Order of Operations 1 - Worksheet€¦ · ACKNOWLEDGMENTS Set E: Multiplying & Dividing Fractions i Workplace Education Manitoba would like to express appreciation to the following

Watch the video for this workbook at www.wem.mb.ca/learning_on_demand.aspx

Companion Workbook to Numeracy: The Basics Video Series

NUMERAC Y:The Basics Workbook

Set E: Multiplying & Dividing Fractions

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Set E: Multiplying & Dividing Fractions i

Workplace Education Manitoba would like to express appreciation to the following for supporting the development of this curriculum:

The Government of Canada Human Resource Skills Development Canada (HRSDC)

and

The Manitoba Government

Industry Workforce Development (IWD), Entrepreneurship, Training and Trade (ETT)

Workplace Education Manitoba would also like to thank the individuals from across Manitoba who provided consultation, content, and feedback.

For more information, visit www.wem.mb.ca

or contact the Project Coordinator Lindsay Laidlaw at [email protected]

Workplace Education Manitoba

1000 Waverley Street Winnipeg, MB, R3T 0P3

©Workplace Education Manitoba, 2012 All rights reserved; no part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form by any means, electronic, mechanical, photocopying, recording, or otherwise without prior written permission of the Publishers. This manual may not be lent, resold, hired out or otherwise disposed by way of trade in any form of binding or cover than that which it is published, without the prior consent of the Publishers.

http://www.wem.mb.ca/

mailto:[email protected]

1


NUMERACY: The Basics Workbook Set E: Multiplying & Dividing Fractions

INTRODUCTION

What is Numeracy: The Basics Workbook?

This workbook is intended to accompany Workplace Education Manitoba’s (WEM) Numeracy: The

Basics Video Series, a set of 50 videos that explain essential numeracy concepts.

The refresher videos cover 25 critical numeracy topics, each broken into concept and practice.

The video series and accompanying downloadable workbooks can be found on the WEM website at

http://www.wem.mb.ca/learning_on_demand.aspx

These Numeracy: The Basics workbooks provide an opportunity for additional skill-building practice.

Numeracy: The Basics topics are:

Order of Operations 1

Order of Operations 2

Adding & Subtracting Fractions 1

Adding & Subtracting Fractions 2

Multiplying & Dividing Fractions

Mixed & Improper Fractions

Operations with Mixed Fractions 1



Adding & Subtracting Decimals

Multiplying Decimals

Dividing Decimals

Order of Operations & Decimals

Decimals, Fractions & Percent 1

Decimals, Fractions & Percent 2

Imperial Conversions

Metric Conversions

Metric and Imperial Conversions

Geometry 1 – Perimeter

Geometry 2 – Area

Geometry 3- Volume

Solving Equations 1

Solving Equations 2

Ratio & Proportion

Averages

http://www.wem.mb.ca/learning_on_demand.aspx

2



MULTIPLYING & DIVIDING FRACTIONS

This workbook contains five skill-building practice sections. Solutions can be found at the end of the

workbook.

Practice Section A

Calculate the following. Express your answer in lowest terms.

1. 3 1

4 2 =

2. 3 1

4 2 =

3. 3 1

4 8 =

4. 3 1

4 8 =

5. 1 1

4 2 =

6. 1 1

4 2 =

7. 7 1

8 4 =

8. 7 1

8 4 =

9. 3

24 =

10. 3

24 =

11. 1 3

2 16 =

3



12. 1 3

2 16 =

13. 5

816

=

14. 5

816

=

15. 5

816

=

16. 5 3

8 4 =

17. 3 3

8 4 =

18. 3 3

8 4 =

19. 3

38 =

20. 3

38 =

21. 9

316

=

22. 9

316

=

23. 1 7

42 8 =

24. 1 7

42 8

=

25. 1 7

42 8

=

4



Practice Section B


1. 1 3 3

2 16 4

2. 1 7 3

2 8 4

3. 9 1 5

16 2 8

4. 3 5 1

4 8 4

5. 3 7 1

4 8 4

6. 13 3 1

16 4 8

7. 15 1 1

16 4 2

8. 3 3 5

8 4 16

9. 3 1 1

8 8 2

10. 9 9 1

32 16 4

11. 11 3 1

16 8 16

12. 3 1

416 2

13. 3 1 1

16 4 2

5



14. 3 3 5

8 4 16

15. 9 1

816 4

16. 5 3 1

16 8 4

17. 3 3 5 1

8 4 32 2

18. 9 1 3 1

16 2 32 8

19. 9 1 3 1

16 2 32 8

20. 3 3 5

44 4 8

Practice Section C


1. 3 1 1 5 7 1 3 1 3 1 5 1 3 1

8 16 4 8 16 4 4 8 4 32 16 4 8 2 =

2. 3 1 1 5 7 1 3 1

8 16 4 8 16 4 4 8

=

3. 3 3 1 1 5 7 1 3

8 4 2 16 32 16 4 8

=

4. 15 3 1 3 3 1 3 1 1

16 4 8 4 16 2 4 8 2

=

5. 3 1 1 3 3 9 3 3 1 1 3 3 1

4 2 2 8 4 16 8 4 2 16 4 16 2

=

6



Practice Section D

In this section, solutions for the practice questions contain commonly-made errors. For each question,

circle the error(s) and give a correct solution.

