Maths ― No Problem! Multiplication and Division, Ages 8-9 (Key Stage 2) (Master Maths At Home) 9780241539347, 024153934X

Table of contents :
Contents
Multiplying by 6, 7 and 9
Multiplying by 11
Multiplying by 12
Multiplying by 1 and 0
Dividing by 6, 7 and 9
Dividing by 11
Dividing by 12
Multiplying multiples of 10 and 100
Multiplying 2-digit numbers
Multiplying 3-digit numbers without renaming
Multiplying 3-digit numbers with renaming
Multiplying multiple numbers
Dividing 2-digit numbers
Dividing 3-digit numbers
Review and challenge
Answers

Citation preview

KS2

8–9 Years

Master Maths at Home

Multiplication and Division 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 1 001–327089–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: 978-0-24153-934-7 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 Multiplying by 6, 7 and 9

4

Multiplying by 11

8

Multiplying by 12

10

Multiplying by 1 and 0

12

Dividing by 6, 7 and 9

14

Dividing by 11

18

Dividing by 12

20

Multiplying multiples of 10 and 100

22

Multiplying 2-digit numbers

24

Multiplying 3-digit numbers without renaming

26

Multiplying 3-digit numbers with renaming

28

Multiplying multiple numbers

30

Dividing 2-digit numbers

32

Dividing 3-digit numbers

36

Review and challenge

40

Answers

46

Ruby

Elliott

Amira

Charles

Lulu

Sam

Oak

Holly

Ravi

Emma

Jacob

Hannah

Multiplying by 6, 7 and 9

Lesson 1

Starter Tuna Tuna Tuna

How many drinks does the shopkeeper have for sale in total?

Tuna Tuna Tu na Tuna

Tuna Tuna Tuna

Tuna Tu na Tuna

330 ml

330 ml 330 ml

330 ml 330 ml

330 ml

330 ml

330 ml

330 ml

330 ml

Tuna Tuna Tuna

Tuna Tuna Tu na Tuna

Tuna

330 ml 330 ml

330 ml 330 ml

330 ml 330 ml

Tuna Tuna Tu na Tuna

330 ml 330 ml

330 ml 330 ml

330 ml 330 ml

330 ml 330 ml

330 ml 330 ml

330 ml 330 ml

330 ml 330 ml

Example 1 There are 5 packs on the shelf. Each pack has 6 drinks.

330 ml 330 ml

12 24 12 6 24 + 6 = 30 4

330 ml 330 ml

Tuna Tuna Tuna

Tuna Tu na Tuna

330 ml 330 ml

We can multiply to find out. I can use counters to help.

330 ml 330 ml

330 ml 330 ml

Tuna Tuna Tu na Tuna

Tuna

330 ml 330 ml

330 ml 330 ml

330 ml 330 ml

330 ml 330 ml

2 × 6 = 12 double 12 = 24 add 6 to 24 = 30

The shopkeeper has 2 packs in his hands as well.

5 × 6 = 30

I already know 5 × 6 = 30. I remember 2 × 6 = 12. I can add 30 and 12.

2 × 6 = 12

30 + 12 = 42 The shopkeeper has 42 drinks for sale in total.

5

2

The shopkeeper found 2 more packs in the storeroom. How many packs does he now have for sale?

Tuna Tuna Tuna

Tuna

Tuna Tuna Tuna

Tuna Tuna Tuna

Tuna Tuna Tuna

Tuna Tuna Tuna

Tuna Tuna

Tuna Tuna Tuna

Tuna Tuna Tuna

Tuna

Tuna Tuna Tuna

Tuna Tuna Tuna

Tuna Tuna

Tuna Tuna Tuna

Tuna

330 ml

330 ml 330 ml

330 ml 330 ml

330 ml 330 ml

330 ml

330 ml

330 ml

330 ml

330 ml 330 ml

330 ml 330 ml

330 ml 330 ml

330 ml 330 ml

330 ml 330 ml

330 ml 330 ml

330 ml 330 ml

330 ml 330 ml

330 ml 330 ml

330 ml 330 ml

330 ml 330 ml

330 ml 330 ml

330 ml 330 ml

330 ml 330 ml

330 ml 330 ml

330 ml

330 ml

330 ml 330 ml

That means there are now 9 packs of 6 cans in total. We can just add another 12 cans.

330 ml 330 ml

330 ml 330 ml

330 ml

330 ml 330 ml

330 ml 330 ml

5 × 6 = 30

2 × 6 = 12

42 + 12 = 54

2 × 6 = 12

9×6

10 × 6

1×6 60 − 6 = 54 The shopkeeper now has 54 drinks for sale. 6

I know 10 × 6 = 60 so I can also subtract 6 from 60 to find the answer.

