Maths ― No Problem! Fractions and Decimals, Ages 8-9 (Key Stage 2) (Master Maths At Home) 9780241539354, 0241539358

Table of contents :
Contents
Counting in hundredths
Mixed numbers
Equivalent fractions
Simplifying mixed numbers
Adding fractions
Subtracting fractions
Adding and subtracting fractions
Fractions of lengths
Fractions of sets
Recognising and writing tenths
Recognising and writing hundredths
Tenths and hundredths as decimals
Comparing and ordering decimals
Rounding decimals
Writing fractions as decimals
Dividing by 10
Dividing by 100
Review and challenge
Answers

Citation preview

KS2

8–9 Years

Master Maths at Home

Fractions and Decimals Scan the QR code to help your child’s learning at home.

mastermathsathome.com

How to use this book Maths — No Problem! created Master Maths at Home to help children develop fluency in the subject and a rich understanding of core concepts. Key features of the Master Maths at Home books include: •

Carefully designed lessons that provide structure, but also allow flexibility in how they’re used.

•

Exercises that allow a flexible approach and can be adapted to suit any child’s cognitive or functional ability.

•

Speech bubbles containing content designed to spark diverse conversations, with many discussion points that don’t have obvious ‘right’ or ‘wrong’ answers.

•

Clearly laid-out pages that encourage children to practise a range of higher-order skills.

•

A community of friendly and relatable characters who introduce each lesson and come along as your child progresses through the series.

•

Rich illustrations that will guide children to a discussion of shapes and units of measurement, allowing them to make connections to the wider world around them.

You can see more guidance on how to use these books at mastermathsathome.com. We’re excited to share all the ways you can learn maths!

Copyright © 2022 Maths — No Problem! Maths — No Problem! mastermathsathome.com www.mathsnoproblem.com [email protected] First published in Great Britain in 2022 by Dorling Kindersley Limited One Embassy Gardens, 8 Viaduct Gardens, London SW11 7BW A Penguin Random House Company

This book was made with Forest Stewardship Council™ certified paper – one small step in DK's commitment to a sustainable future. For more information go to www. dk.com/our-green-pledge

The authorised representative in the EEA is Dorling Kindersley Verlag GmbH. Amulfstr. 124, 80636 Munich, Germany 10 9 8 7 6 5 4 3 2 1 001–327090–Jan/22 All rights reserved. Without limiting the rights under the copyright reserved above, no part of this publication may be reproduced, stored in, or introduced into a retrieval system, or transmitted, in any form, or by any means (electronic, mechanical, photocopying, recording, or otherwise), without the prior written permission of the copyright owner. A CIP catalogue record for this book is available from the British Library. ISBN: 978-0-24153-935-4 Printed and bound in the UK For the curious

www.dk.com

Acknowledgements The publisher would like to thank the authors and consultants Andy Psarianos, Judy Hornigold, Adam Gifford and Dr Anne Hermanson. The Castledown typeface has been used with permission from the Colophon Foundry.

Contents Page Counting in hundredths

4

Mixed numbers

6

Equivalent fractions

10

Simplifying mixed numbers

12

Adding fractions

14

Subtracting fractions

16

Adding and subtracting fractions

18

Fractions of lengths

20

Fractions of sets

22

Recognising and writing tenths

24

Recognising and writing hundredths

26

Tenths and hundredths as decimals

28

Comparing and ordering decimals

30

Rounding decimals

32

Writing fractions as decimals

34

Dividing by 10

36

Dividing by 100

38

Review and challenge

40

Answers

46

Ruby

Elliott

Amira

Charles

Lulu

Sam

Oak

Holly

Ravi

Emma

Jacob

Hannah

Counting in hundredths

Lesson 1

Starter Charles, Holly and Jacob are playing a game. A board is used to keep track of their points. Each square is equal to 1 point. The game ends when all 100 squares are full. What fraction of the board has each child filled so far?

Example Charles has filled

.

He has filled 1 hundredth of the board.

0

1 2 3 4 5 6 7 8 9 10 11 12 100 100 100 100 100 100 100 100 100 100 100 100

1 Charles has filled ____ of the board. 100 4

.

Holly has filled She has filled 7 hundredths of the board.

