Order of Operations 1 - Worksheet · Set H: Operations With Mixed Fractions 2 NUMERACY: The Basics Workbook OPERATIONS WITH MIXED FRACTIONS 2 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 H: Operations with Mixed Fractions 2

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i Set H: Operations with Mixed Fraction 2

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

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1


NUMERACY: The Basics Workbook Set H: Operations With Mixed Fractions 2

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



OPERATIONS WITH MIXED FRACTIONS 2

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 1

18 2 =

3. 1 7

22 8 =

4. 5 5

18 8 =

5. 1 3

1 24 8 =

6. 1 3

1 12 4 =

7. 1 7

2 18 8 =

8. 3 1

2 38 2 =

9. 1 1

2 34 2 =

10. 1

1 64 =

11. 1

1 84 =

3



12. 3 9

14 16 =

13. 3

2 14

=

14. 3

3 18

=

15. 1 7

2 1 14 16

=

Practice Section B

Calculate the following. Express your answer as a mixed fraction in lowest terms.

1. 1 7

3 22 8 =

2. 3 5

2 14 8 =

3. 3 1

2 14 2 =

4. 13 1

4 316 4

=

5. 1 3

4 18 16 =

6. 1 7

4 12 8 =

7. 5 3

3 216 8

=

8. 3 9

5 24 16 =

4



9. 3 7

4 34 8 =

10. 11 27

5 216 32

=

11. 1 11

2 38 16 =

12. 3 7 3

2 2 44 16 8 =

13. 7 5 1

3 1 48 16 2 =

14. 1 1

4 4 34 16

=

15. 3 7 1

6 4 232 8 4

=

Practice Section C

Calculate the following. Express your answer in lowest terms.

1. 1 3 11

12 2 2 4 24 8 16

=

2. 3 11 17 7 3

2 1 2 1 2 14 16 32 8 4 =

3. 3 7 1 1 1

6 4 2 2 4 3232 8 4 4 2

=

4. 3 7 1 1 1

6 4 2 2 4 3232 8 4 4 2

=

5. 1 3 7 1 1 1 11

2 5 4 3 2 4 6 44 16 8 8 4 2 32

=

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.

Solution:

5 3 11 75 2 3 1

8 4 16 2

5 4 16 75 2 3 1

8 3 11 2

5 8 2 5 3 3 4 11 1 16 7

1 8 3 11 2

5 21 13 27 7

1 8 3 11 2

3 (6)5

1

21 13

8 (1) 3

27 7

11 (1) 2

5 3 13 27 7

8 11

36855

88

2. Alex says that 1 7 3 7 3 7 1

3 6 1 6 1 32 8 4 16 4 8 4

.

Donna says that Alex must be wrong because she already calculated that 3 7 1

6 1 34 8 4

.

Who is correct? Prove your answer with calculations.

6



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.

