{"id":395,"date":"2020-08-21T19:43:45","date_gmt":"2020-08-21T23:43:45","guid":{"rendered":"https:\/\/opentextbc.ca\/introalgebra\/chapter\/measurement-review\/"},"modified":"2021-03-24T10:52:51","modified_gmt":"2021-03-24T14:52:51","slug":"measurement-review","status":"publish","type":"chapter","link":"https:\/\/opentextbc.ca\/introalgebra\/chapter\/measurement-review\/","title":{"raw":"2.6 Chapter Review","rendered":"2.6 Chapter Review"},"content":{"raw":"[latexpage]\n

Review Exercises<\/h1>\n

Find Equivalent Fractions<\/h2>\n

In the following exercises, find three fractions equivalent to the given fraction. Show your work, using figures or algebra.<\/p>\n\n\n\n\n\n
1. \\(\\dfrac{1}{4}\\)<\/td>\n2. \\(\\dfrac{1}{3}\\)<\/td>\n<\/tr>\n
3. \\(\\dfrac{5}{6}\\)<\/td>\n4. \\(\\dfrac{2}{7}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Simplify Fractions<\/h2>\n

In the following exercises, simplify.<\/p>\n\n\n\n\n\n\n\n
5. \\(\\dfrac{7}{21}\\)<\/td>\n6. \\(\\dfrac{8}{24}\\)<\/td>\n<\/tr>\n
7. \\(\\dfrac{15}{20}\\)<\/td>\n8. \\(\\dfrac{12}{18}\\)<\/td>\n<\/tr>\n
9. \\(-\\dfrac{168}{192}\\)<\/td>\n10. \\(-\\dfrac{140}{224}\\)<\/td>\n<\/tr>\n
11. \\(\\dfrac{11x}{11y}\\)<\/td>\n12. \\(\\dfrac{15a}{15b}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n

Multiply Fractions<\/h2>\n<\/div>\n

In the following exercises, multiply.<\/p>\n\n\n\n\n\n\n\n
13. \\(\\dfrac{2}{5}\\cdot \\dfrac{1}{3}\\)<\/td>\n14. \\(\\dfrac{1}{2}\\cdot \\dfrac{3}{8}\\)<\/td>\n<\/tr>\n
15. \\(\\dfrac{7}{12}(-\\dfrac{8}{21})\\)<\/td>\n16. \\(\\dfrac{5}{12}(-\\dfrac{8}{15})\\)<\/td>\n<\/tr>\n
17. \\(-28p(-\\dfrac{1}{4})\\)<\/td>\n18. \\(-51q(-\\dfrac{1}{3})\\)<\/td>\n<\/tr>\n
19. \\(\\dfrac{14}{5}(-15)\\)<\/td>\n20. \\(-1(-\\dfrac{3}{8})\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
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Divide Fractions<\/h2>\n<\/div>\n

In the following exercises, divide.<\/p>\n\n\n\n\n\n\n\n\n
21. \\(\\dfrac{1}{2}\\)\u00f7\\(\\dfrac{1}{4}\\)<\/td>\n22. \\(\\dfrac{1}{2}\\)\u00f7\\(\\dfrac{1}{8}\\)<\/td>\n<\/tr>\n
23. \\(-\\dfrac{4}{5}\\)\u00f7\\(\\dfrac{4}{7}\\)<\/td>\n24. \\(-\\dfrac{3}{4}\\)\u00f7\\(\\dfrac{3}{5}\\)<\/td>\n<\/tr>\n
25. \\(\\dfrac{5}{8}\\)\u00f7\\(\\dfrac{a}{10}\\)<\/td>\n26. \\(\\dfrac{5}{6}\\)\u00f7\\(\\dfrac{c}{15}\\)<\/td>\n<\/tr>\n
27. \\(\\dfrac{7p}{12}\\)\u00f7\\(\\dfrac{21p}{8}\\)<\/td>\n28. \\(\\dfrac{5q}{12}\\)\u00f7\\(\\dfrac{15q}{8}\\)<\/td>\n<\/tr>\n
29. \\(\\dfrac{2}{5}\\)\u00f7\\(\\left(-10\\right)\\)<\/td>\n30. \\(-18\\)\u00f7\\(-\\left(\\dfrac{9}{2}\\right)\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n
In the following exercises, simplify.<\/div>\n<\/div>\n\n\n\n\n\n
31. \\(\\dfrac{\\dfrac{2}{3}}{\\dfrac{8}{9}}\\)<\/td>\n32. \\(\\dfrac{\\dfrac{4}{5}}{\\dfrac{8}{15}}\\)<\/td>\n<\/tr>\n
33. \\(\\dfrac{-\\dfrac{9}{10}}{3}\\)<\/td>\n34. \\(\\dfrac{2}{\\dfrac{5}{8}}\\)<\/td>\n<\/tr>\n
35. \\(\\dfrac{\\dfrac{r}{5}}{\\dfrac{s}{3}}\\)<\/td>\n36. \\(\\dfrac{-\\dfrac{x}{6}}{-\\dfrac{8}{9}}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n

