

R eg

al E

du ca

tio

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

223

Decimals

Tenths, Hundredths and Thousandths

R eg

al E

du ca

tio

Anchor Task

224

Let’s Learn The square is divided into 10 equal parts. 1 of the square. 10 We can also write this in decimal form as 0.1.

The colored part shows

tio

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

Tenths

du ca

decimal point

There are 10 tenths in 1 whole. 0.1 1

0.1

al E

0.1

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

0.1

R eg

0.1

Ones 0

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 square. 100 We can also write this in decimal form as 0.01. The colored part shows

Tenths

Hundredths

tio

Ones

We read this number as 'zero point zero one'.

du ca

decimal point

There are 10 hundredths in 1 tenth. 0.01 0.1 1

0.01 0.1

0.01

al E

0.01

0.01 0.1

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

R eg

1 0.1

0.1

0.01

22 6

0.01

Ones

Tenths

Hundredths

4.25 four point two five

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

2 0 . 0

(a)

0 . 9

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) 1

3 . 4

du ca

tio

0 . 0

al E

0 . 4 3

The value of the digit 1 is 10. The value of the digit 3 is 3. The value of the digit 4 is 0.4. The value of the digit 7 is 0.07. 10 + 3 + 0.4 + 0.07 = 13.47

R eg

227

n tio du ca

The square is divided into 1000 equal parts.

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

al E

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

Tenths

Hundredths

Thousandths

decimal point

R eg

There are 10 thousandths in 1 hundredth. 0.001

0.001

0.01

228

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

7 0 . 0

0 . 0

(a)

tio

0 . 2 8

4 . 2

0 . 0

al E

(b)

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

du ca

0 . 2 4

R eg

The value of the digit 6 is 60. The value of the digit 4 is 4. The value of the digit 2 is 0.2. The value of the digit 1 is 0.01. The value of the digit 9 is 0.009. 60 + 4 + 0.2 + 0.01 + 0.009 = 64.219

229

Let’s Practice 1. Write the decimal number shown by the colored parts.

du ca

tio

(a) (b)

al E

R eg

(e) (f)

230

2. Write the decimal number shown by the colored parts.

du ca

tio

(a)

Ones

Tenths

al E

(b)

Ones

Tenths

Hundredths

Tenths

Hundredths

R eg

(c)

Ones

. .

231

0.1

0.01

0.1

0.01

0.1

0.01

al E

(c)

(d)

0.1

0.01

0.001

0.1

R eg (e)

232

tio

(b)

du ca

(a)

3. Write the decimal number shown by the place value disks.

0.001

0.1

0.01

4. Write the value of the digit. (b)

4.8

45.88

35.003

(d)

0.392

du ca

(c)

tio

(a)

5. Read and write the numbers in the place value chart.

al E

(a) The three is in the ones place. The eight is in the tenths place. The two is in the hundredths place. Ones

Tenths

Hundredths

R eg

(b)

The one is in the ones place. The zero is in the tenths place. The two is in the hundredths place. The six is in the thousandths place. Ones

Tenths

Hundredths Thousandths

233

6. Write as words. (a) 0.6

(b) 4.8

tio

(f) 42.35 (g) 0.023

al E

(h) 53.093

du ca

(e) 2.40

7. Write as decimals.

(a) four thousandths

R eg

(b) three and one tenths

(d) two hundred ninety-one thousandths

(e) 3

4 10

(g) 5

74 100

23 4

(f) 5 63 100 (h) 9

56 1,000

Hands On

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

R eg

al E

du ca

tio

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

Ones

Tenths

Hundredths Thousandths

. . . . .

235

At Home

tio

0.81

1. Match.

du ca

0.96

R eg

al E

0.77

236

0.22

0.60

0.06

2. Match.

0.1

0.01

0.1

0.001

0.1

0.001

0.1

0.01

0.1

0.001

R eg

0.01

al E

10.331

0.1

0.01

tio

0.1

du ca

0.1

0.001

1.52

14.21

4.202

1.004

2.6

237

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

8 . 5

al E

(b)

du ca

5 . 7

R eg

(c)

23 8

tio

(a)

4. Fill in the blanks.

(a)

46.9 place. It has a value of

The 6 is in the

place. It has a value of

The 9 is in the

place. It has a value of

The 5 is in the The 3 is in the The 1 is in the The 8 is in the

tio

53.18

du ca

(b)

The 4 is in the

place. It has a value of

. .

place. It has a value of

The 3 is in the

place. It has a value of

The 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

al E

place. It has a value of

(c)

23.089

R eg

The 2 is in the

239

5. Write as words. (a) 5.3

(b) 7.38

tio

du ca

(e) 3.594 (f) 6.402 (g) 64.736

al E

(h) 17.343

6. Write as decimals.

(a) five tenths

(b) two hundred tenths

R eg

(d) six thousandths (e) 4

6 10

(g) 4

85 100

240

(f) 4 12 100 (h) 7

43 1000

Solve It!

