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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
AC
KN
OW
LED
GM
EN
TS
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.
1
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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
Operations with Mixed Fractions 2
Operations with Mixed Fractions 3
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
2
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NUMERACY: The Basics Workbook Set E: Multiplying & Dividing Fractions
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
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NUMERACY: The Basics Workbook Set E: Multiplying & Dividing Fractions
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
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NUMERACY: The Basics Workbook Set E: Multiplying & Dividing Fractions
Practice Section B
Calculate the following. Express your answer in lowest terms.
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
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NUMERACY: The Basics Workbook Set E: Multiplying & Dividing Fractions
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
Calculate the following. Express your answer in lowest terms.
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
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NUMERACY: The Basics Workbook Set E: Multiplying & Dividing Fractions
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
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NUMERACY: The Basics Workbook
SOLUTIONS
Set E Multiplying & Dividing Fractions
Set E: Multiplying & Dividing Fractions Solutions
8
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NUMERACY: The Basics Workbook
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
Set E: Multiplying & Dividing Fractions Solutions
9
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NUMERACY: The Basics Workbook
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
Set E: Multiplying & Dividing Fractions Solutions
10
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NUMERACY: The Basics Workbook
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
Set E: Multiplying & Dividing Fractions Solutions
11
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NUMERACY: The Basics Workbook
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
Set E: Multiplying & Dividing Fractions Solutions
12
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NUMERACY: The Basics Workbook
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
Set E: Multiplying & Dividing Fractions Solutions
13
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NUMERACY: The Basics Workbook
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
Set E: Multiplying & Dividing Fractions Solutions
14
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NUMERACY: The Basics Workbook
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
Set E: Multiplying & Dividing Fractions Solutions
15
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NUMERACY: The Basics Workbook
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
Set E: Multiplying & Dividing Fractions Solutions
16
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NUMERACY: The Basics Workbook
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
Set E: Multiplying & Dividing Fractions Solutions
17
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NUMERACY: The Basics Workbook
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
Set E: Multiplying & Dividing Fractions Solutions
18
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NUMERACY: The Basics Workbook
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
Set E: Multiplying & Dividing Fractions Solutions
19
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NUMERACY: The Basics Workbook
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.