0

1 2 3 4 5 6 7 8 9 10 11 12 100 100 100 100 100 100 100 100 100 100 100 100

7 Holly has filled ____ of the board. 100 .

Jacob has filled He has filled 11 hundredths of the board. 11 Jacob has filled ____ of the board. 100

1 2 3 , , , 100 100 100 4 5 6 7 8 , , , , , 100 100 100 100 100 9 10 11 , , 100 100 100

Practice 1

What fraction of each board is shaded? (a)

(b)

100 2

(c)

100

100

Fill in the blanks on the number line.

13 14 100 100

16 100 5

Mixed numbers

Lesson 2

Starter

How many sandwiches are on the tray?

Example

There are 3 whole sandwiches.

3 3 3 + __ = 3 __ 4 4

There is

We can write 3 and 3 quarters like this.

3 There are 3 __ sandwiches on the tray. 4

6

3 of a sandwich. 4

3

3 is a mixed number. 4

What mixed number is shown?

This is 1.

2 2 1 + __ = 1 __ 5 5 2 1 and 2 fifths is 1 __. 5 2 1 __ is a mixed number. 5 Count in fifths to find the number shown.

This is 2 . 5

When we put a fraction next to a whole number it means we add the two together.

When we write numbers and fractions together we call them a mixed number.

1 2 3 4 1 2 , , , , 1, 1 , 1 5 5 5 5 5 5

7

Practice 1

How many brownies are there in total?

+

=

There are 2

How many rows of stamps are there altogether?

6 +

There are 8

brownies in total.

=

rows of stamps altogether.

3

What are the mixed numbers being shown? (a)

1 2 + __ = 4

2 and 1 quarter is

3 1 + ___ = 10

1 and 3 tenths is

.

(b)

.

(c)

+

4 and

=

thirds is

. 9

Equivalent fractions

Lesson 3

Starter I think the numbers are equal.

Is Jacob correct?

1 3

2 6

Example 2 1 and are 6 3 equal by using bar models.

I split this bar into 3 equal-sized pieces. 1 Each part is . 3

We can check if

When 1 3 2 becomes , 1 larger 6 part becomes 2 smaller parts.

I split this bar into 6 equal-sized pieces. Each part is 1 . 6 The bars show me that 2 1 is equal to . 6 3

1 3 1 6

1 6

1 2 is equal to . 3 6 They are equivalent fractions.

Jacob is correct. 10 327090_MNP_Fractions_and_Decimals_Ages_8-9_KS2.indd 10

17/11/2021 21:24

Are

1 2 3 , and equal? 3 6 9 I can see that 3 1 2 , , and are all 9 3 6 the same amount. They are equivalent fractions.

1 3 1 6 1 9

1 6 1 9

1 9

1 5

1 5

1 5

These are all equivalent fractions too.

1 1 1 1 1 1 10 10 10 10 10 10 1 1 1 1 1 1 1 1 1 15 15 15 15 15 15 15 15 15 9 6 ___ _3_ = ___ = 5 10 15

Practice Find the equivalent fractions. 1

_1_ = 7

3

3 ___ = 10

14 9

3

=

=

12

2

_2_ = 7

4

_5_ = 9

14

45

=

=

6

50

11

Simplifying mixed numbers

Lesson 4

Starter Sam and Amira share 3 full boxes of chocolates.

chocolates

chocolates

I take a full box and 4 chocolates.

I take a full box and 2 chocolates.

How many boxes of chocolates does each of them take?

Example Sam takes 1 and 2 sixths boxes of chocolates.

1

2 can be simplified. 6

chocolates

÷2 2 1 = 6 3 ÷2

12

2 smaller parts become 1 larger part. 1

1 is the simplest form. 3

Amira takes 1 and 4 sixths boxes of chocolates. 4 We can simplify 1 __. 6

chocolates

÷2

4 smaller parts become 2 larger parts.

4 2 = 6 3 1

÷2

2 is the simplest form. 3

2 1 Sam takes 1 __ boxes of chocolates and Ruby takes 1 __ boxes of chocolates. 3 3

Practice 1

Write each mixed number in its simplest form. 3 (b) 2 __ = 9

4 (a) 1 __ = 8

2

Simplify. 6 (a) __ = 8

8 (b) ___ = 10

10 (c) ___ = 12

6 (d) 3 __ = 9

4 (e) 7 ___ = 10

9 (f ) 9 ___ = 12 13

Adding fractions

Lesson 5

Starter

4 1 = + 5 5 1 3 = + 7 7

Can you help the children solve these equations?

