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. −38⋅415
11. (−1415)(920)
- Answer
-
−2150
12. (−910)(2533)
13. (−6384)(−4490)
- Answer
-
1130
14. (−3360)(−4088)
15. 37⋅21n
- Answer
-
9n
16. 56⋅30m
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. −38−y12
Add and Subtract Fractions
In the following exercises, add or subtract.
31. 712+58
- Answer
-
2924
32. 512+38
33. 712−916
- Answer
-
148
34. 716−512
35. −1330+2542
- Answer
-
17105
36. −2330+548
37. −3956−2235
- Answer
-
−5340
38. −3349−1835
39. −23−(−34)
- Answer
-
112
40. −34−(−45)
41. x3+14
- Answer
-
4x+312
42. x5−14
43. ⓐ 23+16
ⓑ 23÷16
- Answer
-
ⓐ 56 ⓑ 4
44. ⓐ −25−18
ⓑ −25·18
45. ⓐ 5n6÷815
ⓑ 5n6−815
- Answer
-
ⓐ 25n16 ⓑ 25n−1630
46. ⓐ 3a8÷712
ⓑ 3a8−712
ⓑ −4k9⋅56
- Answer
-
ⓐ −8x−1518 ⓑ −10k27
48. ⓐ −3y8−43
ⓑ −3y8⋅43
ⓑ −5a3÷(−106)
- Answer
-
ⓐ −5(a+1)3 ⓑ a
50. ⓐ 2b5+815
ⓑ 2b5÷815
In the following exercises, simplify.
51. 5⋅6−3⋅44⋅5−2⋅3
- Answer
-
97
52. 8⋅9−7⋅65⋅6−9⋅2
53. 52−323−5
- Answer
-
−8
54. 62−424−6
55. 7⋅4−2(8−5)9⋅3−3⋅5
- Answer
-
116
56. 9⋅7−3(12−8)8⋅7−6⋅6
57. 9(8−2)−3(15−7)6(7−1)−3(17−9)
- Answer
-
52
58. 8(9−2)−4(14−9)7(8−3)−3(16−9)
59. 23+42(23)2
- Answer
-
54
60. 33−32(34)2
61. (35)2(37)2
- Answer
-
4925
62. (34)2(58)2
63. 213+15
- Answer
-
154
64. 514+13
65. 78−2312+38
- Answer
-
521
66. 34−3514+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. −715−y4
- Answer
-
−28−15y60
72. −38−x11
73. 1112a⋅9a16
- Answer
-
3364
74. 10y13⋅815y
75. 12+23⋅512
- Answer
-
79
76. 13+25⋅34
77. 1−35÷110
- Answer
-
−5
78. 1−56÷112
79. 38−16+34
- Answer
-
2324
80. 25+58−34
81. 12(920−415)
- Answer
-
115
82. 8(1516−56)
83. 58+161924
- Answer
-
1
84. 16+3101430
85. (59+16)÷(23−12)
- Answer
-
133
86. (34+16)÷(58−13)
Evaluate Variable Expressions with Fractions
In the following exercises, evaluate.
87. 710−w when ⓐ w=12 ⓑ w=−12
- Answer
-
ⓐ 15 ⓑ 65
88. 512−w when ⓐ w=14 ⓑ w=−14
89. 2x2y3 when x=−23 and y=−12
- Answer
-
−19
90. 8u2v3 when u=−34 and v=−12
91. a+ba−b when a=−3 and b=8
- Answer
-
−511
92. r−sr+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.
ⓑ What does this checklist tell you about your mastery of this section? What steps will you take to improve?