1.

5 7 22 3

8 16 32 4

5 4 7 2 22 3 8

8 4 16 2 32 4 8

20 14 22 21

32 32 32 32

20 8 21

32 32 32

20 8 21

32 32 32

9

32

=

Practice Section E

Challenge Question. If you can do this one, then you get an A+.

Calculate the answer to each of the questions below by following the ‘rules’ of fractions. Give your

answer in lowest terms.

3 15 1 3 3 1 3 1 1 1 1 7 5 7 5 1 1

4 16 8 4 16 2 4 8 2 2 4 16 32 8 32 4 2

=

7


NUMERACY: The Basics Workbook

SOLUTIONS

Set E Multiplying & Dividing Fractions

Set E: Multiplying & Dividing Fractions Solutions

8



MULTIPLYING & DIVIDING FRACTIONS

Practice Section A

1. Solution:

3 1

4 2

3 1

4 2

3

8

2. Solution:

3 1

4 2

3 2

4 1

3 2

4 1

6

4

3

2

3. Solution:

3 1

4 8

3 1

4 8

3

32

4. Solution:

3 1

4 8

3 8

4 1

3 8

4 1

24

4

6

5. Solution:

1 1

4 2

1 1

4 2

1

8

6. Solution:

1 1

4 2

1 2

4 1

1 2

4 1

2

4

1

2


9



7. Solution:

7 1

8 4

7 1

8 4

7

32

8. Solution:

7 1

8 4

7 4

8 1

28

8

14

4

7

2

9. Solution:

32

4

3 2

4 1

3 2

4 1

6

4

3

2

10. Solution:

3 2

4 1

3 1

4 2

3 1

4 2

3

8

11. Solution:

1 3

2 16

1 3

2 16

3

32

12. Solution:

1 3

2 16

1 16

2 3

1 16

2 3

16

6

8

3


10



13. Solution:

58

16

5 8

16 1

5 8

16 1

40

16

20

8

10

4

5

2

14. Solution:

58

16

5 1

16 8

5 1

16 8

5

128

15. Solution:

58

16

8 16

1 5

8 16

1 5

128

5

16. Solution:

5 3

8 4

5 3

8 4

15

32

17. Solution:

3 3

8 4

3 3

8 4

9

32

18. Solution:

3 3

8 4

3 4

8 3

3 4

8 3

12

24

1

2


11



19. Solution:

33

8

3 3

8 1

3 3

8 1

9

8

20. Solution:

33

8

3 1

8 3

3 1

8 3

3

24

1

8

21. Solution:

93

16

3 9

1 16

3 9

1 16

27

16

22. Solution:

93

16

3 9

1 16

3 16

1 9

(1) 3

16

1 (3) 9

16

3

23. Solution:

1 74

2 8

1 8 4

2 7 1

1

(1) 2

8 (2) 4

7

1

8 2

7 1

16

7

24. Solution:

1 74

2 8

1 8 4

2 7 1

8 4

14 1

8

7 14

4

2

1

8 2

7 1

16

7


12



25. Solution:

1 74

2 8

1 7

2 (2) 8

(1) 4

1

1 7 1

2 2 1

1 7

2 2

1 2

2 7

1

(1) 2

(1) 2

7

1

7

Practice Section B

1. Solution:

1 3 3

2 16 4

1 3 4

2 16 3

1 31

2

4 16

4

1

1 3

1 1 1

2 4 1

1

8

2. Solution:

1 7 3

2 8 4

1 8 4

2 7 3

1

1 2

2 48

7

3

1 8 2

1 7 3

16

21


13



3. Solution:

9 1 5

16 2 8

9 2 5

16 1 8

1 29

16

5

1 4 8

9 1 5

16 1 4

45

64

4. Solution:

3 5 1

4 8 4

3 5 4

4 8 1

3

1 4

1 45

8

1

3 5 1

1 8 1

15

8

5. Solution:

3 7 1

4 8 4

3 8 1

4 7 4

3

1 4

2 8

1

7 4

3 2 1

1 7 4

6

28

3

14

6. Solution:

13 3 1

16 4 8

13 4 1

16 3 8

1 413

16

1

3 2 8

13 1 1

16 3 2

13

96

7. Solution:

15 1 1

16 4 2

15 4 2

16 1 1

15

4 16

1 4

2

1 1

15

2 4

1 21

1

1

15 1 1

2 1 1

15

2

8. Solution:

3 3 5

8 4 16

3 4 5

8 3 16

1 3

1 4

8 1 3

5

4 16

1 1 5

8 1 4

5

32


14



9. Solution:

3 1 1

8 8 2

3 8 2

8 1 1

3

1 8

1 8

2

1 1

3 1 2

1 1 1

6

1

6

10. Solution:

9 9 1

32 16 4

9 16 1

32 9 4

1 9

4 16

32 1 9

1

1 4

1

8 32

1 4

1

1 1

1 1 1

8 1 1

1

8

11. Solution:

11 3 1

16 8 16

11 8 1

16 3 16

11

2 16

1 8

1

3 16

11 1 1

