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1.3E: Exercises

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Practice Makes Perfect

Simplify Fractions

In the following exercises, simplify.

1. −\dfrac{108}{63}

Answer

−\dfrac{12}{7}

2. −\dfrac{104}{48}

3. \dfrac{120}{252}

Answer

\dfrac{10}{21}

4. \dfrac{182}{294}

5. \dfrac{14x^2}{21y}

Answer

\dfrac{2x^2}{3y}

6. \dfrac{24a}{32b^2}

7. −\dfrac{210a^2}{110b^2}

Answer

−\dfrac{21a^2}{11b^2}

8. −\dfrac{30x^2}{105y^2}

Multiply and Divide Fractions

In the following exercises, perform the indicated operation.

9. −\dfrac{3}{4}\left(−\dfrac{4}{9}\right)

Answer

\dfrac{1}{3}

10. −\dfrac{3}{8}⋅\dfrac{4}{15}

11. \left(−\dfrac{14}{15}\right)\left(\dfrac{9}{20}\right)

Answer

−\dfrac{21}{50}

12. \left(−\dfrac{9}{10}\right)\left(\dfrac{25}{33}\right)

13. \left(−\dfrac{63}{84}\right)\left(−\dfrac{44}{90}\right)

Answer

\dfrac{11}{30}

14. \left(−\dfrac{33}{60}\right)\left(−\dfrac{40}{88}\right)

15. \dfrac{3}{7}⋅21n

Answer

9n

16. \dfrac{5}{6}⋅30m

17. \dfrac{3}{4}÷\dfrac{x}{11}

Answer

\dfrac{33}{4x}

18. \dfrac{2}{5}÷\dfrac{y}{9}

19. \dfrac{5}{18}÷\left(−\dfrac{15}{24}\right)

Answer

−\dfrac{4}{9}

20. \dfrac{7}{18}÷\left(−\dfrac{14}{27}\right)

21. \dfrac{8u}{15}÷\dfrac{12v}{25}

Answer

\dfrac{10u}{9v}

22. \dfrac{12r}{25}÷\dfrac{18s}{35}

23. \dfrac{3}{4}÷(−12)

Answer

−\dfrac{1}{16}

24. −15÷\left(−\dfrac{5}{3}\right)

In the following exercises, simplify.

25. −\dfrac{\dfrac{8}{21} }{\dfrac{12}{35}}

Answer

−\dfrac{10}{9}

26. − \dfrac{\dfrac{9}{16} }{\dfrac{33}{40}}

27. −\dfrac{\dfrac{4}{5}}{2}

Answer

−\dfrac{2}{5}

28. \dfrac{\dfrac{5}{3}}{10}

29. \dfrac{\dfrac{m}{3}}{\dfrac{n}{2}}

Answer

\dfrac{2m}{3n}

30. \dfrac{−\dfrac{3}{8}}{−\dfrac{y}{12}}

Add and Subtract Fractions

In the following exercises, add or subtract.

31. \dfrac{7}{12}+\dfrac{5}{8}

Answer

\dfrac{29}{24}

32. \dfrac{5}{12}+\dfrac{3}{8}

33. \dfrac{7}{12}−\dfrac{9}{16}

Answer

\dfrac{1}{48}

34. \dfrac{7}{16}−\dfrac{5}{12}

35. −\dfrac{13}{30}+\dfrac{25}{42}

Answer

\dfrac{17}{105}

36. −\dfrac{23}{30}+\dfrac{5}{48}

37. −\dfrac{39}{56}−\dfrac{22}{35}

Answer

−\dfrac{53}{40}

38. −\dfrac{33}{49}−\dfrac{18}{35}

39. −\dfrac{2}{3}−\left(−\dfrac{3}{4}\right)

Answer

\dfrac{1}{12}

40. −\dfrac{3}{4}−\left(−\dfrac{4}{5}\right)

41. \dfrac{x}{3}+\dfrac{1}{4}

Answer

\dfrac{4x+3}{12}

42. \dfrac{x}{5}−\dfrac{1}{4}

43. ⓐ \dfrac{2}{3}+\dfrac{1}{6}

\dfrac{2}{3}÷\dfrac{1}{6}

Answer

\dfrac{5}{6}4

44. ⓐ −\dfrac{2}{5}−\dfrac{1}{8}

−\dfrac{2}{5}·\dfrac{1}{8}

45. ⓐ \dfrac{5n}{6}÷\dfrac{8}{15}

\dfrac{5n}{6}−\dfrac{8}{15}

Answer

\dfrac{25n}{16}\dfrac{25n−16}{30}

46. ⓐ \dfrac{3a}{8}÷\dfrac{7}{12}

\dfrac{3a}{8}−\dfrac{7}{12}

47. ⓐ −\dfrac{4x}{9}−\dfrac{5}{6}

−\dfrac{4k}{9}⋅\dfrac{5}{6}

Answer

\dfrac{−8x−15}{18}−\dfrac{10k}{27}

48. ⓐ −\dfrac{3y}{8}−\dfrac{4}{3}

−\dfrac{3y}{8}⋅\dfrac{4}{3}

49. ⓐ −\dfrac{5a}{3}+\left(−\dfrac{10}{6}\right)

−\dfrac{5a}{3}÷\left(−\dfrac{10}{6}\right)

Answer

\dfrac{−5(a+1)}{3}a

50. ⓐ \dfrac{2b}{5}+\dfrac{8}{15}

\dfrac{2b}{5}÷\dfrac{8}{15}

Use the Order of Operations to Simplify Fractions

In the following exercises, simplify.

