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Mathematics LibreTexts

1.7E: Exercises

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Practice Makes Perfect

Add and Subtract Fractions with a Common Denominator

In the following exercises, add.

Exercise 1.7E.1

613+513

Answer

1113

Exercise 1.7E.2

415+715

Exercise 1.7E.3

x4+34

Answer

x+34

Exercise 1.7E.4

8q+6q

Exercise 1.7E.5

316+(716)

Answer

58

Exercise 1.7E.6

516+(916)

Exercise 1.7E.7

817+1517

Answer

717

Exercise 1.7E.8

919+1719

Exercise 1.7E.9

613+(1013)+(1213)

Answer

1613

Exercise 1.7E.10

512+(712)+(1112)

In the following exercises, subtract.

Exercise 1.7E.11

1115715

Answer

415

Exercise 1.7E.12

913413

Exercise 1.7E.13

1112512

Answer

12

Exercise 1.7E.14

712512

Exercise 1.7E.15

1921421

Answer

57

Exercise 1.7E.16

1721821

Exercise 1.7E.17

5y878

Answer

5y78

Exercise 1.7E.18

11z13813

Exercise 1.7E.19

23u15u

Answer

38u

Exercise 1.7E.20

29v26v

Exercise 1.7E.21

35(45)

Answer

15

Exercise 1.7E.22

37(57)

Exercise 1.7E.23

79(59)

Answer

29

Exercise 1.7E.24

811(511)

Mixed Practice

In the following exercises, simplify.

Exercise 1.7E.25

518·910

Answer

14

Exercise 1.7E.26

314·712

Exercise 1.7E.27

n545

Answer

n45

Exercise 1.7E.28

611s11

Exercise 1.7E.29

724+224

Answer

frac524

Exercise 1.7E.30

518+118

Exercise 1.7E.31

815÷125

Answer

29

Exercise 1.7E.32

712÷928

Add or Subtract Fractions with Different Denominators

In the following exercises, add or subtract.

Exercise 1.7E.33

12+17

Answer

914

Exercise 1.7E.34

13+18

Exercise 1.7E.35

13(19)

Answer

49

Exercise 1.7E.36

14(18)

Exercise 1.7E.37

712+512

Answer

2924

Exercise 1.7E.38

512+38

Exercise 1.7E.39

712916

Answer

148

Exercise 1.7E.40

716512

Exercise 1.7E.41

2338

Answer

724

Exercise 1.7E.42

5634

Exercise 1.7E.43

1130+2740

Answer

37120

Exercise 1.7E.44

920+1730

Exercise 1.7E.45

1330+2542

Answer

17105

Exercise 1.7E.46

2330+548

Exercise 1.7E.47

39562235

Answer

5340

Exercise 1.7E.48

33491835

Exercise 1.7E.49

23(34)

Answer

112

Exercise 1.7E.50

34(45)

Exercise 1.7E.51

1+78

Answer

158

Exercise 1.7E.52

1310

Exercise 1.7E.53

x3+14

Answer

4x+312

Exercise 1.7E.54

y2+23

Exercise 1.7E.55

y435

Answer

5y1220

Exercise 1.7E.56

x514

Mixed Practice

In the following exercises, simplify.

Exercise 1.7E.57
  1. 23+16
  2. 23÷16
Answer
  1. 56
  2. 4
Exercise 1.7E.58
  1. 2518
  2. 2518
Exercise 1.7E.59
  1. 5n6÷815
  2. 5n6815
Answer
  1. 25n16
  2. 25n1630
Exercise 1.7E.60
  1. 3a8÷712
  2. 3a8712
Exercise 1.7E.61

38÷(310)

Answer

54

Exercise 1.7E.62

512÷(59)

Exercise 1.7E.63

38+512

Answer

124

Exercise 1.7E.64

18+712

Exercise 1.7E.65

5619

Answer

1318

Exercise 1.7E.66

5916

Exercise 1.7E.67

715y4

Answer

2815y60

Exercise 1.7E.68

38x11

Exercise 1.7E.69

1112a9a16

Answer

3364

Exercise 1.7E.70

10y13815y

Use the Order of Operations to Simplify Complex Fractions

In the following exercises, simplify.

Exercise 1.7E.71

23+42(23)2

Answer

54

Exercise 1.7E.72

3332(34)2

Exercise 1.7E.73

(35)2(37)2

Answer

4925

Exercise 1.7E.74

(34)2(58)2

Exercise 1.7E.75

213+15

Answer

154

Exercise 1.7E.76

514+13

Exercise 1.7E.77

782312+38

Answer

521

Exercise 1.7E.78

343514+25

Exercise 1.7E.79

12+23512

Answer

79

Exercise 1.7E.80

13+2534

Exercise 1.7E.81

135÷110

Answer

5

Exercise 1.7E.82

156÷112

Exercise 1.7E.83

23+16+34

Answer

1912

Exercise 1.7E.84

23+14+35

Exercise 1.7E.85

3816+34

Answer

2324

Exercise 1.7E.86

25+5834

Exercise 1.7E.87

12(920415)

Answer

115

Exercise 1.7E.88

8(151656)

Exercise 1.7E.89

58+161924

Answer

1

Exercise 1.7E.90

16+3101430

Exercise 1.7E.91

(59+16)÷(2312)

Answer

133

Exercise 1.7E.92

(34+16)÷(5813)

Evaluate Variable Expressions with Fractions

In the following exercises, evaluate.

Exercise 1.7E.93

x+(56) when 

  1. x=13
  2. x=16
Answer
  1. 12
  2. 1
Exercise 1.7E.94

x+(1112) when 

  1. x=1112
  2. x=34
Exercise 1.7E.95

x25 when 

  1. x=35
  2. x=35
Answer
  1. 15
  2. 1
Exercise 1.7E.96

x13 when 

  1. x=23
  2. x=23
Exercise 1.7E.97

710w when 

  1. w=12
  2. w=12
Answer
  1. 15
  2. 65
Exercise 1.7E.98

512w when 

  1. w=14
  2. w=14
Exercise 1.7E.99

2x2y3 when x=23 and y=12

Answer
19
Exercise 1.7E.100

8u2v3 when u=34 and v=12

Exercise 1.7E.101

a+bab when a=3,b=8

Answer
511
Exercise 1.7E.102

rsr+s when r=10,s=5

Everyday Math

Exercise 1.7E.103

Decorating Laronda is making covers for the throw pillows on her sofa. For each pillow cover, she needs 12 yard of print fabric and \frac{3}{8}\) yard of solid fabric. What is the total amount of fabric Laronda needs for each pillow cover?

Answer

78 yard

Exercise 1.7E.104

Baking Vanessa is baking chocolate chip cookies and oatmeal cookies. She needs 12 cup of sugar for the chocolate chip cookies and 14 of sugar for the oatmeal cookies. How much sugar does she need altogether?

Writing Exercises

Exercise 1.7E.105

Why do you need a common denominator to add or subtract fractions? Explain.

Answer

Answers may vary

Exercise 1.7E.106

How do you find the LCD of 2 fractions?

Self Check

ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

This is a table that has five rows and four columns. In the first row, which is a header row, the cells read from left to right “I can…,” “Confidently,” “With some help,” and “No-I don’t get it!” The first column below “I can…” reads “add and subtract fractions with different denominators,” “identify and use fraction operations,” “use the order of operations to simplify complex fractions,” and “evaluate variable expressions with fractions.” The rest of the cells are blank.

ⓑ After looking at the checklist, do you think you are well-prepared for the next chapter? Why or why not?

 


1.7E: Exercises is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts.

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