Practice Fill in the blanks. 1

9×7=

10 × 7 =

1×7= 2

2×9= 5×9=

2×9= 1×9= 3

(a) 4 × 6 =

(b) 3 × 9 =

(c) 8 × 7 =

(d) 6 × 7 =

(e) 5 × 6 =

(f ) 5 × 9 =

(g) 7 × 9 =

(h) 9 × 7 =

(i)

× 6 = 60

(l)

× 7 = 49

(j)

× 7 = 28

(k)

× 9 = 36

7

Multiplying by 11

Lesson 2

Starter Each time Elliott’s mum buys a coffee, the coffee shop stamps her loyalty card. When she has bought 10 coffees, the next coffee is free. Today she received her 6th free coffee. How many coffees has Elliott’s mum had in total since she started using the loyalty cards?

Example

Elliott’s mum has filled 6 loyalty cards in total. Each loyalty card is equal to 11 coffees. bought 6 × 10 = 60

8

free 6×1=6

6 × 11 = 6 × 10 + 6 × 1 = 60 + 6 = 66 Elliott’s mum has had 66 coffees in total since she started using the loyalty cards.

Practice Fill in the blanks. 1

8 × 10 = 8 × 11 =

8×1= +

8 × 11 = 2

3

(a) 5 × 10 =

(b) 5 × 1 =

(c) 5 × 11 =

(d) 3 × 10 =

(e) 3 × 1 =

(f ) 3 × 11 =

(g) 9 × 10 =

(h) 9 × 1 =

(i)

(a) 1 × 11 =

(b) 7 × 11 =

(c) 2 × 11 =

(d) 10 × 11 =

(e) 4 × 11 =

(f ) 11 × 11 =

9 × 11 =

9

Multiplying by 12

Lesson 3

Starter 12 12 12 12 12 12

12 12 12 12 12 12

£5.00

How many doughnuts are in the boxes in total?

Example Each box has 12 doughnuts.

12

10 × 12 = 120

2 × 12 = 24

120 + 24 = 144 There are 144 doughnuts in the boxes in total. 10

There are 12 boxes in total. We need to multiply 12 by 12.

1 20 + 24 1 44

Practice 1

2

3

Multiply. (a) 7 × 10 =

(b) 7 × 2 =

(c) 7 × 12 =

(d) 4 × 10 =

(e) 4 × 2 =

(f ) 4 × 12 =

(g) 3 × 10 =

(h) 3 × 2 =

(i)

3 × 12 =

Multiply. (a) 5 × 12 =

(b) 1 × 12 =

(c) 6 × 12 =

(d) 11 × 12 =

A farmer collects 3 dozen eggs from his chickens on Monday. On Tuesday he collects twice as many eggs as he did on Monday. On Wednesday he collects only 1 dozen eggs.

1 dozen = 12

Monday

1 dozen 1 dozen 1 dozen

Tuesday

1 dozen 1 dozen 1 dozen 1 dozen 1 dozen 1 dozen

Wednesday

?

1 dozen

(a) How many dozens of eggs does he collect over the 3 days? The farmer collects

dozens of eggs over the 3 days.

(b) How many eggs does he collect in total over the 3 days? He collects

eggs in total over the 3 days. 11

Multiplying by 1 and 0

Lesson 4

Starter How many cupcakes are left each time one box is sold?

4C

es up cak cak up es 4C

4C

es up cak cak up es 4C

4C

es up cak cak up es 4C

Example The shop starts with 3 boxes of 4 cupcakes.

4C es up cak cak up es 4C

4C es up cak cak up es 4C

3 boxes of 4 cupcakes 3 × 4 = 12

4C es up cak cak up es 4C

If 1 box is sold, there will be 2 boxes of 4 cupcakes left.

4C es up cak cak up es 4C

4C es up cak cak up es 4C

2 boxes of 4 cupcakes 2×4=8 1 box of 4 cupcakes 1×4=4

12

4C es up cak cak up es 4C

0 boxes of 4 cupcakes 0×4=0

4C es up cak cak up es 4C

4C es up cak cak up es 4C

4C es up cak cak up es 4C

4C es up cak cak up es 4C

The baker will need to prepare more boxes.

