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Companion Workbook to Numeracy: The Basics Video Series
NUMERAC Y:The Basics Workbook
Set G: Operations with Mixed Fractions 1
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Set G: Operations with Mixed Fraction 1
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.
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NUMERACY: The Basics Workbook Set G: Operations With Mixed Fractions 1
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
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NUMERACY: The Basics Workbook Set G: Operations With Mixed Fractions 1
OPERATIONS WITH MIXED FRACTIONS 1
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 as a mixed fraction in lowest terms.
1. 1 1
12 2
=
2. 1 2
14 4
=
3. 1 3
18 8
=
4. 5 1
28 8
=
5. 7 3
1 28 4
=
6. 1 3
12 8
=
7. 1 7
2 18 8
=
8. 5 3
1 18 4
=
9. 3 1
1 18 4
=
10. 1 5
2 12 8
=
11. 1 1
2 18 2
=
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NUMERACY: The Basics Workbook Set G: Operations With Mixed Fractions 1
12. 3 9
14 16
=
13. 3
2 18
=
14. 1
3 24
=
15. 1 1
4 14 2
=
Practice Section B
Calculate the following. Express your answer as a mixed fraction in lowest terms.
1. 1 7
3 24 8
=
2. 3 5
2 14 16
=
3. 3 1
2 18 2
=
4. 1 7
4 12 8
=
5. 1 3
3 116 4
=
6. 13 1
4 216 4
=
7. 5 1
3 416 2
=
8. 3 9
5 24 16
=
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NUMERACY: The Basics Workbook Set G: Operations With Mixed Fractions 1
9. 3 7
4 34 8
=
10. 5 29
4 216 32
=
11. 3 7
3 28 16
=
12. 5 3 5
2 18 4 16
=
13. 3 7 1
2 316 8 2
=
14. 1 7
3 2 18 16
=
15. 3 7 1
5 232 8 4
=
Practice Section C
Calculate the following. Express your answer in lowest terms.
1. 3 3 1
4 28 4 2
=
2. 3 7 9
4 2 34 8 16
=
3. 1 5 19
6 3 24 16 32
=
4. 7 1 11
7 2 3 18 4 16
=
5. 3 7 1 7
4 2 3 2 34 8 2 16
=
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NUMERACY: The Basics Workbook Set G: Operations With Mixed Fractions 1
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. Calculate the answer by performing the correct order of operations.
Express your answer as a mixed fraction in lowest terms.
5 3 11
5 2 3 18 4 16
Solution:
5 3 115 2 3 1
8 4 16
5 8 2 5 4 3 3 16 1 11
1 8 4 16
5 16 19 2 15 4 27
1 16 8 2 4 4 16
80 38 60 27
16 16 16 16
30 2 12 2
16 16 8
Practice Section E
Challenge Question. If you can do this one, then you get an A+.
Calculate the answer by following the correct order of operations. Give your answer as a mixed fraction
in lowest terms.
3 3 13 7 7
5 2 3 2 18 4 16 32 8
=
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NUMERACY: The Basics Workbook
SOLUTIONS
Set G Operations with Mixed Fractions 1
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NUMERACY: The Basics Workbook Set G: Operations With Mixed Fractions 1 Solutions
OPERATIONS WITH MIXED FRACTIONS 1
Practice Section A
1. Solution:
1 11
2 2
2 1 1 1
2 2
3 1
2
4
2
2
2. Solution:
1 21
4 4
4 1 1 2
4 4
5 2
4
7 31
4 4
3. Solution:
1 31
8 8
8 1 1 3
8 8
9 3
8
12
8
3 11
2 2
4. Solution:
5 12
8 8
5 8 2 1
8 8
5 17
8
22
8
62
8
32
4
5. Solution:
7 31 2
8 4
8 1 7 4 2 3
8 4
15 11 2
8 4 2
15 22
8 8
37 54
8 8
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NUMERACY: The Basics Workbook Set G: Operations With Mixed Fractions 1 Solutions
6. Solution:
1 31
2 8
2 1 1 3
2 8
3 4 3
2 4 8
12 3
8 8
9 11
8 8
7. Solution:
1 72 1
8 8
8 2 1 8 1 7
8 8
17 15
8 8
2
8
1
4
8. Solution:
5 31 1
8 4
8 1 5 4 1 3
8 4
13 7 2
8 4 2
13 14
8 8
27 33
8 8
9. Solution:
3 11 1
8 4
8 1 3 4 1 1
8 4
11 5 2
8 4 2
11 10
8 8
1
8
10. Solution:
1 52 1
2 8
2 2 1 8 1 5
2 8
5 4 13
2 4 8
20 13
8 8
7
8
11. Solution:
1 12 1
8 2
8 2 1 2 1 1
8 2
17 3 4
8 2 4
17 12
8 8
29 53
8 8