2 3 16

11

96

12. Solution:

3 14

16 2

3 4 2

16 1 1

3

4 16

1 4

2

1 1

3

2 4

1 21

1

1

3 1 1

2 1 1

3

2

13. Solution:

3 1 1

16 4 2

3 1

16 8

3 8

16 1

3

2 16

1 8

1

3 1

2 1

3

2


15



14. Solution:

3 3 5

8 4 16

3 15

8 64

3 64

8 15

1 3

1 8

8 64 5 15

1 8

1 5

8

5

15. Solution:

9 18

16 4

98

64

8 64

1 9

512

9

16. Solution:

5 3 1

16 8 4

5 3

16 32

5 32

16 3

5

1 16

2 32

3

5 2

1 3

10

3

17. Solution:

3 3 5 1

8 4 32 2

3 4 32 2

8 3 5 1

1 3

2 8

1 4 1 3

32 2

5 1

1

1 2

1 21 32

1 5

1

1 1 32 1

1 1 5 1

32

5


16



18. Solution:

9 1 3 1

16 2 32 8

9 1 32 1

16 2 3 8

3 9

1 16

2 321

2

1 3

1

8

3 1

1 1 2

1 2

1

1 8

3 1 1 1

1 1 1 8

3

8

19. Solution:

9 1 3 1

16 2 32 8

9 1 32 1

16 2 3 8

9 32 1

16 6 8

3 9

1 16

2 32 2 6

1

8

1 23

1

1 2

1

8

3 1 1

1 1 8

3

8

20. Solution:

3 3 54

4 4 8

3 15 4

4 32 1

3 32 1

4 15 4

1 3

1 4

8 32 5 15

1

4

2 81

1

1

5 1 4

1 2 1

1 5 1

2

5


17



Practice Section C

1. Solution:

3 3 5 5 1

8 4 16 32 2

3 4 5 32 2

8 3 16 5 1

(1) 3

2 8

(1) 4

(1) 3

(1) 5

(1)16

2 32

(1) 5

2

1

1

(1) 2

1 1 (1) 2

1 1

2

1 1

1 1 1 1 2

1 1 1 1 1

2

1

2

2. Solution:

3 1 3 13

4 2 8 2

3 1 3 3 2

4 2 1 8 1

3 3 6

4 2 8

3 2 8

4 3 6

(1) 3

(1) 4

(1) 2

(1) 3

2 8 3 6

1 1 2

1 1 3

2

3

3. Solution:

7 3 3 5 1

16 4 4 8 2

7 4 3 8 2

16 3 4 5 1

28 24 2

48 20 1

7 28

12 48

6 24 5 20

2

1

7 6 2

12 5 1

7

2 12

(1) 6

2

5 1

7

(1) 2

1 (1) 2

5

1

7 1 1

1 5 1

7

5


18



4. Solution:

3 3 5 5 36

8 4 16 32 16

3 4 5 32 6 3

8 3 16 5 1 16

(1) 3

2 8

(1) 4

(1) 3

(1) 5

(1)16

2 32

(1) 5

6 3

1 16

3 61 2

2 1

3

1 8 16

1 2 9

2 1 8

1 2 8

2 1 9

1

(1) 2

(1) 2

8

1 9

1 1 8

1 1 9

8

9

5. Solution:

3 3 5 5 25 54

16 4 32 32 64 16

(1) 4

3

1 4 16

15 5 125

128 32 1024

3 75 125

4 4096 1024

3 4096 125

4 75 1024

4 40963

4

3 75

5 125

(1)1024

3 4 5

4 3 1

(1) 3

(1) 4

(1) 4

(1) 3

5

1

1 1 5

1 1 1

5

1

5


19



Practice Section D

1. Solution:

Although the brackets in B mean that the division is done before the multiplication, all three

expressions are equal to 1

8. This means that Jim is correct. (Note that the brackets in C make it

no different than A.)

1 3 3A.

2 16 4

1 3 4

2 16 3

1 (1) 3

2

4 16

(1) 4

(1) 3

1 1 1

2 4 1

1

8

1 3 3B.

2 16 4

1 3 4

2 16 3

1 (1) 3

2

4 16

(1) 4

(1) 3

1 1 1

2 4 1

1

8

1 3 3C.

2 16 4

3 4

32 3

(1) 3

8 32

(1) 4

(1) 3

1 1

8 1

1

8

Practice Section E

Solution:

Hannah

140 7

4

140 7 40

4

280 10

$290

Jack

140 6

2

140 6 40

2

240 20

$260

If Jack makes $260 a week, he earns $290 $260 $30 less than Hannah. If Jack works an extra 4

hours, he will make $26 which will total $286. If he works 4½ hours, he will still not have enough since

an extra 4½ hours is $29.25 yielding $289.25. Jack will have to work 5 extra hours a week to earn.

Documents

Order of Operations 1 - Worksheet€¦ · ACKNOWLEDGMENTS Set E: Multiplying & Dividing Fractions i Workplace Education Manitoba would like to express appreciation to the following