4C es up cak cak up es 4C

4C es up cak cak up es 4C

4C es up cak cak up es 4C

4C es up cak cak up es 4C

4C es up cak cak up es 4C

4C es up cak cak up es 4C

4C es up cak cak up es 4C

4C es up cak cak up es 4C

4C es up cak cak up es 4C

4C es up cak cak up es 4C

4C es up cak cak up es 4C

3 boxes of 0 cupcakes 3×0=0 3 boxes of 1 cupcake 3×1=3 3 boxes of 2 cupcakes 3×2=6 3 boxes of 3 cupcakes 3×3=9 3 boxes of 4 cupcakes 3 × 4 = 12

Practice Fill in the blanks. 1

7×0=

2

8× 11 ×

3

× 1 = 12

4

5

×9=9

6

=8 =0 ×6=0 13

Dividing by 6, 7 and 9

Lesson 5

Starter Can you help Ravi solve these equations?

24 ÷ 6 = ?

45 ÷ 9 = ?

56 ÷ 7 = ?

Example 9 There are 45 in total. There are 9 in each row.

There are 5 rows. 45 ÷ 9 = 5

14

5

There are 24 in total. There are 6 in each row.

6 4

There are 4 rows. 24 ÷ 6 = 4 7

There are 8 rows of 7 .

8

56 ÷ 7 = 8

Practice Fill in the blanks. 1

(a)

in each row.

There are

rows.

There are 48 ÷

=

15

(b)

There are

in

each row. There are

rows. =

27 ÷

in

There are

(c)

each row. There are 35 ÷ 2

(a) Circle the counters to show groups of 7.

There are

groups

There are 7 groups of

(c) 35 ÷ 7 = 16

counters.

Divide. (a) 54 ÷ 9 =

=

(b) Circle the counters to show 7 equal groups.

of 7 counters. 3

rows.

(b) 60 ÷ 6 = (d) 72 ÷ 9 =

(e) 49 ÷ 7 =

(f ) 18 ÷ 6 =

(g) 36 ÷ 9 =

(h) 42 ÷ 7 =

(i)

(j)

42 ÷ 6 =

(k) 28 ÷ 7 = 4

(l) 21 ÷ 7 =

A baker bakes bread in batches of 6 loaves at a time. By lunchtime he has baked 48 loaves. How many batches has he baked so far?

The baker has baked 5

81 ÷ 9 =

batches so far.

Fifty-six children sign up for the netball club. Each netball team needs 7 players. How many netball teams can the club have with 56 children?

The netball club can have

teams. 17

Dividing by 11

Lesson 6

Starter Amira’s mum and dad are setting up the tables for their nephew’s wedding. There are 88 chairs and 11 tables.

How many chairs should go around each table?

Example We need to divide 88 by 11. 8

I know that 8 × 11 = 88. It is in the same family of multiplication and division facts as 88 ÷ 11. This is the family of multiplication and division facts for 8 and 11.

11

8 × 11 = 88 88 ÷ 8 = 11

11 × 8 = 88 88 ÷ 11 = 8

If 8 × 11 = 88 then 88 ÷ 11 = 8. 18

Practice 1

2

Divide. (a) 22 ÷ 11 =

(b) 11 ÷ 11 =

(c) 33 ÷ 11 =

(d) 66 ÷ 11 =

(e) 88 ÷ 11 =

(f ) 44 ÷ 11 =

Complete the family of division and multiplication facts. 99 ÷ 11 = 9×

3

99 ÷ =

= ×

=

Charles has 10 times as many trading cards as Oak has. Altogether, they have 77 trading cards.

77

How many trading cards does Oak have?

Oak has

trading cards. 19

Dividing by 12

Lesson 7

Starter Amira has 48 game cards. She needs to make stacks of 12 cards for a game. How many stacks can she make? b

me ga rd a o

Example

I know that 4 × 12 = 48.

If 4 × 12 = 48 then 48 ÷ 12 = 4. Amira can make 4 stacks of 12 cards. 20

48 ÷ 12 = 4

Practice 1

2

Divide. (a) 60 ÷ 12 =

(b) 84 ÷ 12 =

(c) 12 ÷ 12 =

(d) 120 ÷ 12 =

(e) 132 ÷ 12 =

(f ) 144 ÷ 12 =

Complete the family of division and multiplication facts. 72 ÷

72 ÷ 12 = 12 ×

3

=

= ×

=

There are 96 people waiting to ride a rollercoaster. Only 12 people at a time can ride. How many times will the rollercoaster need to go around so that everyone gets a ride?

The rollercoaster will need to go around gets a ride.

times so that everyone 21

Multiplying multiples of 10 and 100

Lesson 8

Starter

How many tens and how many hundreds are shown?