Simplify Expressions Written with a Fraction Bar<\/h2>\n<\/div>\n

In the following exercises, simplify.<\/p>\n\n\n\n\n\n\n\n\n\n
37. \\(\\dfrac{4+11}{8}\\)<\/td>\n38. \\(\\dfrac{9+3}{7}\\)<\/td>\n<\/tr>\n
39. \\(\\dfrac{30}{7-12}\\)<\/td>\n40. \\(\\dfrac{15}{4-9}\\)<\/td>\n<\/tr>\n
41. \\(\\dfrac{22-14}{19-13}\\)<\/td>\n42. \\(\\dfrac{15+9}{18+12}\\)<\/td>\n<\/tr>\n
43. \\(\\dfrac{5\\cdot 8}{-10}\\)<\/td>\n44. \\(\\dfrac{3\\cdot 4}{-24}\\)<\/td>\n<\/tr>\n
45. \\(\\dfrac{15\\cdot 5-{5}^{2}}{2\\cdot 10}\\)<\/td>\n46. \\(\\dfrac{12 \\cdot 9-{3}^{2}}{3\\cdot 18}\\)<\/td>\n<\/tr>\n
47. \\(\\dfrac{2+4\\left(3\\right)}{-3-{2}^{2}}\\)<\/td>\n48. \\(\\dfrac{7+3\\left(5\\right)}{-2-{3}^{2}}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
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Translate Phrases to Expressions with Fractions<\/h2>\n<\/div>\n

In the following exercises, translate each English phrase into an algebraic expression.<\/p>\n\n\n\n\n
49. the quotient of c<\/em> and the sum of d<\/em> and 9.<\/td>\n50. the quotient of the difference of h<\/em> and k<\/em>, and \\(-5\\).<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
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Add and Subtract Fractions with a Common Denominator<\/h2>\n<\/div>\n

In the following exercises, add.<\/p>\n\n\n\n\n\n\n
51. \\(\\dfrac{4}{9}+\\dfrac{1}{9}\\)<\/td>\n52. \\(\\dfrac{2}{9}+\\dfrac{5}{9}\\)<\/td>\n<\/tr>\n
53. \\(\\dfrac{y}{3}+\\dfrac{2}{3}\\)<\/td>\n54. \\(\\dfrac{7}{p}+\\dfrac{9}{p}\\)<\/td>\n<\/tr>\n
55. \\(-\\dfrac{1}{8}+\\left(-\\dfrac{3}{8}\\right)\\)<\/td>\n56. \\(-\\dfrac{1}{8}+\\left(-\\dfrac{5}{8}\\right)\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n
\n

In the following exercises, subtract.<\/p>\n\n\n\n\n\n\n
57. \\(\\dfrac{4}{5}-\\dfrac{1}{5}\\)<\/td>\n58. \\(\\dfrac{4}{5}-\\dfrac{3}{5}\\)<\/td>\n<\/tr>\n
59. \\(\\dfrac{y}{17}-\\dfrac{9}{17}\\)<\/td>\n60. \\(\\dfrac{x}{19}-\\dfrac{8}{19}\\)<\/td>\n<\/tr>\n
61. \\(-\\dfrac{8}{d}-\\dfrac{3}{d}\\)<\/td>\n62. \\(-\\dfrac{7}{c}-\\dfrac{7}{c}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n
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Add or Subtract Fractions with Different Denominators<\/h2>\n<\/div>\n