5 7 = + 9 9

Example 4 5

4 1 5 + = 5 5 5 If we add 1 fifth to 4 fifths we get 5 fifths.

1 7

+

If we add 1 seventh to 3 sevenths we get 4 sevenths. 14

1 5

+

3 7

5 5

=

=

5 fifths is equal to 1.

4 7

5 9

7 9

+

_4_ + _1_ = 1 5 5 _1_ + _3_ = _4_ 7 7 7 _5_ + _7_ = 1 _3_ 9 9 9

12 9

=

5 ninths plus 7 ninths is equal to 12 ninths. 12 ninths is more than 1. We can simplify 12 ninths to 1 and 3 ninths.

Practice 1

Fill in the blanks. (a) +

=

(b) +

2

2 1 (a) __ + __ = 7 7

=

2 3 (b) __ + __ = 5 5

= 15

Subtracting fractions

Lesson 6

Starter 2 Jacob puts __ of 1 tray of lasagne in a container. 9 How much lasagne is left?

Example 1=

Method 1 9 2 2 2 − __ = 1 __ − __ 9 9 9 7 = 1 __ 9 7 There are 1 __ trays of lasagne left. 9 16

Method 2 2 18 2 2 − __ = ___ − __ 9 9 9 16 = ___ 9 16 7 ___ = 1 __ 9 9

9 9

Practice 1

Subtract and fill in the blanks. Give your final answer as a mixed number. (a) 5 1 1 2 − __ = 1 __ − __ = 5 5 5 (b) 3 7 3 3 − __ = 2 __ − __ = 7 7 7 9 5 5 (c) 8 − __ = 7 __ − __ = 9 9 9 1 (d) 4 − __ = 3

2

−

Subtract and simplify the fraction. 10 4 4 (a) 4 − ___ = 3 ___ − ___ = 10 10 10

3

=

6 8 6 (b) 7 − __ = 6 __ − __ = 8 8 8

Subtract and give your final answer as a mixed number. 4 10 4 (a) 2 − __ = ___ − __ 5 5 5

5 21 5 (b) 3 − __ = ___ − __ 7 7 7

6 = __ 5

=

=

= 17

Adding and subtracting fractions

Lesson 7

Starter Elliott brings some pizza to the table. 3 Ruby takes __ of the pizza from Elliott. 5 How much pizza does Elliott have left?

Example Find how much pizza Elliott has to start with.

2 2 1 + __ = 1 __ 5 5 2 2 __ 1 Elliott had 1 __ pizzas. 5 5 3 Find the amount of pizza Elliott has left after Ruby took __ of the pizza. 5 2 1 5

3 2 Subtract __ from 1 __. 5 5 2 3 7 3 1 __ − __ = __ − __ 5 5 5 5 4 = __ 5 4 Elliott has __ of the pizza left. 5 18

1=

5 5

Practice 1

2 1 There are 1 __ pepperoni pizzas. There is __ of a cheese pizza. 5 5 1

4 If Jacob eats __ of the pizzas, how much pizza will be left altogether? 5 2 1 Add 1 __ and __. 5 5 Find the total amount of pizzas 1_ _2_ _ 1 + = to start with. 5 5 3 4 Subtract __ from 1 __. 5 5 3 4 8 4 1 __ − __ = __ − __ = 5 5 5 5 2

Subtract what Jacob eats from the total amount.

6 4 Emma has __ l of orange juice and __ l of apple juice. 7 7 5 She uses __ l of juice to make a smoothie. 7 What is the total amount of juice left after Emma makes the smoothie?

Find the total amount of juice. 5 Subtract __ l from the total amount of juice. 7 There is

_4_ + _6_ = 7 7 5 − __ = 7

l of juice left after Emma makes the smoothie. 19

Fractions of lengths

Lesson 8

Starter Jacob and his friends go on a 16-mile bike ride. After 30 minutes, they have 1 cycled __ of the total distance. 4 How many more miles do they need to cycle?

Example The entire bike ride is 16 miles. We need to find 1 quarter of 16.

We can divide to find out. 16 ÷ 4 = 4 Each part is 4 miles. 1 4 4

3 4 4

4 16

4

If we split 16 into 4 equal parts, how much is each part?