Example

Each of these has 8 tens. 8 tens = 80 3 × 8 tens = 24 tens 24 tens = 240

Each of these has 9 hundreds. 9 hundreds = 900 2 × 9 hundreds = 18 hundreds 18 hundreds = 1800 22

Practice Fill in the blanks. 1

× 4 tens =

tens

3 × 40 =

2

5×

hundreds =

hundreds

5 × 800 =

3

(a) 5 × 50 =

(b) 6 × 30 =

(c) 2 × 600 =

(d)

(e) 8 × 900 =

(f ) 6 ×

× 300 = 1200 = 4200

23

Multiplying 2-digit numbers

Lesson 9

Starter How many of each type of drink are there?

Fruit Drinks 15 Pack

Water 12 Pack

Fruit Drinks 15 Pack

Water 12 Pack

Example We can multiply 12 by 4 to find how many water bottles there are in total. 1

12 × 10

2 4 8

2 4×2=8 1

12 × 10 4 × 12 = 48 There are 48 bottles of water in total. 24

4 8

2

4 × 10 = 40

2

+

4

0

4

8

Water 12 Pack

Fruit Drinks 15 Pack

Water 12 Pack

We multiply 15 by 3 to find the total number of fruit drinks.

1 ×

5 3

Multiply the ones. 1 ×

1

5 3

1

1

×

5

5

15

3

1 ten 5

5

Multiply the tens and then add. 1

1

5

×

1

3 3

×

5 +

5 3

1

5

3

0

4

5

15 × 3 = 45 There are 45 fruit drinks in total.

Practice Multiply. 1

14 × 2 = 1 × +

2

37 × 6 =

4 2

3 ×

7 6

+

25

Multiplying 3-digit numbers without renaming

Lesson 10

Starter Ravi is shopping with his family. They need 4 new kitchen chairs. The 4 chairs they like cost £122 each. How much do the 4 chairs cost in total?

£122

£122

£122

Example

We need to multiply 122 by 4.

1

Multiply the ones.

2

×

2 4 8

1

Multiply the tens.

2

×

100

2

20

2

122

4 8 8

26

122

0

100

20

2

£122

1

Multiply the hundreds.

2

×

2

122

4 8

Add.

+

8

0

4

0

0

4

8

8

100

20

2

The 4 chairs cost £488 in total.

Practice 1

2

232 × 3 = 2

3

×

2

4

3

4

+

1 2

+

4

430 × 2 =

×

3

×

+

3

431 × 2 =

3

201 × 4 =

0 2

2 ×

0

1 4

+

27

Multiplying 3-digit numbers with renaming Starter

Lesson 11

New Delhi Jaipur

A bus does a round trip 3 days a week from New Delhi to Jaipur. The distance each way is 324 km. How many kilometres does the bus travel each week?

Example The bus does six trips in total: three trips to Jaipur and three trips back to New Delhi. We need to multiply 324 by 6.

Multiply the ones. 3

2

2

×

4 6 4

First multiply the ones. 4 ones × 6 = 24 ones. Place a 4 in the ones place and a 2 above the tens place to show 2 tens.

Multiply the tens. 1

3

2

2

×

6 4

28

4 4

Next multiply the tens. 2 tens × 6 = 12 tens. Add 2 tens to the 12 tens to make 14 tens. Write a 4 in the tens place and a 1 above the hundreds place to show 1 hundred.

Multiply the hundreds. 1

2

3

2

Multiply the hundreds. 3 hundreds × 6 = 18 hundreds. Add the 1 hundred to the 18 hundreds to make 19 hundreds. Write a 1 in the thousands place and a 9 in the hundreds place.

4

×

6 1

9

4

4

324 × 6 = 1944 The coach travels 1944 km each week.

Practice Multiply. 1

2

435 × 4 = 4

3

×

3

7

6

825 × 2 = 5 2

576 × 6 =

9 5

2

×

6

7 3

8

9

4

3

×

5

469 × 5 =

×

3

4

475 × 9 =

×

5

5 4

4

337 × 3 =

5 ×

7

6 6

29

Multiplying multiple numbers

Lesson 12

Starter Charles and his dad are baking fairy cakes for the school bake sale. They bake 2 trays in each batch. The trays hold 6 fairy cakes each. By the end of the day they bake 4 batches. How many fairy cakes do they bake in total?

Example 1 They bake 2 trays of 6 fairy cakes 4 times. That is 2 × 6 × 4. First, we need to find out how many fairy cakes are in each batch.

30

2 × 6 = 12 There are 12 fairy cakes in each batch.

2 × 6 × 4 is the same as 12 × 4. 12

12

12

12

2 × 6 × 4 = 12 × 4 = 48 They bake 48 fairy cakes in total. 2 First I calculated that there are 4 batches of 2 trays.