In the following exercises, add or subtract.<\/p>\n\n\n\n\n\n\n\n\n\n
63. \\(\\dfrac{1}{3}+\\dfrac{1}{5}\\)<\/td>\n64. \\(\\dfrac{1}{4}+\\dfrac{1}{5}\\)<\/td>\n<\/tr>\n
65. \\(\\dfrac{1}{5}-\\left(-\\dfrac{1}{10}\\right)\\)<\/td>\n66. \\(\\dfrac{1}{2}-\\left(-\\dfrac{1}{6}\\right)\\)<\/td>\n<\/tr>\n
67. \\(\\dfrac{2}{3}+\\dfrac{3}{4}\\)<\/td>\n68. \\(\\dfrac{3}{4}+\\dfrac{2}{5}\\)<\/td>\n<\/tr>\n
69. \\(\\dfrac{11}{12}-\\dfrac{3}{8}\\)<\/td>\n70. \\(\\dfrac{5}{8}-\\dfrac{7}{12}\\)<\/td>\n<\/tr>\n
71. \\(-\\dfrac{9}{16}-\\left(-\\dfrac{4}{5}\\right)\\)<\/td>\n72. \\(-\\dfrac{7}{20}-\\left(-\\dfrac{5}{8}\\right)\\)<\/td>\n<\/tr>\n
73. \\(1+\\dfrac{5}{6}\\)<\/td>\n74. \\(1-\\dfrac{5}{9}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n

Use the Order of Operations to Simplify Complex Fractions<\/h2>\n<\/div>\n

In the following exercises, simplify.<\/p>\n\n\n\n\n\n
75. \\(\\dfrac{{\\left(\\dfrac{1}{5}\\right)}^{2}}{2+{3}^{2}}\\)<\/td>\n76. \\(\\dfrac{{\\left(\\dfrac{1}{3}\\right)}^{2}}{5+{2}^{2}}\\)<\/td>\n<\/tr>\n
77. \\(\\dfrac{\\dfrac{2}{3}+\\dfrac{1}{2}}{\\dfrac{3}{4}-\\dfrac{2}{3}}\\)<\/td>\n78. \\(\\dfrac{\\dfrac{3}{4}+\\dfrac{1}{2}}{\\dfrac{5}{6}-\\dfrac{2}{3}}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n

Evaluate Variable Expressions with Fractions<\/h2>\n<\/div>\n

In the following exercises, evaluate.<\/p>\n\n\n\n\n\n\n
79. \\(x+\\dfrac{1}{2}\\) when\na) \\(x=-\\dfrac{1}{8}\\)\nb) \\(x=-\\dfrac{1}{2}\\)<\/td>\n80. \\(x+\\dfrac{2}{3}\\) when\na) \\(x=-\\dfrac{1}{6}\\)\nb) \\(x=-\\dfrac{5}{3}\\)<\/td>\n<\/tr>\n
81. \\(4{p}^{2}q\\) when \\(p=-\\dfrac{1}{2}\\) and \\(q=\\dfrac{5}{9}\\)<\/td>\n82. \\(5{m}^{2}n\\) when \\(m=-\\dfrac{2}{5}\\) and \\(n=\\dfrac{1}{3}\\)<\/td>\n<\/tr>\n
83. \\(\\dfrac{u+v}{w}\\) when\n\\(u=-4,v=-8,w=2\\)<\/td>\n84. \\(\\dfrac{m+n}{p}\\) when\n\\(m=-6,n=-2,p=4\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
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\u00a0Name and Write Decimals<\/h2>\n<\/div>\n

In the following exercises, write as a decimal.<\/p>\n\n\n\n\n\n
85. Eight and three hundredths<\/td>\n86. Nine and seven hundredths<\/td>\n<\/tr>\n
87. One thousandth<\/td>\n88. Nine thousandths<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n
\n

In the following exercises, name each decimal.<\/p>\n\n\n\n\n\n
89. 7.8<\/td>\n90. 5.01<\/td>\n<\/tr>\n
91. 0.005<\/td>\n92. 0.381<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n
\n
\n

