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1.4E: Exercises

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Practice Makes Perfect

Simplify Fractions

In the following exercises, simplify.

1. 10863

Answer

127

2. 10448

3. 120252

Answer

1021

4. 182294

5. 14x221y

Answer

2x23y

6. 24a32b2

7. 210a2110b2

Answer

21a211b2

8. 30x2105y2

Multiply and Divide Fractions

In the following exercises, perform the indicated operation.

9. 34(49)

Answer

13

10. 38415

11. (1415)(920)

Answer

2150

12. (910)(2533)

13. (6384)(4490)

Answer

1130

14. (3360)(4088)

15. 3721n

Answer

9n

16. 5630m

17. 34÷x11

Answer

334x

18. 25÷y9

19. 518÷(1524)

Answer

49

20. 718÷(1427)

21. 8u15÷12v25

Answer

10u9v

22. 12r25÷18s35

23. 34÷(12)

Answer

116

24. 15÷(53)

In the following exercises, simplify.

25. 8211235

Answer

109

26. 9163340

27. 452

Answer

25

28. 5310

29. m3n2

Answer

2m3n

30. 38y12

Add and Subtract Fractions

In the following exercises, add or subtract.

31. 712+58

Answer

2924

32. 512+38

33. 712916

Answer

148

34. 716512

35. 1330+2542

Answer

17105

36. 2330+548

37. 39562235

Answer

5340

38. 33491835

39. 23(34)

Answer

112

40. 34(45)

41. x3+14

Answer

4x+312

42. x514

43. ⓐ 23+16

23÷16

Answer

564

44. ⓐ 2518

25·18

45. ⓐ 5n6÷815

5n6815

Answer

25n1625n1630

46. ⓐ 3a8÷712

3a8712

47. ⓐ 4x956

4k956

Answer

8x151810k27

48. ⓐ 3y843

3y843

49. ⓐ 5a3+(106)

5a3÷(106)

Answer

5(a+1)3a

50. ⓐ 2b5+815

2b5÷815

Use the Order of Operations to Simplify Fractions

In the following exercises, simplify.

51. 56344523

Answer

97

52. 89765692

53. 523235

Answer

8

54. 624246

55. 742(85)9335

Answer

116

56. 973(128)8766

57. 9(82)3(157)6(71)3(179)

Answer

52

58. 8(92)4(149)7(83)3(169)

59. 23+42(23)2

Answer

54

60. 3332(34)2

61. (35)2(37)2

Answer

4925

62. (34)2(58)2

63. 213+15

Answer

154

64. 514+13

65. 782312+38

Answer

521

66. 343514+25

Mixed Practice

In the following exercises, simplify.

67. 38÷(310)

Answer

54

68. 312÷(59)

69. 38+512

Answer

124

70. 18+712

71. 715y4

Answer

2815y60

72. 38x11

73. 1112a9a16

Answer

3364

74. 10y13815y

75. 12+23512

Answer

79

76. 13+2534

77. 135÷110

Answer

5

78. 156÷112

79. 3816+34

Answer

2324

80. 25+5834

81. 12(920415)

Answer

115

82. 8(151656)

83. 58+161924

Answer

1

84. 16+3101430

​​​​​​​

85. (59+16)÷(2312)

Answer

133

86. (34+16)÷(5813)

Evaluate Variable Expressions with Fractions

In the following exercises, evaluate.

87. 710w when ⓐ w=12w=12

Answer

1565

88. 512w when ⓐ w=14w=14

​​​​​​​​​​​​​​

89. 2x2y3 when x=23 and y=12

Answer

19

90. 8u2v3 when u=34 and v=12

​​​​​​​​​​​​​​

91. a+bab when a=3 and b=8

Answer

511

92. rsr+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 1.4E: 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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