6 6

6 6

6 6

6 6

Each tray has 6 fairy cakes. That is 4 × 2 × 6.

4 × 2 × 6 = 8 × 6 = 48 They bake 48 fairy cakes in total.

Practice Draw lines to match. 3×2×6

56

7×2×4

6×3×4

60

2×3×6

5×3×4

36

3×4×5

2×4×7

72

3×6×4 31

Dividing 2-digit numbers

Lesson 13

Starter Mr Gifford is expecting 78 teachers for his training course. He wants the same number of teachers at each table. Should he put 6 teachers at each table or 4 teachers at each table?

Shapes

Colours

triangle

red green

circle

yellow square

blue

rectangle

orange

Example

We can divide to check. Let’s start with 78 ÷ 6.

We can split 78 into 60 and 18. 60 ÷ 6 = 10 18 ÷ 6 = 3

78 60

If Mr Gifford puts out 13 tables he can have 6 people at each table.

32

78 18

60

18

10

3

What about 78 ÷ 4? 78

We can split 78 into 40 and 38. We can then split the 38 into 36 and 2.

78 38

40

38

40

36

10

2

36

2

9

40 ÷ 4 = 10 36 ÷ 4 = 9 What about the 2?

remainder

What if we do it this way? 36 ones ÷ 4

4 tens ÷ 4 1 4

7 − −

8

4

4

7 −

3

8

3

6 2

−

8

4

4 −

3

8

3

6 2

−

1

9

7

8

4 3

8

3

6 2 remainder

We can have 19 tables of 4 teachers but 2 teachers will be left out. 78 ÷ 6 = 13 78 ÷ 4 = 19 remainder 2 Mr Gifford should put 6 teachers at each table if he wants equal numbers of teachers at each table. 33

Practice 1

Circle to show 3 equal groups.

48 ÷ 3 = 2

Divide. (a) 72 ÷ 4 =

(b) 54 ÷ 3 =

(c) 87 ÷ 5 =

(d) 99 ÷ 7 =

remainder

5

8

remainder

7

(e) 95 ÷ 3 =

3

34

7

9

9

9

7

(f ) 97 ÷ 4 =

9

5

4

3

At the end of a card game, Hannah has 3 times as many points as Oak has. Sam has twice as many points as Oak has. In total, they have 72 points. How many points does Oak have?

Oak has 4

points.

Five friends are playing a game of cards. The 52 cards are shared equally with all the players. Any remaining cards are not used. How many cards does each player get? How many cards are not used?

Each player gets

cards.

cards are not used. 35

Dividing 3-digit numbers

Lesson 14

Starter 609 ÷ 3 = 364 ÷ 7 = 400 ÷ 6 = How can we divide these numbers?

Example

We can divide 609 by 3 using long division.

6 hundreds ÷ 3

9 ones ÷ 3

2 3

6 −

0

9

6

3

6 −

9 −

9 0

609 ÷ 3 = 203 36

0

9

6

3 −

9 −

9 0

2

0

3

6

0

9

6 9

−

9 0

364 14 ÷ 7 = 2

We can split 364 into 350 and 14.

350

14

50

2

350 is 35 tens. 35 tens ÷ 7 = 5 tens 350 ÷ 7 is 50.

We then add the two quotients. 50 + 2 = 52 364 ÷ 7 = 52

We can do it this way as well. 5 7 −

3

6

3

5

4

7 − −

5

2

3

6

4

3

5

7 −

1

4

1

4

5

2

3

6

4

3

5

−

1

4

1

4 0

400 We can divide 400 by 6 in the same way.

360 60

40 36 6

4 remainder 37

6 6 −

4

0

3

6

0

6 − −

6

6

4

0

0

3

6

6 −

4

0

3

6

6

6

4

0

0

3

6

−

4

0

3

6 4

400 ÷ 6 = 66 remainder 4

Practice Divide. 1

5

3

5

2

5

5

2

0

756 ÷ 6 =

6

4

520 ÷ 8 =

8

38

2

525 ÷ 5 =

7

5

6

9

3

693 ÷ 7 =

7

6

5

8

7

2

4

3

0

5

0

9

7

3

9

5

4

5

9

2

0

3

9

0

0

839 ÷ 4 =

4

12

395 ÷ 7 =

9

920 ÷ 4 =

4

10

6

945 ÷ 9 =

9

8

569 ÷ 5 =

5

11

8

300 ÷ 6 =

6

9

6

824 ÷ 8 =

8

400 ÷ 3 =

3

4

39

Review and challenge 1

Fill in the blanks. (a)