Round Decimals<\/h2>\n<\/div>\n<\/div>\n

In the following exercises, round each number to the nearest a) hundredth b) tenth c) whole number.<\/p>\n\n\n\n\n\n
93. 5.7932<\/td>\n94. 3.6284<\/td>\n<\/tr>\n
95. 12.4768<\/td>\n96. 25.8449<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n
\n

Add and Subtract Decimals<\/h2>\n<\/div>\n<\/div>\n

In the following exercises, add or subtract.<\/p>\n\n\n\n\n\n\n\n\n
97. \\(18.37+9.36\\)<\/td>\n98. \\(256.37-85.49\\)<\/td>\n<\/tr>\n
99. \\(15.35-20.88\\)<\/td>\n100. \\(37.5+12.23\\)<\/td>\n<\/tr>\n
101. \\(-4.2+\\left(-9.3\\right)\\)<\/td>\n102. \\(-8.6+\\left(-8.6\\right)\\)<\/td>\n<\/tr>\n
103. \\(100-64.2\\)<\/td>\n104. \\(100-65.83\\)<\/td>\n<\/tr>\n
105. \\(2.51+40\\)<\/td>\n106. \\(9.38+60\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n
\n

Multiply and Divide Decimals<\/h2>\n<\/div>\n<\/div>\n

In the following exercises, multiply.<\/p>\n\n\n\n\n\n\n
107. \\(\\left(0.3\\right)\\left(0.4\\right)\\)<\/td>\n108. \\(\\left(0.6\\right)\\left(0.7\\right)\\)<\/td>\n<\/tr>\n
109. \\(\\left(8.52\\right)\\left(3.14\\right)\\)<\/td>\n110. \\(\\left(5.32\\right)\\left(4.86\\right)\\)<\/td>\n<\/tr>\n
111. \\(\\left(0.09\\right)\\left(24.78\\right)\\)<\/td>\n112. \\(\\left(0.04\\right)\\left(36.89\\right)\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n
\n

In the following exercises, divide.<\/p>\n\n\n\n\n\n\n
113. 0.15 \u00f7 5<\/td>\n114. 0.27 \u00f7 3<\/td>\n<\/tr>\n
115. \\$8.49 \u00f7 12<\/td>\n116. \\$16.99 \u00f7 9<\/td>\n<\/tr>\n
117. 12 \u00f7 0.08<\/td>\n118. 5 \u00f7 0.04<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n
\n
\n

Convert Decimals and Fractions<\/h2>\n<\/div>\n<\/div>\n

In the following exercises, write each decimal as a fraction.<\/p>\n\n\n\n\n\n\n
119. 0.08<\/td>\n120. 0.17<\/td>\n<\/tr>\n
121. 0.425<\/td>\n122. 0.184<\/td>\n<\/tr>\n
123. 1.75<\/td>\n124. 0.035<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n
\n

In the following exercises, convert each fraction to a decimal.<\/p>\n\n\n\n\n\n\n\n
125. \\(\\dfrac{2}{5}\\)<\/td>\n126. \\(\\dfrac{4}{5}\\)<\/td>\n<\/tr>\n
127. \\(-\\dfrac{3}{8}\\)<\/td>\n128. \\(-\\dfrac{5}{8}\\)<\/td>\n<\/tr>\n
129. \\(\\dfrac{5}{9}\\)<\/td>\n130. \\(\\dfrac{2}{9}\\)<\/td>\n<\/tr>\n
131. \\(\\dfrac{1}{2}+6.5\\)<\/td>\n132. \\(\\dfrac{1}{4}+10.75\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n

Identify Integers, Rational Numbers, Irrational Numbers, and Real Numbers<\/h2>\n

In the following exercises, write as the ratio of two integers.<\/p>\n\n\n\n\n
133. a) 9 b) 8.47<\/td>\n134. a) \\(-15\\)b) 3.591<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
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In the following exercises, list the a) rational numbers, b) irrational numbers.<\/p>\n\n\n\n\n
135. \\(0.84,0.79132\\text{\u2026},1.\\stackrel{\\text{-}}{3}\\)<\/td>\n136. \\(2.3\\stackrel{\\text{-}}{8},0.572,4.93814\\text{\u2026}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n
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\n