4

4

4

16 They need to 3 cycle of 16 miles. 4 3 of 16 is 12. 4

Jacob and his friends need to cycle another 12 miles. 20

4

Practice 1

One metre is equal to 1000 millimetres. 3 How many millimetres are in __ of a metre? 4

There are 2

3 millimetres in __ of a metre. 4

A lorry driver is driving home after work. 1 After driving 24 miles he is __ of the way home. 5

24 He then drives half of the remaining distance before stopping for petrol. How many more miles does the lorry driver need to drive before he gets home?

The lorry driver needs to drive

miles before he gets home. 21

Fractions of sets

Lesson 9

Starter 1 Sam has a dozen eggs. He uses __ of 4 the eggs to make breakfast. How many eggs does Sam have left?

12

gs eg

Example One dozen eggs is 12 eggs.

1 4

1 4

1 4

1 12 − 3 = 9 Sam has 9 eggs left. 22

1 4

1 of 12 eggs 4 is 3 eggs. Sam uses 3 eggs to make breakfast.

Practice 1

Holly and her cousin come back from the shop with a box of 20 chocolates. 1 They eat __ of the chocolates. How many chocolates are left? 5 ?

20 There are 2

chocolates left.

Charles buys 15 apples from the store on Sunday. 1 During the first week, he eats __ of his apples. 3 (a) How many apples does Charles eat during the first week?

15 Charles eats

apples during the first week.

1 (b) During the second week, Charles eats __ of the remaining apples. 2 How many apples are left after the second week?

There are

apples left after the second week. 23

Recognising and writing tenths

Lesson 10

Starter

1

1 ___ 10

A farmer has 2 equal-sized fields. He has ploughed 1 whole field. He has also ploughed 1 part of the second field. How can we describe the amount he has ploughed in each field?

Example

1 ___ = 1 tenth 10 1 We can write ___ as 0.1. 10 We read 0.1 as 1 tenth. 1 is 10 times the size of 0.1.

1

1 ___ 10 0.1 is a decimal. The dot is a decimal point.

1 The farmer has ploughed 1 and ___ or 1.1 of his fields. 10 24

3 tenths 3 ___ = 0.3 10 7 tenths 7 ___ = 0.7 10

Practice Write the decimal shown by the shaded part. =1

1 4 4 tenths = ___ = 10

2 tenths =

=

tenths =

=

3

25

Recognising and writing hundredths

Lesson 11

Starter =1 = 1 tenth =? What does the final shaded part stand for?

Example When 1 is divided into 100 equal parts, each part becomes 1 hundredth. =1

1 1 hundredth = ____ 100 We read 0.01 as 1 hundredth. =1

10 10 hundredths = ____ = 0.1 100 10 The shaded part stands for ____ or 0.1. 100 26

1 is 0.01 100 when written as a decimal.

Practice Write the decimal shown by the shaded part. =1

This bar has 100 equal-sized parts.

1

3 hundredths =

100

=

2

19 hundredths =

=

31 hundredths =

=

3

27

Tenths and hundredths as decimals

Lesson 12

Starter

This bar has 100 equal-sized parts. Three of the parts are shaded.

=1

How much of the bars are shaded in total?

Example Show the tenths and hundredths using 0.1 and

0.01

.

= 0.2 = 0.03

0.1

0.1

0.01 0.01 0.01

ones

tenths

hundredths

0

2

3

2 tenths + 3 hundredths = 23 hundredths 2 The digit 2 stands for ___. 10 3 The digit 3 stands for ____. 100 We read 0.23 as 23 hundredths. 23 ____ is 0.23 when written as a decimal. 100

28

2 tenths = 20 hundredths

Show the ones, tenths and hundredths using

, 0.1 and

=1

0.01

0.1

= 0.2 = 0.03 23 1 ____ is 1.23 when written as a decimal. 100

.

0.1

0.01 0.01 0.01

ones

tenths

hundredths

1

2

3

We read 1.23 as one and twenty-three hundredths.

Show 1.23 on a number line.

1.23 0

0.5

1

1.5

The amount of the bars that are shaded is 1.23.

Practice 1

What does the digit 7 stand for in each number? (a)

0.71

(b)

0.37

(c)

1.97

(d)

7.25

(e) 12.37

2

(f ) 76.19

The digit 8 stands for

.

The digit 5 stands for

.