9×6=

(b)

10 × 6 =

2×6= 2×6=

5×6=

1×6 = (c)

2×7= 2×7=

4×7=

40

8×7=

(d)

11 × 7 =

10 × 7 = 2

Fill in the blanks. (a) 6 × 5 =

(b) 7 × 8 =

(c) 9 × 3 =

(d) 5 ×

(e)

3

× 9 = 63

5

(f )

= 35 ×

= 49

Multiply. (a) 5 × 10 =

4

1×7=

(b) 5 × 1 =

(c) 5 × 11 =

(a) 10 × 9 =

(b) 2 × 9 =

(c) 12 × 9 =

(d) 11 × 10 =

(e) 11 × 2 =

(f ) 11 × 12 =

Multiply.

Fill in the blanks. (a) 7 × 0 =

(b)

× 12 = 12

(c) 6 ×

=0 41

6

(a) Circle to show groups of 7.

(b) Circle to show 7 equal groups.

There are

stars.

There are

There are stars.

groups of 7

There are 7 groups of stars.

÷7= 7

÷7=

A large bag of rice weighs 6 times as much as a small bag of rice. Together they weigh 14 kg. How much does each bag of rice weigh?

14 kg

42

stars.

The small bag of rice weighs

kg.

The large bag of rice weighs

kg.

8

9

Divide. (a) 54 ÷ 9 =

(b) 64 ÷ 8 =

(c) 42 ÷ 7 =

(d) 66 ÷ 11 =

A gardener has 96 flowers he would like to plant equally into 12 flower pots. How many flowers should he put in each pot? 96

?

The gardener should put

10

flowers in each pot.

Fill in the blanks. (a) 3 × 60 =

(b) 5 × 40 =

(c) 3 × 200 =

(d)

(e) 9 × 700 =

(f ) 7 ×

× 300 = 1500 = 4900

43

11

Fill in the blanks. (b) 43 × 7 =

(a) 32 × 6 = 3 ×

2

4

6

×

+

3 7

+

(c) 579 × 4 =

(d) 645 × 5 = 5

×

7

6

9 4

×

4

5 5

+

12

A baker bakes 6 batches of 4 trays of muffins in one day. Each tray holds 6 muffins. He then needs to package his muffins into boxes of 12 muffins. How many muffins does he bake in one day?

The baker bakes The baker can fill 44

muffins in one day. boxes of 12 muffins.

13

Divide. (a) 74 ÷ 3 = 3

(b) 85 ÷ 9 = 7

4

9

(c) 879 ÷ 6 = 6

14

8

8

5

(d) 456 ÷ 8 = 7

9

8

4

5

6

Jacob has 6 times as many trading cards as Ruby has. Hannah has 5 times as many trading cards as Ruby has. In total all 3 children have 144 trading cards. How many trading cards do both Jacob and Hannah have altogether?

144

Jacob and Hannah have

trading cards altogether. 45

Answers Page 7

1

2 (a)

10 × 7 =

2

70

2×9=

18

2×9=

18

1×9=

9

9×7=

63

1×7=

7

There are 6 groups of 7 counters. (b)

5×9=

45

3 (a) 4 × 6 = 24 (b) 3 × 9 = 27 (c) 8 × 7 = 56 (d) 6 × 7 = 42 (e) 5 × 6 = 30 (f ) 5 × 9 = 45 (g) 7 × 9 = 63 (h) 9 × 7 = 63 (i) 10 × 6 = 60 (j) 4 × 7 = 28 (k) 4 × 9 = 36 (l) 7 × 7 = 49 Page 9

Page 11

1 8 × 10 = 80, 8 × 1 = 8, 8 × 11 = 80 + 8, 8 × 11 = 88 2 (a) 5 × 10 = 50 (b) 5 × 1 = 5 (c) 5 × 11 = 55 (d) 3 × 10 = 30 (e) 3 × 1 = 3 (f ) 3 × 11 = 33 (g) 9 × 10 = 90 (h) 9 × 1 = 9 (i) 9 × 11 = 99 3 (a) 1 × 11 = 11 (b) 7 × 11 = 77 (c) 2 × 11 = 22 (d) 10 × 11 = 110 (e) 4 × 11 = 44 (f ) 11 × 11 = 121 1 (a) 7 × 10 = 70 (b) 7 × 2 = 14 (c) 7 × 12 = 84 (d) 4 × 10 = 40 (e) 4 × 2 = 8 (f ) 4 × 12 = 48 (g) 3 × 10 = 30 (h) 3 × 2 = 6 (i) 3 × 12 = 36 2 (a) 5 × 12 = 60 (b) 1 × 12 = 12 (c) 6 × 12 = 72 (d) 11 × 12 = 132 3 (a) The farmer collects 10 dozen eggs over the 3 days. (b) He collects 120 eggs in total over the 3 days.