In the following exercises, list the a) whole numbers, b) integers, c) rational numbers, d) irrational numbers, e) real numbers for each set of numbers.<\/p>\n\n\n\n\n
137. \\(-4,0,\\dfrac{5}{6} ,17 ,5.2537\\text{\u2026}\\)<\/td>\n138. \\(-2, 0.\\stackrel{\\text{-}}{36},\\dfrac{13}{3},6.9152\\text{\u2026},10\\dfrac{1}{2}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n
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Locate Fractions on the Number Line<\/h2>\n<\/div>\n<\/div>\n

In the following exercises, locate the numbers on a number line.<\/p>\n\n\n\n\n\n
139. \\(\\dfrac{2}{3},\\dfrac{5}{4},\\dfrac{12}{5}\\)<\/td>\n140. \\(\\dfrac{1}{3},\\dfrac{7}{4},\\dfrac{13}{5}\\)<\/td>\n<\/tr>\n
141. \\(2\\dfrac{1}{3},-2\\dfrac{1}{3}\\)<\/td>\n142. \\(1\\dfrac{3}{5},-1\\dfrac{3}{5}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\nIn the following exercises, order each of the following pairs of numbers, using < or >.\n
\n
\n\n\n\n\n
143. \\(-1\\) ___ \\(-\\dfrac{1}{8}\\)<\/td>\n144. \\(-3\\dfrac{1}{4}\\)___ \\(-4\\)<\/td>\n<\/tr>\n
145. \\(-\\dfrac{7}{9}\\) ___ \\(-\\dfrac{4}{9}\\)<\/td>\n146. \\(-2\\) ___ \\(-\\dfrac{19}{8}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Locate Decimals on the Number Line<\/h2>\n<\/div>\n<\/div>\n

In the following exercises, locate on the number line.<\/p>\n\n\n\n\n\n
147. 0.3<\/td>\n148. -0.2<\/td>\n<\/tr>\n
149. -2.5<\/td>\n150. 2.7<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
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\n

In the following exercises, order each of the following pairs of numbers, using < or >.<\/p>\n\n\n\n\n\n
151. 0.9 ___ 0.6<\/td>\n152. 0.7 ___ 0.8<\/td>\n<\/tr>\n
153. -0.6 ___ -0.59<\/td>\n154. -0.27 ___ -0.3<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n
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Use the Commutative and Associative Properties<\/h2>\n<\/div>\n

In the following exercises, use the Associative Property to simplify.<\/p>\n\n\n\n\n\n
155. \\(-12\\left(4m\\right)\\)<\/td>\n156. \\(30\\left(\\dfrac{5}{6}q\\right)\\)<\/td>\n<\/tr>\n
157. \\(\\left(a+16\\right)+31\\)<\/td>\n158. \\(\\left(c+0.2\\right)+0.7\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n
\n

In the following exercises, simplify.<\/p>\n\n\n\n\n\n\n\n
159. \\(6y+37+\\left(-6y\\right)\\)<\/td>\n160. \\(\\dfrac{1}{4}+\\dfrac{11}{15}+\\left(-\\dfrac{1}{4}\\right)\\)<\/td>\n<\/tr>\n
161. \\(\\dfrac{14}{11}\\cdot \\dfrac{35}{9}\\cdot \\dfrac{14}{11}\\)<\/td>\n162. \\(-18\\cdot 15 \\cdot \\dfrac{2}{9}\\)<\/td>\n<\/tr>\n
163. \\(\\left(\\dfrac{7}{12}+\\dfrac{4}{5}\\right)+\\dfrac{1}{5}\\)<\/td>\n164. \\(\\left(3.98d+0.75d\\right)+1.25d\\)<\/td>\n<\/tr>\n
165. \\(11x+8y+16x+15y\\)<\/td>\n166. \\(52m+\\left(-20n\\right)+\\left(-18m\\right)+\\left(-5n\\right)\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n
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Use the Identity and Inverse Properties of Addition and Multiplication<\/h2>\n<\/div>\n<\/div>\n

In the following exercises, find the additive inverse of each number.<\/p>\n\n\n\n\n
\n

167.<\/p>\na) \\(\\dfrac{1}{3}\\)\nb) \\(5.1\\)\nc) \\(-14\\)\nd) \\(-\\dfrac{8}{5}\\)<\/td>\n