1 1 3 5 7 1 1 1 11

4 2 5 5 4 3 2 4 6 4 62 4 16 8 8 8 4 2 32

=

7


NUMERACY: The Basics Workbook

SOLUTIONS

Set H Operations with Mixed Fractions 2

8


NUMERACY: The Basics Workbook Set H: Operations With Mixed Fractions 2 Solutions

OPERATIONS WITH MIXED FRACTIONS 2

Practice Section A

1. Solution:

1 11

2 2

2 1 1 1

2 2

3 1

2 2

3

4

2. Solution:

1 11

8 2

8 1 1 2

8 1

9 2

8 1

18

8

9 12

4 4

3. Solution:

1 72

2 8

2 2 1 7

2 8

5 7

2 8

35 32

16 16

4. Solution:

5 51

8 8

8 1 5 8

8 5

13

(1) 8

(1) 8

5

13 32

5 5

5. Solution:

1 31 2

4 8

4 1 1 8 2 3

4 8

5 19

4 8

95 312

32 32

6. Solution:

1 31 1

2 4

2 1 1 4 1 3

2 4

3 7

2 4

21 52

8 8

9



7. Solution:

1 72 1

8 8

8 2 1 8

8 8 1 7

17 8

8 15

17

(1) 8

(1) 8

15

17 21

15 15

8. Solution:

3 12 3

8 2

8 2 3 2 3 1

8 2

19 7

8 2

133 58

16 16

9. Solution:

1 12 3

4 2

4 2 1 2

4 2 3 1

9 2

4 7

9

(2) 4

(1) 2

7

9

14

10. Solution:

11 6

4

4 1 1 6

4 1

5

2 4

3 6

1

15 17

2 2

11. Solution:

11 8

4

4 1 1 8

4 1

5 1

4 8

5

32

12. Solution:

3 91

4 16

4 1 3 16

4 9

7 16

4 9

112 4 13 3

36 36 9

10



13. Solution:

32 1

4

2 4

1 4 1 3

2 4

1 7

8 11

7 7

14. Solution:

33 1

8

3 8 1 3

1 8

3 11

1 8

33 14

8 8

15. Solution:

1 72 1 1

4 16

2 4 16 1 7

1 4 1 1 16

2 4 23

1 5 16

(1) 2

(1) 4

1

23

5 (2) (4)