Page 13

1 7 × 0 = 0 2 8 × 1 = 8 3 12 × 1 = 12 4 11 × 0 = 0 51×9=9 60×6=0

Page 15

1 (a)

There are 6 in each row. There are 8 rows. 48 ÷ 6 = 8

6

8

There are 7 groups of 6 counters. 3 (a) 54 ÷ 9 = 6 (b) 60 ÷ 6 = 10 (c) 35 ÷ 7 = 5 (d) 72 ÷ 9 = 8 Page 17

(e) 49 ÷ 7 = 7 (f ) 18 ÷ 6 = 3 (g) 36 ÷ 9 = 4 (h) 42 ÷ 7 = 6 (i) 42 ÷ 6 = 7 (j) 81 ÷ 9 = 9 (k) 28 ÷ 7 = 4 (l) 21 ÷ 7 = 3 4 The baker has baked 8 batches so far. 5 The netball club can have 8 teams.

Page 19

(a) 22 ÷ 11 = 2 (b) 11 ÷ 11 = 1 (c) 33 ÷ 11 = 3 (d) 66 ÷ 11 = 6 (e) 88 ÷ 11 = 8 (f ) 44 ÷ 11 = 4 2 99 ÷ 11 = 9, 99 ÷ 9 = 11, 9 × 11 = 99, 11 × 9 = 99 3 Oak has 7 trading cards.

Page 21

1 (a) 60 ÷ 12 = 5 (b) 84 ÷ 12 = 7 (c) 12 ÷ 12 = 1 (d) 120 ÷ 12 = 10 (e) 132 ÷ 12 = 11 (f ) 144 ÷ 12 = 12 2 72 ÷ 12 = 6, 72 ÷ 6 = 12, 12 × 6 = 72, 6 × 12 = 72 3 The rollercoaster will need to go around 8 times so that everyone gets a ride.

Page 23

1 3 × 4 tens = 12 tens, 3 × 40 = 120 2 5 × 8 hundreds = 40 hundreds, 5 × 800 = 4000 3 (a) 5 × 50 = 250 (b) 6 × 30 = 180 (c) 2 × 600 = 1200 (d) 4 × 300 = 1200 (e) 8 × 900 = 7200 (f ) 6 × 700 = 4200

Page 25

1 14 × 2 = 28 1 4 × 2

2 37 × 6 = 222 3 7 × 6 4

2

+ 2

0

+ 11

8

0

2

8

2

2

2

8 Page 16

9

(b) 3 (c)

7

5

46

There are 9 in each row. There are 3 rows. 27 ÷ 9 = 3 There are 7 in each row. There are 5 rows. 35 ÷ 7 = 5

Page 27

1 232 × 3 = 696 2 3 2 ×

3

2 431 × 2 = 862 4 3 1 ×

2

6 +

2

9

0

6

0

6

0

0

+ 8

0

0

6

9

6

8

6

2

3 430 × 2 = 860 4 3 0 ×

4 201 × 4 = 804 2 0 1

2

×

4

0

Page 29

6

0

+ 8

0

0

8

6

0

1 435 × 4 = 1740 1 2 4 3 × 1

7

4

5 4

4

0

3 475 × 9 = 4275 4 6 4 7 ×

5 9

4

2

7

Page 31

3

4

0

+ 8

0

0

8

0

4

2 337 × 3 = 1011 1 2 3 3 × 1

0

1

4 825 × 2 = 1650 1 8 2 × 1

6

5

8

1 5 2 0

3

4

5

Page 39

6

56

7×2×4

6×3×4

60

2×3×6

5×3×4

36

3×4×5

72

7 5 2

7

1 9 − 7 2 − 2

4 9

Page 35

3 Oak has 12 points. 4 Each player gets 10 cards. 2 cards are not used.

0 0 0 3 4 4 4 0 0 0 0 0 0

4 693 ÷ 7 = 99 7

6 − 6 −

9 9 3 6 6

6 945 ÷ 9 = 105 1 0 9 9 4 − 9 4 − 4 8 920 ÷ 4 = 230 2 3 4 9 2 − 8 1 2 − 1 2 0

6 6 0 9 3 3 3 0 5 5 5 5 0 0 0

11 395 ÷ 7 = 56 remainder 3 12 400 ÷ 3 = 133 remainder 1 1 3 3 5 6 3 4 0 0 7 3 9 5 − 3 − 3 5 1 0 4 5 − 9 − 4 2 1 0 3 − 9 1

