1.3E: Exercises
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- Jul 25, 2021
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Practice Makes Perfect
Simplify Fractions
In the following exercises, simplify.
1. −\dfrac{108}{63}
- Answer
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−\dfrac{12}{7}
2. −\dfrac{104}{48}
3. \dfrac{120}{252}
- Answer
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\dfrac{10}{21}
4. \dfrac{182}{294}
5. \dfrac{14x^2}{21y}
- Answer
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\dfrac{2x^2}{3y}
6. \dfrac{24a}{32b^2}
7. −\dfrac{210a^2}{110b^2}
- Answer
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−\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
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\dfrac{1}{3}
10. −\dfrac{3}{8}⋅\dfrac{4}{15}
11. \left(−\dfrac{14}{15}\right)\left(\dfrac{9}{20}\right)
- Answer
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−\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
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\dfrac{11}{30}
14. \left(−\dfrac{33}{60}\right)\left(−\dfrac{40}{88}\right)
15. \dfrac{3}{7}⋅21n
- Answer
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9n
16. \dfrac{5}{6}⋅30m
17. \dfrac{3}{4}÷\dfrac{x}{11}
- Answer
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\dfrac{33}{4x}
18. \dfrac{2}{5}÷\dfrac{y}{9}
19. \dfrac{5}{18}÷\left(−\dfrac{15}{24}\right)
- Answer
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−\dfrac{4}{9}
20. \dfrac{7}{18}÷\left(−\dfrac{14}{27}\right)
21. \dfrac{8u}{15}÷\dfrac{12v}{25}
- Answer
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\dfrac{10u}{9v}
22. \dfrac{12r}{25}÷\dfrac{18s}{35}
23. \dfrac{3}{4}÷(−12)
- Answer
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−\dfrac{1}{16}
24. −15÷\left(−\dfrac{5}{3}\right)
In the following exercises, simplify.
25. −\dfrac{\dfrac{8}{21} }{\dfrac{12}{35}}
- Answer
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−\dfrac{10}{9}
26. − \dfrac{\dfrac{9}{16} }{\dfrac{33}{40}}
27. −\dfrac{\dfrac{4}{5}}{2}
- Answer
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−\dfrac{2}{5}
28. \dfrac{\dfrac{5}{3}}{10}
29. \dfrac{\dfrac{m}{3}}{\dfrac{n}{2}}
- Answer
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\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
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\dfrac{29}{24}
32. \dfrac{5}{12}+\dfrac{3}{8}
33. \dfrac{7}{12}−\dfrac{9}{16}
- Answer
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\dfrac{1}{48}
34. \dfrac{7}{16}−\dfrac{5}{12}
35. −\dfrac{13}{30}+\dfrac{25}{42}
- Answer
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\dfrac{17}{105}
36. −\dfrac{23}{30}+\dfrac{5}{48}
37. −\dfrac{39}{56}−\dfrac{22}{35}
- Answer
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−\dfrac{53}{40}
38. −\dfrac{33}{49}−\dfrac{18}{35}
39. −\dfrac{2}{3}−\left(−\dfrac{3}{4}\right)
- Answer
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\dfrac{1}{12}
40. −\dfrac{3}{4}−\left(−\dfrac{4}{5}\right)
41. \dfrac{x}{3}+\dfrac{1}{4}
- Answer
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\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
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ⓐ \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
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ⓐ \dfrac{25n}{16} ⓑ \dfrac{25n−16}{30}
46. ⓐ \dfrac{3a}{8}÷\dfrac{7}{12}
ⓑ \dfrac{3a}{8}−\dfrac{7}{12}
ⓑ −\dfrac{4k}{9}⋅\dfrac{5}{6}
- Answer
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ⓐ \dfrac{−8x−15}{18} ⓑ −\dfrac{10k}{27}
48. ⓐ −\dfrac{3y}{8}−\dfrac{4}{3}
ⓑ −\dfrac{3y}{8}⋅\dfrac{4}{3}
ⓑ −\dfrac{5a}{3}÷\left(−\dfrac{10}{6}\right)
- Answer
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ⓐ \dfrac{−5(a+1)}{3} ⓑ a
50. ⓐ \dfrac{2b}{5}+\dfrac{8}{15}
ⓑ \dfrac{2b}{5}÷\dfrac{8}{15}
In the following exercises, simplify.
51. \dfrac{5⋅6−3⋅4}{4⋅5−2⋅3}
- Answer
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\dfrac{9}{7}
52. \dfrac{8⋅9−7⋅6}{5⋅6−9⋅2}
53. \dfrac{5^2−3^2}{3−5}
- Answer
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−8
54. \dfrac{6^2−4^2}{4−6}
55. \dfrac{7⋅4−2(8−5)}{9⋅3−3⋅5}
- Answer
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\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
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\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
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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
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\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
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\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
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\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
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\dfrac{5}{4}
68. −\dfrac{3}{12}÷\left(−\dfrac{5}{9}\right)
69. −\dfrac{3}{8}+\dfrac{5}{12}
- Answer
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\dfrac{1}{24}
70. −\dfrac{1}{8}+\dfrac{7}{12}
71. −\dfrac{7}{15}−\dfrac{y}{4}
- Answer
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\dfrac{−28−15y}{60}
72. −\dfrac{3}{8}−\dfrac{x}{11}
73. \dfrac{11}{12a}⋅\dfrac{9a}{16}
- Answer
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\dfrac{33}{64}
74. \dfrac{10y}{13}⋅\dfrac{8}{15y}
75. \dfrac{1}{2}+\dfrac{2}{3}⋅\dfrac{5}{12}
- Answer
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\dfrac{7}{9}
76. \dfrac{1}{3}+\dfrac{2}{5}⋅\dfrac{3}{4}
77. 1−\dfrac{3}{5}÷\dfrac{1}{10}
- Answer
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−5
78. 1−\dfrac{5}{6}÷\dfrac{1}{12}
79. \dfrac{3}{8}−\dfrac{1}{6}+\dfrac{3}{4}
- Answer
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\dfrac{23}{24}
80. \dfrac{2}{5}+\dfrac{5}{8}−\dfrac{3}{4}
81. 12\left(\dfrac{9}{20}−\dfrac{4}{15}\right)
- Answer
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\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
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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
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\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
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ⓐ \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
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−\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
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−\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
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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?