The digit 4 stands for

.

ones

tenths

hundredths

5

8

4

29

Comparing and ordering decimals

Lesson 13

Starter

3

2

5

3

2

5

Lulu and Ravi each use their cards to make a number. Lulu makes the smaller number and Ravi makes the greater number. Which numbers could they have made?

Example

2

makes

3

5

0.1

0.1 0.01 0.01 0.01

0.1

0.01 0.01

5

makes

0.1

2

3

0.1 0.01 0.01 0.01

ones

tenths

hundredths

ones

tenths

hundredths

2

3

5

5

2

3

2.35 < 5.23 2.35 is the smaller number. 5.23 is the greater number. 30

Compare 5.23 and 5.32. ones

tenths

hundredths

ones

tenths

hundredths

5

2

3

5

3

2

Both numbers have the same amount of ones. Compare the hundredths. 5.23 is less than 5.32. 5.23 < 5.32

5.23 = 5 ones + 23 hundredths 5.32 = 5 ones + 32 hundredths

23 hundredths is less than 32 hundredths.

Practice 1

Which number is greater? (a) 0.43 or 0.34?

2

0.1

0.1

0.1

0.1 0.01 0.01 0.01

0.1

0.1

0.1 0.01 0.01 0.01 0.01

(b) 0.58 or 0.85?

(c) 0.65 or 0.59?

(d) 1.28 or 0.78?

(e) 2.67 or 2.76?

Put the following numbers in order from smallest to greatest. (a) 0.34, 0.43, 0.38 , smallest

(b) 3.45, 4.35, 3.54 ,

, greatest

smallest

, greatest 31

Rounding decimals

Lesson 14

Starter

1.9 kg

4.2 kg

6.5 kg

Estimate the mass of each item, rounded to the nearest kg.

Example

1.9 kg kg

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2

1.9 kg is closer to 2 kg than to 1 kg. 1.9 kg ≈ 2 kg We use ≈ to mean approximately. 4.2 kg kg 4

4.1

4.2

4.3

4.4

4.5

4.6

4.7

4.8

4.9

5

4.2 kg is closer to 4 kg than to 5 kg. 4.2 kg ≈ 4 kg

32

6.5 kg kg 6

6.1

6.2

6.3

6.4

6.5

6.6

6.5 kg ≈ 7 kg

6.8

6.9

7

6.5 kg is exactly halfway between 6 kg and 7 kg. We round up to 7 kg.

Practice 1

6.7

Round the following measurements to the nearest centimetre. (a) (b) (d)

(c) 0 cm 1

2

2

3

4

5

6

7

8

9

10

11

12

13

14

15

(a) 9.5 cm ≈

cm

(b) 11.2 cm ≈

cm

(c) 5.3 cm ≈

cm

(d) 6.4 cm ≈

cm

Estimate the total mass of the 2 boxes by rounding to the nearest kg.

21.3 kg

24.6 kg

21.3 kg ≈ kg +

24.6 kg ≈ kg =

kg

The total mass of the 2 boxes is approximately

kg. 33

Writing fractions as decimals

Lesson 15

Starter

1 = 2

1 How can Charles write __ as a decimal? 2

Example _1_ = 5 tenths 2 _1_ = 0.5 2 1 Charles writes __ as 0.5. 2 1 Write __ as a decimal. 4

×5 1 5 = 2 10 ×5

× 25 1 25 = 4 100 × 25

1 __ = 25 hundredths 4 1 __ = 0.25 4 34

3 Write __ as a decimal. 4

× 25 3 75 = 4 100 × 25

3 __ = 75 hundredths 4 3 __ = 0.75 4

Practice Fill in the blanks. 1

2

1 (a) __ = 5

10

2 (b) __ = 5

10

4 (c) __ = 5

10

1 (a) __ = 2

100

1 (b) __ = 4

100

3 (c) __ = 4

100

=

tenths =

=

tenths =

=

tenths =

=

hundredths =

=

hundredths =

=

hundredths =

35

Dividing by 10

Lesson 16

Starter Miss A’liya needs to cut 4 sheets of art paper so that she can put an equal amount of art paper on each of the 10 tables in the classroom. What fraction of a whole sheet of art paper will Miss A’liya put on each table?