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NUMERACY: The Basics Workbook Set G: Operations With Mixed Fractions 1 Solutions
12. Solution:
3 91
4 16
4 1 3 9
4 16
7 4 9
4 4 16
28 9
16 16
37 52
16 16
13. Solution:
32 1
8
8 1 32
8
2 8 11
1 8 8
16 11
8 8
5
8
14. Solution:
13 2
4
4 2 13
4
3 4 9
1 4 4
12 9
4 4
21 15
4 4
15. Solution:
1 14 1
4 2
4 1 1 14
4 2
4 4 5 1 2
1 4 4 2 2
16 5 2
4 4 4
13 13
4 4
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NUMERACY: The Basics Workbook Set G: Operations With Mixed Fractions 1 Solutions
Practice Section B
1. Solution:
1 73 2
4 8
4 3 1 8 2 7
4 8
13 2 23
4 2 8
26 23
8 8
49 16
8 8
2. Solution:
3 52 1
4 16
4 2 3 16 1 5
4 16
11 4 21
4 4 16
44 21
16 16
23 71
16 16
3. Solution:
3 12 1
8 2
8 2 3 2 1 1
8 2
19 3 4
8 2 4
19 12
8 8
7
8
4. Solution:
1 74 1
2 8
2 4 1 8 1 7
2 8
9 4 15
2 4 8
36 15
8 8
21 52
8 8
5. Solution:
1 33 1
16 4
16 3 1 4 1 3
16 4
49 7 4
16 4 4
49 28
16 16
21 51
16 16
6. Solution:
13 14 2
16 4
16 4 13 4 2 1
16 4
77 9 4
16 4 4
77 36
16 16
41 92
16 16
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NUMERACY: The Basics Workbook Set G: Operations With Mixed Fractions 1 Solutions
7. Solution:
5 13 4
16 2
16 3 5 2 4 1
16 2
53 9 8
16 2 8
53 72
16 16
125 137
16 16
8. Solution:
3 95 2
4 16
4 5 3 16 2 9
4 16
23 4 41
4 4 16
92 41
16 16
51 33
16 16
9. Solution:
3 74 3
4 8
4 4 3 8 3 7
4 8
19 2 31
4 2 8
38 31
8 8
69 58
8 8
10. Solution:
5 294 2
16 32
16 4 5 32 2 29
16 32
69 2 93
16 2 32
138 93
32 32
45 131
32 32
11. Solution:
3 73 2
8 16
8 3 3 7 2
8 16 1
27 2 7 2 16
8 2 16 1 16
54 7 32
16 16 16
79 154
16 16
12. Solution:
5 3 52 1
8 4 16
8 2 5 4 1 3 5
8 4 16
21 2 7 4 5
8 2 4 4 16
42 28 5
16 16 16
19 31
16 16
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NUMERACY: The Basics Workbook Set G: Operations With Mixed Fractions 1 Solutions
13. Solution:
3 7 12 3
16 8 2
16 2 3 7 2 3 1
16 8 4
35 7 2 7 8
16 8 2 2 8
35 14 56
16 16 16
77 134
16 16
14. Solution:
1 73 2 1
8 16
3 8 2 1 16 1 7
1 8 16
3 16 17 2 23
1 16 8 2 16
48 34 23
16 8 16
37 52
16 16
15. Solution:
3 7 15 2
32 8 4
3 8 5 7 4 2 1
32 8 4
3 47 9
32 8 4
3 47 4 9 8
32 8 4 4 8
3 188 72
32 32 32
119 233
32 32
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NUMERACY: The Basics Workbook Set G: Operations With Mixed Fractions 1 Solutions
Practice Section C
1. Solution:
3 3 14 2
8 4 2
3 4 4 3 2 2 1
8 4 2
3 19 5
8 4 2
3 19 2 5 4
8 4 2 2 4
3 38 20
8 8 8
21 52
8 8
2. Solution:
3 7 94 2 3
4 8 16
4 4 3 8 2 7 16 3 9
4 8 16
19 23 57
4 8 16
19 4 23 2 57
4 4 8 2 16
76 46 57
16 16 16
65 14
16 16
3. Solution:
1 5 196 3 2
4 16 32
4 6 1 16 3 5 32 2 19
4 16 32
25 8 53 2 83
4 8 16 2 32
200 106 83
32 32 32
11
32
4. Solution:
7 1 117 2 3 1
8 4 16
7 8 2 7 4 3 1 16 1 11
1 8 4 16
7 16 23 2 13 4 27
1 16 8 2 4 4 16
112 46 52 27
16 16 16 16
91 115
16 16
5. Solution:
3 7 1 74 2 3 2 3
4 8 2 16
4 4 3 8 2 7 3 2 1 16 2 7 3
4 8 2 16 1
19 4 23 2 7 8 39 3 16
4 4 8 2 2 8 16 1 16
76 46 56 39 48
16 16 16 16 16
173 1310
16 16
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NUMERACY: The Basics Workbook Set G: Operations With Mixed Fractions 1 Solutions
Practice Section D
1. Solution:
One error is in line 2 where 8 2 5 19 instead of 8 2 5 21 .
There are also two errors on the last line: 80 38 60 27 31(not 30) and the fraction
30 14 71 1
16 16 8, (not
12
8). The last two errors would still result in a deduction because they are
independent from the error in line 2.
The correct solution is:
5 3 115 2 3 1
8 4 16
5 8 2 5 4 3 3 16 1 111
1 8 4 16
5 16 21 2 15 4 27
1 16 8 2 4 4 16
80 42 60 27
16 16 16 16
35 32
16 16
Practice Section E
Solution:
3 3 13 7 75 2 3 2 1
8 4 16 32 8
43 11 61 71 15
8 4 16 32 8
43 4 11 8 61 2 71 15 4
8 4 4 8 16 2 32 8 4
172 88 122 71 60
32 32 32 32 32
172 34 11
32 32 32
172 34 11
32 32 32
195 36
32 32