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

al E

du ca

tio

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

R eg

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

2 41

Comparing and Ordering Decimals Let’s Learn

Tenths

Hundredths

du ca

Ones

tio

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

Compare 4.55 and 4.44. Which number is smaller?

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

Tenths

Hundredths

al E

Ones

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

Tenths

Hundredths

R eg

Ones

4 tenths is smaller than 5 tenths. So, 4.44 is smaller than 4.55. We write:

2 42

4.44 < 4.55

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

Tenths

Hundredths

Thousandths

tio

Ones

du ca

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

Tenths

Hundredths

Thousandths

al E

6 thousandths is greater than 4 thousandths. We write:

3.276 > 3.274

R eg

We can compare decimals on a number line too!

3.27

3.274

3.276

3.28

243

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

0.49

0.45

0.5

tio

0.4

0.46

0.49 > 0.46

0.46 < 0.49

0.46 is smaller than 0.49

du ca

0.49 is greater than 0.46

(b) Compare 1.224 and 1.214. 1.214

1.22

al E

1.21

1.224

1.23

1.224 > 1.214

1.214 < 1.224

1.224 is greater than 1.214

1.214 is smaller than 1.224

R eg

6.637

6.615

6.61

6.62

6.637 > 6.615 6.637 is greater than 6.615

2 44

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

tio

Ones

3.829

al E

3.841

du ca

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

R eg

greatest

85,580 3.828

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

245

Arrange the decimals from the smallest to the greatest. (a) 0.99, 0.9 and 0.95

0.9

0.95

0.99

0.95

tio

0.9

0.99 > 0.95 and 0.99 > 0.9 0.99 is the greatest.

du ca

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

smallest

85,580 0.99

greatest

(b) 0.543, 0.548 and 0.546

0.546

al E

0.543

0.54

0.548

0.545 0.546

0.543

smallest

0.55 85,580 0.548 greatest

R eg

9.783

9.78

9.781

smallest

2 46

9.788

9.785 9.783

9.79 85,580 9.788 greatest

Let’s Practice 1. Write the decimal represented by the place value disks. Check the greater number. 0.1

0.1

(c)

0.1

0.001

0.1

0.01

R eg

0.01 0.01 0.01 0.01 0.001

0.1

0.01

du ca 1

0.001 0.001 0.001 0.001

(d)

tio

al E

(b)

(a)

0.01 0.01 0.001 0.001

0.1

0.01 0.01 0.01 0.001

247

2. Write the numbers in the place value chart and compare. (a) Compare 3.783 and 3.793. .

Tenths

Hundredths

tio

. .

Thousandths

Ones

du ca

(b) Compare 6.494 and 6.944. Ones

Tenths

Hundredths

Thousandths

Hundredths

Thousandths

al E

R eg

Ones

2 48

. . .

Tenths

3. Write the numbers on the number line and compare.

0.545 is greater than

du ca

0.55

tio

0.54

(a) Compare 0.546 and 0.548.

(b) Compare 3.435 and 3.456.

3.44

al E

3.43

is smaller than

3.45

3.46

2.37

2.38

R eg

2.35

2.36

is smaller than

249

7.948

17.948

(b)

13.853

13.875

(c)

1,204.39

1,204.387

5. Check the greatest number. (a)

0.34

(b)

12.033

0.33

12.33

(c)

0.002

0.005

5.001

al E

6. Arrange the numbers from the greatest to the smallest. (a) 3.673 3.574 4.768

(b) 0.385 0.384 0.38

R eg

(d) 9.999 10 9.9

25 0

1.34

du ca

0.347

tio

(a)

4. Check the smaller number.

Solve It! What do you call an alligator in a vest?

0.004

0.044

3.952

1.06

2.03

3.97

3.963

5.118

du ca

tio

To find the answer, arrange the numbers from the smallest to the greatest. Write the matching letters in the boxes according to their order.