168.\na) \\(-\\dfrac{7}{8}\\)\nb) \\(-0.03\\)\nc) \\(17\\)\nd) \\(\\dfrac{12}{5}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n
\n\nIn the following exercises, find the multiplicative inverse of each number.\n\n\n\n
169. a) 10 b) \\(-\\dfrac{4}{9}\\) c) 0.6<\/td>\n170. a) \\(-\\dfrac{9}{2}\\) b) \\(-7\\) c) 2.1<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n
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Use the Properties of Zero<\/h2>\n<\/div>\n<\/div>\n

In the following exercises, simplify.<\/p>\n\n\n\n\n\n
171. \\(83\\cdot 0\\)<\/td>\n172. \\(\\dfrac{0}{9}\\)<\/td>\n<\/tr>\n
173. \\(\\dfrac{5}{0}\\)<\/td>\n174. \\(0\\)\\div \\(\\dfrac{2}{3}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
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\n

In the following exercises, simplify.<\/p>\n\n\n\n\n\n\n
175. \\(43+39+\\left(-43\\right)\\)<\/td>\n176. \\(\\left(n+6.75\\right)+0.25\\)<\/td>\n<\/tr>\n
177. \\(\\dfrac{5}{13}\\cdot 57 \\cdot \\dfrac{13}{5}\\)<\/td>\n178. \\(\\dfrac{1}{6}\\cdot17\\cdot12\\)<\/td>\n<\/tr>\n
179. \\(\\dfrac{2}{3}\\cdot 28 \\cdot \\dfrac{3}{7}\\)<\/td>\n180. \\(9\\left(6x-11\\right)+15\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n
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Simplify Expressions Using the Distributive Property<\/h2>\n<\/div>\n