Example Divide 4 by 10. 1 10

1 10

1 10

1 10

Each sheet of paper is divided into 10 equal pieces. 4 Each table has ___ of a sheet of paper. 10 4 ÷ 10 = 4 tenths = 0.4

4 tenths is 10 times smaller than 4.

Miss A'liya will put 0.4 of a sheet of art paper on each table. 36

What if Miss A’liya cuts 24 sheets of art paper so that she can put an equal amount of art paper on each of the 10 tables in the classroom? Divide 24 by 10.

1 10

1 10

1 10

24 = 20 + 4

÷ 10

tens

ones

tenths

2

4

tens

ones

tenths

2

4

1 10

20 ÷ 10 = 2 4 ÷ 10 = 0.4 24 ÷ 10 = 2.4 The digits move to a place 10 times smaller when a number is divided by 10.

There will be 2.4 sheets of art paper on each table.

Practice Divide. 1

2

7 ÷ 10 = 7

63 ÷ 10 = 63

37

Dividing by 100

Lesson 17

Starter Each tray of toffee is cut so the same number of pieces can be put into 100 bags of mixed sweets.

How much of a tray of toffee does Ravi put into each bag of mixed sweets?

Example Each piece is 1 hundredth of a tray of toffee.

1 100

2 ÷ 100 = 2 hundredths = 0.02 38

1 100

ones ÷ 100

tenths

hundredths

ones

tenths

hundredths

0

0

2

2 hundredths is 100 times smaller than 2.

2

The digit 2 moves from the ones to the hundredths when it becomes 100 times smaller. Ravi puts 0.02 of a tray of toffee into each bag of mixed sweets.

Practice 1

Fill in the blanks. (a) 4 ÷ 100 =

hundredths

hundredths

=

= (c) 23 ÷ 100 =

(b) 9 ÷ 100 =

tenths

hundredths

= 2

Divide. (a) 5 ÷ 10 = 0.5

(b) 9 ÷ 10 = 0.9

5 ÷ 100 =

9 ÷ 100 =

(c) 20 ÷ 100 = 0.2

(d) 40 ÷ 100 = 0.4

3 ÷ 100 = 0.03

7 ÷ 100 = 0.07

23 ÷ 100 =

47 ÷ 100 = 39

Review and challenge 1

Fill in the blanks. (a) 0

1 10

9 10

1

(b) 56 100

2

64 65 100 100

Write the following numbers on the number line. The first one has been done for you. 5 3 1 3 1 (a) 1 __, 2 __, __, 1 __, 2 __ 8 8 4 4 2 1

0

1

5 8

2

3

3 1 1 4 (b) ___, 1 __, 1 __, __ 10 5 2 5 3 10

0 40

1

2

3

Find the equivalent fractions. 1 (a) __ = 5 5 (b) __ = 6

7 (c) ___ = 10

4

5

10

12

40

3 = ___ = 15

=

=

20

15

49

=

=

30

100

Add and give your final answer in its simplest form. 4 5 (a) __ + __ = 8 8

+

=

5 6 (b) 1 __ + __ = 9 9

+

=

Subtract and give your final answer in its simplest form. 5 (a) 1 − __ 9

=

−

=

2 4 (b) 2 __ − __ = 5 5

−

=

41

6

1 Ruby has a 4-l container full of water. She uses __ l of water to fill a glass. 4 How many glasses can Ruby fill? 1l

1 l 4

Ruby can fill 7

glasses.

Write each decimal shown below in the place-value chart and fill in the blanks. (a)

0.1

0.1

0.1

0.1

0.1

0.1

tenths

tenths

3 ones + 2 tenths = (b)

ones

0.1

ones

tenths

hundredths

0.01 0.01 0.01

5 tenths + 3 hundredths = hundredths is 42

hundredths when written as a decimal.

8

Fill in the blanks.

3.79

(a) The digit

7 stands for ___. 10

(b) The digit

is in the

hundredths place. (c) The digit 3 is in the place.

9

Arrange the numbers from smallest to greatest. (b) 6.54, 5.64, 6.45

(a) 0.54, 0.55, 0.45 , smallest

10

,

, greatest

,

smallest

greatest

Round the following masses to the nearest kilogram. (a)

3.8 kg ≈

(b)

3.8 kg

kg

5.3 kg ≈

(c)

5.3 kg

kg

13.5 kg ≈

13.5 kg

kg

43

11

12

44

Draw lines to match.