9 8 1

(e) 95 ÷ 3 = 31 remainder 2 (f ) 97 ÷ 4 = 24 remainder 1 3 1 2 4 3 9 5 4 9 7 − 9 − 8 5 1 7 − 3 − 1 6 2 1

5 0

6 6

9 569 ÷ 5 = 113 remainder 4 10 839 ÷ 4 = 209 remainder 3 1 1 3 2 0 9 5 5 6 9 4 8 3 9 − 5 − 8 6 3 9 − 5 − 3 6 1 9 3 − 1 5 4

(c) 87 ÷ 5 = 17 remainder 2 (d) 99 ÷ 7 = 14 remainder 1 7 7

6 2 8 4 4

−

48 ÷ 3 = 16 2 (a) 72 ÷ 4 = 18 (b) 54 ÷ 3 = 18 1 8 − 5 3 − 3

5 5 0

5 824 ÷ 8 = 103 1 0 8 8 2 − 8 2 − 2

3×6×4

2 756 ÷ 6 = 126 1 2 6 7 5 − 6 1 5 − 1 2 3 − 3

5 5

7 300 ÷ 6 = 50 5 6 3 0 − 3

1

5

5 − 4 −

6 576 × 6 = 3456 4 3 5 7 6 × 6

5

1 525 ÷ 5 = 105 1 0 5 5 2 − 5 2 − 2

3 520 ÷ 8 = 65

7 3

3×2×6

2×4×7 Page 34

0

5

5 469 × 5 = 2345 4 3 4 6 9 × 5 2

Page 38

Page 40

1 (a)

9×6=

54

10 × 6 =

60

47

Answers continued (b) 2 × 6 = 2×6=

5×6=

12

1×6 =

6

(c) 2 × 7 =

14

2×7=

14

4×7=

Page 44

12

11 (a) 32 × 6 = 192 3

30

×

(d) 77

70

1×7=

8

0

+ 2

8

0

2

3

0

1

Page 42

7

2

4 3

6

2

8

0

+ 2

0

0

0

2

3

1

6

3

6

2

4

×

5 5

3

2 7 − 6 1 − 1

4 4

9

2

1 6 8 − 6 2 − 2 −

There are 56 stars. There are 8 groups of 7 stars. 56 ÷ 7 = 8 14

8 − 8

4 2 2

(c) 879 ÷ 6 = 146 remainder 3

6 (a)

(b)

(d) 645 × 5 = 3225 9

2

5

13 (a) 74 ÷ 3 = 24 remainder 2 (b) 85 ÷ 9 = 9 remainder 4

7

2 (a) 6 × 5 = 30 (b) 7 × 8 = 56 (c) 9 × 3 = 27 (d) 5 × 7 = 35 (e) 7 × 9 = 63 (f ) 7 × 7 = 49 3 (a) 5 × 10 = 50 (b) 5 × 1 = 5 (c) 5 × 11 = 55 4 (a) 10 × 9 = 90 (b) 2 × 9 = 18 (c) 12 × 9 = 108 (d) 11 × 10 = 110 (e) 11 × 2 = 22 (f ) 11 × 12 = 132 5 (a) 7 × 0 = 0 (b) 1 × 12 = 12 (c) 6 × 0 = 0

1

12 The baker bakes 144 muffins in one day. The baker can fill 12 boxes of 12 muffins. Page 45

10 × 7 =

1

9 5

28

7 2

1

×

11 × 7 =

×

2

(c) 579 × 4 = 2316

56

3

+ 1

1

Page 41

4

6 1

8×7=

(b) 43 × 7 = 301 2

4 7 7 4 3 3

6 9

(d) 456 ÷ 8 = 57 8

4 − 4 −

9 6 3

9 5 1 4

5 5 0 5 5

7 6 6 6 0

Jacob Ruby Hannah

Jacob and Hannah have 132 trading cards altogether. There are 35 stars. There are 7 groups of 5 stars. 35 ÷ 7 = 5 7 The small bag of rice weighs 2 kg. The large bag of rice weighs 12 kg. Page 43

48

8 (a) 54 ÷ 9 = 6 (b) 64 ÷ 8 = 8 (c) 42 ÷ 7 = 6 (d) 66 ÷ 11 = 6 9 The gardener should put 8 flowers in each pot. 10 (a) 3 × 60 = 180 (b) 5 × 40 = 200 (c) 3 × 200 = 600 (d) 5 × 300 = 1500 (e) 9 × 700 = 6300 (f ) 7 × 700 = 4900

144