R eg

al E

smallest

v t s r

2.401

1.006

1.26

5.109

2.3

5.4

greatest

2 51

At Home 1. Add the place values and compare.

tio

3 + 0.2 + 0.01 + 0.003 =

(a) 3 + 0.2 + 0.003 =

du ca

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

al E

(d) 0.1 + 0.002 =

R eg

20 + 0.2 =

(e) 300 + 0.9 + 0.002 =

300 + 1 + 0.2 + 0.09 + 0.002 =

252

2. Write the numbers in the place value chart and compare. (a) Compare 4.395 and 4.935. .

Tenths

Hundredths

tio

. .

Thousandths

Ones

du ca

(b) Compare 9.873 and 9.812. Ones

Tenths

Hundredths

Thousandths

Hundredths

Thousandths

al E

R eg

Ones

Tenths

. .

253

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

2.5

du ca

2.49

2.51

tio

2.48

(a) Compare 2.483 and 2.502.

(b) Compare 3.001 and 3.024.

3 >

3.02

al E

3.01

4. Arrange the numbers from the greatest to the smallest. (a) 4.395 4.312 4.295

R eg

(b) 10.094 10.493 10.385

(d) 35.309 0.039 39.305

254

3.03

5. Circle the numbers that are smaller than 0.85.

3.85

0.845

0.325

0.5

0.8

0.21

tio

0.856

6. Write the fractions as decimals and compare.

145 = 100

88 = 10

88 = 100

130 = 100

40 = 100

56 = 100

(b) (c)

du ca

121 = (a) 100

(d) 570 = 1000

al E

7. Use the symbols >, < and = to fill in the blanks. 54 (b) 89.95

89.75

1.254 (d) 15.376

13.563

(e) 2.002

2.002 (f) 35.01

R eg

(a) 3.64

(g) 8

8.001 (h) 24.99

1.35 25.003

2 55

Rounding and Estimation

R eg

al E

du ca

tio

Anchor Task

2 56

Let’s Learn

du ca

tio

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

32.46

32.5

al E

When rounding to the nearest whole number, we look at the digit in the tenths place. The digit in the tenths place is 4, so we round down. 32.46 rounded off to the nearest whole number is 32. Michelle weighs approximately 32 kg.

R eg

Round 18.62 to the nearest whole number.

18.62

18.5

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

2 57

Round 4.75 to one decimal place.

4.7

4.75

4.8

4.75

du ca

4.75 rounded off to one decimal place is 4.8.

tio

hen rounding to one decimal place, we look at the digit in the W hundredths place. The digit in the hundredths place is 5, so we round up.

Halle's Math score was 57.893. Find Halle's score when rounded to two decimal places. The digit in the thousandths place is 3, so we round down.

al E

Rounded off to two decimal places, Halle's score is 57.89. 57.893 ≈ 57.89

R eg

Find Halle's score rounded to one decimal place.

258

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

Let’s Practice 1. Fill in the missing numbers. (a)

7.698

7.5

tio

rounded off to the nearest

≈

(b)

3.512

3.55

3.5

du ca

whole number is

3.6

al E

rounded off to

one decimal place is

≈

R eg

(c)

4.125

4.12

4.13

rounded off to

two decimal places is

4.128

≈

259

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

≈ kilograms.

The average beaver weighs about

tio

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

minutes.

du ca

Sophie runs 5 kilometers in about

4. A new book costs $23.78. Round the cost to one decimal place.

≈

A new book costs about $

al E

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

There are about

days in a year.

R eg

6. Wyatt is 143.893 centimeters tall. Round his height to two decimal places.

≈

Wyatt is about

centimeters tall.

7. A dam passes 123,495.913 liters of water every year. Round the number of liters to two decimal places.

≈

The dam passes about

26 0

liters every year.

8. Round the numbers to the nearest whole number. (b) 2.5 ≈ (d) 9.53 ≈

(e) 4.593 ≈

(f) 1,305.5 ≈

9. Round the numbers to one decimal place.

tio

(a) 4.63 ≈

(b) 11.111 ≈

(d) 3.01 ≈

(f) 1.493 ≈

(e) 3.953 ≈

du ca

(a) 6.496 ≈

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

(d) 8.483 ≈

(f) 2.690 ≈

al E

(b) 2.485 ≈

R eg

(e) 3.507 ≈

261

At Home 1. Fill in the missing numbers. (a)

tio

4.5

4.8

rounded off to the nearest

≈

(b)

du ca

whole number is

3.53

3.55

3.5

rounded off to

al E

one decimal place

3.6

≈

2. Round the numbers to different place values.

R eg

(a)

2,697.386

2 62

≈ when rounded to the nearest whole number. ≈ when rounded to one decimal place. ≈ when rounded to two decimal place.