0.47

1 2 ___ 10

3.19

71 6 ____ 100

2.1

47 ____ 100

6.71

19 3 ____ 100

9.03

7 6 ___ 10

6.7

3 9 ____ 100

Write each measurement as a decimal. 1 (a) 3 __ kg = 2

kg

1 (b) 5 __ m = 4

m

3 (c) 2 __ m = 4

m

3 (d) 4 __ kg = 4

kg

13

1 Sam has __ the number of comic books that Holly has. 2 3 Holly has __ the number of comic books that Lulu has. 4 If Lulu has 24 comic books, how many comic books do the 3 children have altogether?

The children have 14

comic books altogether.

Round the following masses to the nearest kilogram to estimate the total mass of the three suitcases. 13.6 kg

12.9 kg

The total mass of the three suitcases is approximately

14.5 kg

kg. 45

Answers Page 5 Page 8

Page 9

Page 11 Page 13

Page 15 Page 17

Page 19

Page 21

Page 23

Page 25 Page 27

46

9 43 79 1 (a) ____ (b) ____ (c) ____ 2 100 100 100

13 14 15 16 100 100 100 100

19 100

22 23 100 100

1 1 1 1 3 + __ = 3 __ . There are 3 __ brownies in total. 6 6 6 1 1 1 2 6 + __ = 6 __. There are 6 __ rows of stamps altogether. 5 5 5 3 3 3 1 1 1 3 (a) 2 + __ = 2 __. 2 and 1 quarter is 2 __. (b) 1 + ___ = 1 ___. 1 and 3 tenths is 1 ___. 4 4 4 10 10 10 2 2 2 (c) 4 + __ = 4 __. 4 and 2 thirds is 4 __. 3 3 3 2 4 3 9 12 5 25 50 3 6 1 2 1 __ = ___ = ___ 2 __ = ___ = ___ 3 ___ = ___ = ___ 4 __ = ___ = ___ 7 14 21 7 14 21 10 30 40 9 45 90 3 6 3 8 4 10 5 6 2 2 4 1 1 4 1 (a) 1 __ = 1 __ (b) 2 __ = 2 __ 2 (a) __ = __ (b) ___ = __ (c) ___ = __ (d) 3 __ = 3 __ (e) 7 ___ = 7 __ 3 3 5 8 2 9 8 4 10 5 12 6 9 10 9 3 (f ) 9 ___ = 9 __ 4 12 3 4 7 5 5 2 1 3 2 3 5 4 1 (a) __ + __ = __ (b) __ + __ = 1 __ 2 (a) __ + __ = __ (b) __ + __ = __ = 1 7 7 7 5 5 5 8 8 8 6 6 6 5 1 3 5 9 5 1 4 7 3 4 4 1 (a) 2 − __ = 1 __ − __ = 1 __ (b) 3 − __ = 2 __ − __ = 2 __ (c) 8 − __ = 7 __ − __ = 7 __ 5 5 5 5 7 7 7 7 9 9 9 9 3 1 2 10 4 3 6 8 6 1 4 1 (d) 4 − __ = 3 __ − __ = 3 __ 2 (a) 4 − ___ = 3 ___ − ___ = 3 __ (b) 7 − __ = 6 __ − __ = 6 __ 3 3 3 3 5 4 10 10 10 8 8 8 5 21 5 16 2 4 10 4 6 1 3 (a) 2 − __ = ___ − __ = __ = 1 __ (b) 3 − __ = ___ − __ = ___ = 2 __ 5 5 5 5 5 7 7 7 7 7 3 3 4 8 4 4 4 6 10 10 5 5 5 1 2 1 1 __ + __ = 1 __, 1 __ – __ = __ – __ = __ 2 __ + __ = ___, ___ – __ = __. There is __ l of juice left after 5 5 5 5 5 5 5 5 7 7 7 7 7 7 7 Emma makes the smoothie. 3 1 There are 750 millimetres in __ of a metre. 2 The lorry driver needs to drive 48 miles 4 before he gets home. 1 There are 16 chocolates left. 2 (a) Charles eats 5 apples during the first week. (b) There are 5 apples left after the second week. 8 9 4 1 4 tenths = ___ = 0.4 2 8 tenths = ___ = 0.8 3 9 tenths = ___ = 0.9 10 10 10 3 19 1 3 hundredths = ____ = 0.03 2 19 hundredths = ____ = 0.19 100 100 31 3 31 hundredths = ____ = 0.31 100

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1 (a) 7 tenths (b) 7 hundredths (c) 7 hundredths (d) 7 ones (e) 7 hundredths (f ) 7 tens 2 (a) The digit 8 stands for 8 tenths. The digit 5 stands for 5 ones. The digit 4 stands for 4 hundredths.

