1.4E: Exercises
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
-
\(\dfrac{29}{24}\)
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
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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
-
ⓐ \(\dfrac{25n}{16}\) ⓑ \(\dfrac{25n−16}{30}\)
46. ⓐ \(\dfrac{3a}{8}÷\dfrac{7}{12}\)
ⓑ \(\dfrac{3a}{8}−\dfrac{7}{12}\)
ⓑ \(−\dfrac{4k}{9}⋅\dfrac{5}{6}\)
- Answer
-
ⓐ \(\dfrac{−8x−15}{18}\) ⓑ \(−\dfrac{10k}{27}\)
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
-
\(\dfrac{5}{2}\)
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.
ⓑ What does this checklist tell you about your mastery of this section? What steps will you take to improve?