≈ when rounded to the nearest whole number.

154.396

≈ when rounded to one decimal place.

(b)

du ca

tio

≈ when rounded to two decimal places.

3. Round the numbers to the nearest whole number. (a) 2.64 ≈ (c) 4.682 ≈

(d) 6.93 ≈

(f) 17.205 ≈

al E

(e) 7.5 ≈

(b) 1.9 ≈

4. Round the numbers to one decimal place. (b) 4.76 ≈

(d) 77.765 ≈

(e) 4.115 ≈

(f) 9.997 ≈

R eg

(a) 1.23 ≈

5. Round the numbers to two decimal places. (a) 1.386 ≈

(b) 7.255 ≈

(d) 9.752 ≈

(e) 99.975 ≈

(f) 545.368 ≈

263

Looking Back 1. Write as words.

(a) 0.9

tio

(b) 2.5 (c) 8.38

(e) 1.493 (f) 0.003 (g) 86.535

al E

(h) 34.351

du ca

(d) 13.47

2. Write as decimals.

(a) eight thousandths

R eg

(b) two and eight tenths

(d) two hundred forty-one thousandths

(e) 2

6 10

(g) 55

264

64 10

(f) 11 86 100 (h) 5

353 1000

2.583

2.582

(b)

1.395

13.95

(c)

145.395

145.359

4. Check the greatest number.

9.99

(b)

1.603

(c)

0.001

9.009

du ca

(a)

tio

(a)

3. Check the smaller number.

16.03

1.613

0.01

0.1

al E

5. Arrange the numbers from the greatest to the smallest. (a) 6.497 6.5 64.972

(b) 0.111 0.121 1.111

R eg

(d) 13.090 12.992 139.9

265

6. Circle the numbers that are smaller than 0.901.

0.325

0.344

0.91

0.921

0.899

tio

0.9

7. Write the fractions as decimals and compare.

135 = 100

35 = 10

222 = 100

24 = 100

86 = 100

23 = 100

(b) (c)

du ca

35 = (a) 100

(d) 234 = 1000

al E

8. Use the symbols >, < and = to fill in the blanks. (a) 5.385

1.254 (d) 15.376

R eg

53.8 (b) 1.021

(e) 4.593

(g) 9

2 66

4.193 (f) 11.203

9.001 (h) 32.406

1.021 13.563 11.23 32.451

9. Round the numbers to different places values.

≈ when rounded to one decimal place.

tio

679.875

≈ when rounded to the nearest whole number.

du ca

≈ when rounded to two decimal places.

10. Round the numbers to the nearest whole number. (a) 3.975 ≈ (c) 2.35 ≈

(d) 9.9 ≈

(f) 18.995 ≈

al E

(e) 1.03 ≈

(b) 3.54 ≈

11. Round the numbers to one decimal place. (b) 2.466 ≈

(d) 24.395 ≈

(e) 2.564 ≈

(f) 68.78 ≈

R eg

(a) 5.963 ≈

12. Round the numbers to two decimal places. (a) 4.647 ≈

(b) 5.496 ≈

(d) 7.437 ≈

(e) 43.594 ≈

(f) 243.549 ≈

2 67

n tio du ca al E

R eg

© Blue Ring Media Pty Ltd ACN 161 590 496 2013 - 2021. This publication would not have been possible without the tireless effort of our production team. Special thanks to: Daniel Cole, Matthew Cole, Wang Hui Guan, Kevin Mahoney, Winston Goh, Jesse Singer, Joseph Anderson, Halle Taylor-Pritchard, Sophie Taylor-Pritchard, Tejal Thakur, Natchanuch Nakapat,Varasinun Mathanattapat, Kanungnit Pookwanmuang, Saijit Lueangsrisuk Original Illustrations: Natchanuch Nakapat, GraphicsRF, Blue Ring Media and Interact Images Royalty-free images: Shutterstock, Adobe Stock