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1 (a) 0.43 (b) 0.85 (c) 0.65 (d) 1.28 (e) 2.76 2 (a) 0.34, 0.38, 0.43 (b) 3.45, 3.54, 4.35

Page 33

1 (a) 9.5 cm ≈ 10 cm (b) 11.2 cm ≈ 11 cm (c) 5.3 cm ≈ 5 cm (d) 6.4 cm ≈ 6 cm 2 21.3 kg ≈ 21 kg, 24.6 kg ≈ 25 kg, 21 kg + 25 kg = 46 kg. The total mass of the 2 boxes is approximately 46 kg.

Page 35

2 4 1 2 4 8 1 (a) __ = ___ = 2 tenths = 0.2 (b) __ = ___ = 4 tenths = 0.4 (c) __ = ___ = 8 tenths = 0.8 5 10 5 10 5 10 1 50 1 25 2 (a) __ = ____ = 50 hundredths = 0.5 (b) __ = ____ = 25 hundredths = 0.25 4 2 100 100 3 75 (c) __ = ____ = 75 hundredths = 0.75 4 100

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1 7 ÷ 10 = 0.7 2 63 ÷ 10 = 6.3

Page 39

1 (a) 4 ÷ 100 = 4 hundredths = 0.04 (b) 9 ÷ 100 = 9 hundredths = 0.09 (c) 23 ÷ 100 = 2 tenths 3 hundredths = 0.23 2 (a) 5 ÷ 100 = 0.05 (b) 9 ÷ 100 = 0.09 (c) 23 ÷ 100 = 0.23 (d) 47 ÷ 100 = 0.47

Page 40

1 (a)

0

2 (a)

1 10

3 10

Page 42

7 10

1 4

1

0

Page 41

4 10 5 3 1 8 4

1

9 10 2

1

(b)

56 100

(b)

3 1 2 8 2

2

3

3 10

0

58 59 60 100 100 100 4 5

64 65 100 100 1

1 5

1

1

1 2

2

3 5 10 15 25 1 2 4 7 28 49 70 4 5 1 1 3 (a) __ = ___ = ___ = ___ (b) __ = ___ = ___ = ___ (c) ___ = ___ = ___ = ____ 4 (a) __ + __ = 1 + __ = 1 __ 5 10 15 20 6 12 18 30 8 8 8 8 10 40 70 100 5 6 2 5 9 5 2 3 11 4 4 7 4 (b) 1 __ + __ = 1 + __ = 2 __ 5 (a) 1 – __ = __ – __ = __ (b) 2 __ – __ = 1 __ – __ = 1 __ 5 5 5 5 5 9 9 9 9 9 9 9 9 6 Ruby can fill 16 glasses. 7 (a) (b)

ones

tenths

hundredths

0

5

3

ones

tenths

3

2

3 ones + 2 tenths = 32 tenths

5 tenths + 3 hundredths = 53 hundredths 53 hundredths is 0.53 when written as a decimal.

47

Answers continued Page 43

Page 44

7 8 (a) The digit 7 stands for ___. (b) The digit 9 is in the hundredths place. 10 (c) The digit 3 is in the ones place. 9 (a) 0.45, 0.54, 0.55 (b) 5.64, 6.45, 6.54 10 (a) 3.8 kg ≈ 4 kg (b) 5.3 kg ≈ 5 kg (c) 13.5 kg ≈ 14 kg 11

0.47

1 2 ___ 10

3.19

71 6 ____ 100

2.1

47 ____ 100

6.71

19 3 ____ 100

9.03

7 6 ___ 10

6.7

3 9 ____ 100

3 3 1 1 12 (a) 3 __ kg = 3.5 kg (b) 5 __ m = 5.25 m (c) 2 __ m = 2.75 m (d) 4 __ kg = 4.75 kg 4 4 4 2 Page 45

48

13 The children have 51 comic books altogether. 14 The total mass of the three suitcases is approximately 42 kg.