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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 \PageIndex{65}

\frac{5}{6}−\frac{1}{9}

Answer

\frac{13}{18}

Exercise \PageIndex{66}

\frac{5}{9}−\frac{1}{6}

Exercise \PageIndex{67}

−\frac{7}{15}−\frac{y}{4}

Answer

\frac{-28-15y}{60}

Exercise \PageIndex{68}

−\frac{3}{8}−\frac{x}{11}

Exercise \PageIndex{69}

\frac{11}{12a} \cdot \frac{9a}{16}

Answer

\frac{33}{64}

Exercise \PageIndex{70}

\frac{10y}{13} \cdot \frac{8}{15y}

Use the Order of Operations to Simplify Complex Fractions

In the following exercises, simplify.

Exercise \PageIndex{71}

\frac{2^{3}+4^{2}}{\left(\frac{2}{3}\right)^{2}}

Answer

54

Exercise \PageIndex{72}

\frac{3^{3}-3^{2}}{\left(\frac{3}{4}\right)^{2}}

Exercise \PageIndex{73}

\frac{\left(\frac{3}{5}\right)^{2}}{\left(\frac{3}{7}\right)^{2}}

Answer

\frac{49}{25}

Exercise \PageIndex{74}

\frac{\left(\frac{3}{4}\right)^{2}}{\left(\frac{5}{8}\right)^{2}}

Exercise \PageIndex{75}

\frac{2}{\frac{1}{3}+\frac{1}{5}}

Answer

\frac{15}{4}

Exercise \PageIndex{76}

\frac{5}{\frac{1}{4}+\frac{1}{3}}

Exercise \PageIndex{77}

\frac{\frac{7}{8}-\frac{2}{3}}{\frac{1}{2}+\frac{3}{8}}

Answer

\frac{5}{21}

Exercise \PageIndex{78}

\frac{\frac{3}{4}-\frac{3}{5}}{\frac{1}{4}+\frac{2}{5}}

Exercise \PageIndex{79}

\frac{1}{2}+\frac{2}{3} \cdot \frac{5}{12}

Answer

\frac{7}{9}

Exercise \PageIndex{80}

\frac{1}{3}+\frac{2}{5} \cdot \frac{3}{4}

Exercise \PageIndex{81}

1-\frac{3}{5} \div \frac{1}{10}

Answer

-5

Exercise \PageIndex{82}

1-\frac{5}{6} \div \frac{1}{12}

Exercise \PageIndex{83}

\frac{2}{3}+\frac{1}{6}+\frac{3}{4}

Answer

\frac{19}{12}

Exercise \PageIndex{84}

\frac{2}{3}+\frac{1}{4}+\frac{3}{5}

Exercise \PageIndex{85}

\frac{3}{8}−\frac{1}{6}+\frac{3}{4}

Answer

\frac{23}{24}

Exercise \PageIndex{86}

\frac{2}{5}+\frac{5}{8}−\frac{3}{4}

Exercise \PageIndex{87}

12\left(\frac{9}{20}-\frac{4}{15}\right)

Answer

\frac{11}{5}

Exercise \PageIndex{88}

8\left(\frac{15}{16}-\frac{5}{6}\right)

Exercise \PageIndex{89}

\frac{\frac{5}{8}+\frac{1}{6}}{\frac{19}{24}}

Answer

1

Exercise \PageIndex{90}

\frac{\frac{1}{6}+\frac{3}{10}}{\frac{14}{30}}

Exercise \PageIndex{91}

\left(\frac{5}{9}+\frac{1}{6}\right) \div\left(\frac{2}{3}-\frac{1}{2}\right)

Answer

\frac{13}{3}

Exercise \PageIndex{92}

\left(\frac{3}{4}+\frac{1}{6}\right) \div\left(\frac{5}{8}-\frac{1}{3}\right)

Evaluate Variable Expressions with Fractions

In the following exercises, evaluate.

Exercise \PageIndex{93}

x+\left(-\frac{5}{6}\right) \text { when }

  1. x = \frac{1}{3}
  2. x=-\frac{1}{6}
Answer
  1. -\frac{1}{2}
  2. -1
Exercise \PageIndex{94}

x+\left(-\frac{11}{12}\right) \text { when }

  1. x = \frac{11}{12}
  2. x=-\frac{3}{4}
Exercise \PageIndex{95}

x - \frac{2}{5} \text { when }

  1. x = \frac{3}{5}
  2. x=-\frac{3}{5}
Answer
  1. \frac{1}{5}
  2. -1
Exercise \PageIndex{96}

x-\frac{1}{3} \text { when }

  1. x=\frac{2}{3}
  2. x=-\frac{2}{3}
Exercise \PageIndex{97}

\frac{7}{10}-w \text { when }

  1. w=\frac{1}{2}
  2. w=-\frac{1}{2}
Answer
  1. \frac{1}{5}
  2. \frac{6}{5}
Exercise \PageIndex{98}

\frac{5}{12}-w \text { when }

  1. w=\frac{1}{4}
  2. w=-\frac{1}{4}
Exercise \PageIndex{99}

2 x^{2} y^{3} \text { when } x=-\frac{2}{3} \text { and } y=-\frac{1}{2}

Answer
-\frac{1}{9}
Exercise \PageIndex{100}

8 u^{2} v^{3} \text { when } u=-\frac{3}{4} \text { and } v=-\frac{1}{2}

Exercise \PageIndex{101}

\frac{a+b}{a-b} \text { when } a=-3, b=8

Answer
-\frac{5}{11}
Exercise \PageIndex{102}

\frac{r-s}{r+s} \text { when } r=10, s=-5

Everyday Math

Exercise \PageIndex{103}

Decorating Laronda is making covers for the throw pillows on her sofa. For each pillow cover, she needs \frac{1}{2} 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

\frac{7}{8} yard

Exercise \PageIndex{104}

Baking Vanessa is baking chocolate chip cookies and oatmeal cookies. She needs \frac{1}{2} cup of sugar for the chocolate chip cookies and \frac{1}{4} of sugar for the oatmeal cookies. How much sugar does she need altogether?

Writing Exercises

Exercise \PageIndex{105}

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

Answer

Answers may vary

Exercise \PageIndex{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?


This page titled 1.7E: Exercises is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by OpenStax via source content that was edited to the style and standards of the LibreTexts platform.

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