16

23

5 2

23 32

10 10

11



Practice Section B

1. Solution:

1 73 2

2 8

2 3 1 8

2 8 2 7

7 8

2 23

7

(1) 2

(4) 8

23

7 4

23

28 51

23 23

2. Solution:

3 52 1

4 8

4 2 3 8 1 5

4 8

11 13

4 8

143 154

32 32

3. Solution:

3 12 1

4 2

4 2 3 2 1 1

4 2

11 3

4 2

33 14

8 8

4. Solution:

13 14 3

16 4

16 4 13 4 3 1

16 4

77 13

16 4

1001 4115

64 64

5. Solution:

1 34 1

8 16

8 4 1 16 1 3

8 16

33

1 8

2 16

19

66 93

19 19

6. Solution:

1 74 1

2 8

2 4 1 8 1 7

2 8

9 15

2 8

135 78

16 16

12



7. Solution:

5 33 2

16 8

16 3 5 8 2 3

16 8

53 19

16 8

1007 1117

128 128

8. Solution:

3 95 2

4 16

4 5 3 16

4 16 2 9

23 16

4 41

23

1 4

4 16

41

92 102

41 41

9. Solution:

3 74 3

4 8

4 4 3 8

4 8 3 7

19 8

4 31

19

(1) 4

2 8

31

38 71

31 31

10. Solution:

11 275 2

16 32

16 5 11 8

16 32 2 27

91 32

16 91

(1) 91

(1)16

2 32

(1) 91

2

11. Solution:

1 112 3

8 16

8 2 1 11 3

8 16 1

17

(1) 8

2 16

3

11 1

17 2 3

1 11 1

102 39

11 11

12. Solution:

3 7 32 2 4

4 16 8

4 2 3 16 2 7 8

4 16 8 4 3

11 39

4 2 16

(1) 8

35

429 1491

280 280

13



13. Solution:

7 5 13 1 4

8 16 2

8 3 7 16 2

8 16 1 5 2 4 1

31

(1) 8

2 16

2

21 9

124

189

14. Solution:

1 14 4 3

4 16

4 4 4 1 16

1 4 16 3 1

(1) 4

17

1 (1) 4

16

49

272 275

49 49

15. Solution:

3 7 16 4 2

32 8 4

32 6 3 8 4 7 4

32 8 4 2 1

195 39 4

32 8 9

195 39

32 2 8

(1) 4

9

195 39

32 18

195

16 32

9 18

39

1755 507 132 2

624 624 16

14



Practice Section C

1. Solution:

1 3 1112 2 2 4 2

4 8 16

12 4 8 2 3 16 1

1 4 2 1 8 16 4 11 2

4 12

2 4

1 3 9

19

(1) 8

2 16

1

75 (1) 2

4 2 19 2

3 75

304 791

225 225

2. Solution:

3 11 17 7 32 1 2 1 2 1

4 16 32 8 4

4 2 3 16 1 11 32 8 1 7 1 4

4 16 32 2 17 8 2 4 1 3

11

(1) 4

(1) 27

(1)16

(1) 2

32

(1) 3 81

5 15

1

8 (1) 2

(1) 4

7

11 5

8 7

55

56

15



3. Solution:

3 7 1 1 16 4 2 2 4 32

32 8 4 4 2

32 6 3 8 4 4 2 32

32 8 4 7 4 2 1 4 2 1 2 4 1 1

195 8 4 4 2 32

32 39 9 9 9 1

5 195

(1) 32

8

1 39

4 4 2 (1) 32

9 9 9

1

5 8 4 4 2

9 9 9

1280 5511

729 729

4. Solution:

3 7 1 1 16 4 2 2 4 32

32 8 4 4 2

32 6 3 8 4 7 4 4 2 1 2 32

32 8 4 2 1 4 2 4 1 1

195 39 4 9 2 32

32 8 9 4 9 1

195 39

32 (2) 8

(1) 4

(1) 9

9

(2) 4

(1) 2

(1) 9

32

1

195 39 1 32

32 18 2 1

195 18 2 32

32 39 1 1

(5)195

(1) 32

18

(1) 39

2 (1) 32

1

1

180

16



5. Solution:

1 3 7 1 1 1 112 5 4 3 2 4 6 4

4 16 8 8 4 2 32

4 2 1 16 8 4 7 8 3 1 4 2 4 1 6 32

4 16 5 3 8 8 4 2 1 2 1 32 4 11

9 16 39 25 4 9 6 32

4 83 8 8 9 2 1 139

9

(1) 4

(4)16

39 25

83 8 (2) 8

(1) 4

9

9 (1) 2

(3) 6

32

1 139

36 39 25 864

83 8 18 139

36 39 18 139

83 8 25 864

(1) (9)

36 39

83 (1) (4)

8

(9)18

139

25 96 864

39 9 139

83 25 96

48789 1504114

199200 199200

17



Practice Section D

1. Solution:

In line 2, the two mixed fractions that are divided, 3

34

and 11

116

, were flipped before being

changed to improper fractions. There is also an error made in line 5 when reducing the fractions

where 21 3 6 instead of 7.

The correct answer is:

5 3 11 75 2 3 1

8 4 16 2

5 8 2 5 4 16 7

1 8 4 3 3 16 1 11 2

5 21 4 16 7

1 8 15 27 2

(1) 5

(7) 21

1

(1) 8

(2) 4

(1) (3) 15

(2)16

7

27 (1) 2

7 2 2 7

27

196 77

27 27

2. Solution:

Alex is incorrect because the expression does not equal 3. (See below.)

Donna is correct in saying that 3 7 1

6 1 34 8 4

, but this does not mean that Alex must be

wrong.

The correct answer is:

18



1 7 3 7 3 7 13 6 1 6 1

2 8 4 16 4 8 4

2 3 1 1 7 4 1 3 16 6 4 1 3 8 1

2 6 8 4 7 1 4 7 4

7 1 7 7 16 6 7 8 1

2 6 8 4 7 1 4 7 4

7

(1) 2

1 7

6 (1) 8

(1) 7

(1) (2)

4

16

(1) 7

(3) 6

(1) 7

1

(1) (2) 4

(1) (2)

8

(1) 7

1

(1) 4

7 73

6 4

49 3 24

24 1 24

49 72

24

23

24

Practice Section E

Solution:

1 1 3 5 7 1 1 1 114 2 5 5 4 3 2 4 6 4 6

2 4 16 8 8 8 4 2 32

2 4 1 4 2 1 16 8 1 8 4 7 8 3 1 4 2 4 1 6 32 6

2 4 16 5 3 5 5 8 8 4 2 1 2 1 32 4 11 1

9 9 16 8 1

2 4 83 5 5

39 25 4 9 6 32 6

8 8 9 2 1 139 1

9

(1) 2

9

(1) 4

(2) (4)

16 8 1 39 25

83 5 5 8 (2) 8

(1) 4

9

9 (1) 2

(3) 6

32 6

1 139 1

162 8 1 39 18 864 6

83 5 5 8 25 139 1

162 (1) 8

83

1 39

5 5 (1) 8

18 864 6

25 139 1

589545216 548459181

7210625 7210625

This is the simplest form for this fraction.

Documents

Order of Operations 1 - Worksheet · Set H: Operations With Mixed Fractions 2 NUMERACY: The Basics Workbook OPERATIONS WITH MIXED FRACTIONS 2 This workbook contains five skill-building