51. \dfrac{5⋅6−3⋅4}{4⋅5−2⋅3}

Answer

\dfrac{9}{7}

52. \dfrac{8⋅9−7⋅6}{5⋅6−9⋅2}

53. \dfrac{5^2−3^2}{3−5}

Answer

−8

54. \dfrac{6^2−4^2}{4−6}

55. \dfrac{7⋅4−2(8−5)}{9⋅3−3⋅5}

Answer

\dfrac{11}{6}

56. \dfrac{9⋅7−3(12−8)}{8⋅7−6⋅6}

57. \dfrac{9(8−2)−3(15−7)}{6(7−1)−3(17−9)}

Answer

\dfrac{5}{2}

58. \dfrac{8(9−2)−4(14−9)}{7(8−3)−3(16−9)}

59. \dfrac{2^3+4^2}{\left(\dfrac{2}{3}\right)^2}

Answer

54

60. \dfrac{3^3−3^2}{\left(\dfrac{3}{4}\right)^2}

61. \dfrac{\left(\dfrac{3}{5}\right)^2}{\left(\dfrac{3}{7}\right)^2}

Answer

\dfrac{49}{25}

62. \dfrac{\left(\dfrac{3}{4}\right)^2}{\left(\dfrac{5}{8}\right)^2}

63. \dfrac{2}{\dfrac{1}{3}+\dfrac{1}{5}}

Answer

\dfrac{15}{4}

64. \dfrac{5}{\dfrac{1}{4}+\dfrac{1}{3}}

65. \dfrac{\dfrac{7}{8}−\dfrac{2}{3}}{\dfrac{1}{2}+\dfrac{3}{8}}

Answer

\dfrac{5}{21}

66. \dfrac{\dfrac{3}{4}−\dfrac{3}{5}}{\dfrac{1}{4}+\dfrac{2}{5}}

Mixed Practice

In the following exercises, simplify.

67. −\dfrac{3}{8}÷\left(−\dfrac{3}{10}\right)

Answer

\dfrac{5}{4}

68. −\dfrac{3}{12}÷\left(−\dfrac{5}{9}\right)

69. −\dfrac{3}{8}+\dfrac{5}{12}

Answer

\dfrac{1}{24}

70. −\dfrac{1}{8}+\dfrac{7}{12}

71. −\dfrac{7}{15}−\dfrac{y}{4}

Answer

\dfrac{−28−15y}{60}

72. −\dfrac{3}{8}−\dfrac{x}{11}

73. \dfrac{11}{12a}⋅\dfrac{9a}{16}

Answer

\dfrac{33}{64}

74. \dfrac{10y}{13}⋅\dfrac{8}{15y}

75. \dfrac{1}{2}+\dfrac{2}{3}⋅\dfrac{5}{12}

Answer

\dfrac{7}{9}

76. \dfrac{1}{3}+\dfrac{2}{5}⋅\dfrac{3}{4}

77. 1−\dfrac{3}{5}÷\dfrac{1}{10}

Answer

−5

78. 1−\dfrac{5}{6}÷\dfrac{1}{12}

79. \dfrac{3}{8}−\dfrac{1}{6}+\dfrac{3}{4}

Answer

\dfrac{23}{24}

80. \dfrac{2}{5}+\dfrac{5}{8}−\dfrac{3}{4}

81. 12\left(\dfrac{9}{20}−\dfrac{4}{15}\right)

Answer

\dfrac{11}{5}

82. 8\left(\dfrac{15}{16}−\dfrac{5}{6}\right)

83. \dfrac{\dfrac{5}{8}+\dfrac{1}{6}}{\dfrac{19}{24}}

Answer

1

84. \dfrac{\dfrac{1}{6}+\dfrac{3}{10}}{\dfrac{14}{30}}

​​​​​​​

85. \left(\dfrac{5}{9}+\dfrac{1}{6}\right)÷\left(\dfrac{2}{3}−\dfrac{1}{2}\right)

Answer

\dfrac{13}{3}

86. \left(\dfrac{3}{4}+\dfrac{1}{6}\right)÷\left(\dfrac{5}{8}−\dfrac{1}{3}\right)

Evaluate Variable Expressions with Fractions

In the following exercises, evaluate.

87. \dfrac{7}{10}−w when ⓐ w=\dfrac{1}{2}w=−\dfrac{1}{2}

Answer

\dfrac{1}{5}\dfrac{6}{5}

88. 512−w when ⓐ w=\dfrac{1}{4}w=−\dfrac{1}{4}

​​​​​​​​​​​​​​

89. 2x^2y^3 when x=−\dfrac{2}{3} and y=−\dfrac{1}{2}

Answer

−\dfrac{1}{9}

90. 8u^2v^3 when u=−\dfrac{3}{4} and v=−\dfrac{1}{2}

​​​​​​​​​​​​​​

91. \dfrac{a+b}{a−b} when a=−3 and b=8

Answer

−\dfrac{5}{11}

92. \dfrac{r−s}{r+s} when r=10 and s=−5

Writing Exercises

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

Answer

Answers will vary.

94. How do you find the LCD of 2 fractions?

95. Explain how you find the reciprocal of a fraction.

Answer

Answers will vary.

96. Explain how you find the reciprocal of a negative number.

Self Check

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

This table has 4 columns, 5 rows and a header row. The header row labels each column I can, confidently, with some help and no, I don’t get it. The first column has the following statements: simplify fractions, multiply and divide fractions, add and subtract fractions, use the order of operations to simplify fractions, evaluate variable expressions with fractions. The remaining columns are blank.

ⓑ What does this checklist tell you about your mastery of this section? What steps will you take to improve?


This page titled 1.3E: Exercises is shared under a CC BY license and was authored, remixed, and/or curated by OpenStax.

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