Order of Operations 1 - Worksheet€¦ · Set G: Operations With Mixed Fractions 1 NUMERACY: The Basics Workbook OPERATIONS WITH MIXED FRACTIONS 1 This workbook contains five skill-building

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 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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1


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

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

2



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

=

3



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

=

4



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

=

5



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

=

6


NUMERACY: The Basics Workbook

SOLUTIONS

Set G Operations with Mixed Fractions 1

7


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

8



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

9



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

10



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

11



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

12



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

13



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

14



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

Documents

Order of Operations 1 - Worksheet€¦ · Set G: Operations With Mixed Fractions 1 NUMERACY: The Basics Workbook OPERATIONS WITH MIXED FRACTIONS 1 This workbook contains five skill-building