In the following exercises, simplify using the Distributive Property.<\/p>\n\n\n\n\n\n\n\n
181. \\(7\\left(x+9\\right)\\)<\/td>\n182. \\(9\\left(u-4\\right)\\)<\/td>\n<\/tr>\n
183. \\(-3\\left(6m-1\\right)\\)<\/td>\n184. \\(-8\\left(-7a-12\\right)\\)<\/td>\n<\/tr>\n
185. \\(\\dfrac{1}{3}\\left(15n-6\\right)\\)<\/td>\n186. \\(\\left(y+10\\right)\\cdot p\\)<\/td>\n<\/tr>\n
187. \\(\\left(a-4\\right)-\\left(6a+9\\right)\\)<\/td>\n188. \\(4\\left(x+3\\right)-8\\left(x-7\\right)\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Review Exercise Answers<\/h1>\n
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
1. \\(\\dfrac{2}{8},\\dfrac{3}{12},\\dfrac{4}{16}\\) answers may vary<\/td>\n3. \\(\\dfrac{10}{12},\\dfrac{15}{18},\\dfrac{20}{24}\\) answers may vary<\/td>\n5. \\(\\dfrac{1}{3}\\)<\/td>\n<\/tr>\n
7. \\(\\dfrac{3}{4}\\)<\/td>\n9. \\(-\\dfrac{7}{8}\\)<\/td>\n11. \\(\\dfrac{x}{y}\\)<\/td>\n<\/tr>\n
13. \\(\\dfrac{2}{15}\\)<\/td>\n15. \\(-\\dfrac{2}{9}\\)<\/td>\n17. \\(7p\\)<\/td>\n<\/tr>\n
19. \\(-42\\)<\/td>\n21. 2<\/td>\n23. \\(-\\dfrac{7}{5}\\)<\/td>\n<\/tr>\n
25. \\(\\dfrac{25}{4a}\\)<\/td>\n27. \\(\\dfrac{2}{9}\\)<\/td>\n29. \\(-\\dfrac{1}{25}\\)<\/td>\n<\/tr>\n
31. \\(\\dfrac{3}{4}\\)<\/td>\n33. \\(-\\dfrac{3}{10}\\)<\/td>\n35. \\(\\dfrac{3r}{5s}\\)<\/td>\n<\/tr>\n
37. \\(\\dfrac{15}{8}\\)<\/td>\n39. \\(-6\\)<\/td>\n41. \\(\\dfrac{4}{3}\\)<\/td>\n<\/tr>\n
43. \\(-4\\)<\/td>\n45. \\(\\dfrac{5}{21}\\)<\/td>\n47. \\(-2\\)<\/td>\n<\/tr>\n
49. \\(\\dfrac{c}{d+9}\\)<\/td>\n51. \\(\\dfrac{5}{9}\\)<\/td>\n53. \\(\\dfrac{y+2}{3}\\)<\/td>\n<\/tr>\n
55. \\(-\\dfrac{1}{2}\\)<\/td>\n57. \\(\\dfrac{3}{5}\\)<\/td>\n59. \\(\\dfrac{y-9}{17}\\)<\/td>\n<\/tr>\n
61. \\(-\\dfrac{11}{d}\\)<\/td>\n63. \\(\\dfrac{8}{15}\\)<\/td>\n65. \\(\\dfrac{3}{10}\\)<\/td>\n<\/tr>\n
67. \\(\\dfrac{17}{12}\\)<\/td>\n69. \\(\\dfrac{13}{24}\\)<\/td>\n71. \\(\\dfrac{19}{80}\\)<\/td>\n<\/tr>\n
73. \\(\\dfrac{11}{6}\\)<\/td>\n75. \\(\\dfrac{1}{275}\\)<\/td>\n77. 14<\/td>\n<\/tr>\n
79. a) \\(\\dfrac{3}{8}\\) b) 0<\/td>\n81. \\(\\dfrac{5}{9}\\)<\/td>\n83. \\(-6\\)<\/td>\n<\/tr>\n
85. 8.03<\/td>\n87. 0.001<\/td>\n89. seven and eight tenths<\/td>\n<\/tr>\n
91. five thousandths<\/td>\n93. a) 5.79 b) 5.8 c) 6<\/td>\n95. a) 12.48 b) 12.5 c) 12<\/td>\n<\/tr>\n
97. 27.73<\/td>\n99. \u22125.53<\/td>\n101. \u221213.5<\/td>\n<\/tr>\n
103. 35.8<\/td>\n105. 42.51<\/td>\n107. 0.12<\/td>\n<\/tr>\n
109. 26.7528<\/td>\n111. 2.2302<\/td>\n113. 0.03<\/td>\n<\/tr>\n
115. \\$0.71<\/td>\n117. 150<\/td>\n119. \\(\\dfrac{2}{25}\\)<\/td>\n<\/tr>\n
121. \\(\\dfrac{17}{40}\\)<\/td>\n123. \\(\\dfrac{7}{4}\\)<\/td>\n125. 0.4<\/td>\n<\/tr>\n
127. \\(-0.375\\)<\/td>\n129. \\(0.\\stackrel{\\text{\u2013}}{5}\\)<\/td>\n131. 7<\/td>\n<\/tr>\n
133. a) \\(\\dfrac{9}{1}\\) b) \\(\\dfrac{847}{100}\\)<\/td>\n\n
<\/div>\n
135. a) \\(0.84,1.\\stackrel{\\text{\u2013}}{3}\\) b) \\(0.79132\\text{\u2026}\\),<\/div><\/td>\n
137. a) 0, 17 b) -4,0,17 c) \\(-4,0,\\dfrac{5}{6},17\\) d) \\(5.2537\\text{\u2026}\\) e) \\(-4,0,17,\\dfrac{5}{6}, 5.2537\\text{\u2026}\\)<\/td>\n<\/tr>\n
139. \"This<\/span><\/td>\n141. \"This<\/span><\/td>\n143. <<\/td>\n<\/tr>\n
145. ><\/td>\n147. \"This<\/span><\/td>\n149. \"This<\/span><\/td>\n<\/tr>\n
<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
151. ><\/td>\n153. ><\/td>\n155. \\(-48m\\)<\/td>\n<\/tr>\n
157. \\(a+47\\)<\/td>\n159. 37<\/td>\n161. \\(\\dfrac{35}{9}\\)<\/td>\n<\/tr>\n
163. \\(1\\dfrac{7}{12}\\)<\/td>\n165. \\(27x+23y\\)<\/td>\n167. a) \\(-\\dfrac{1}{3}\\) b) \\(-5.1\\) c) 14 d) \\(\\dfrac{8}{5}\\)<\/td>\n<\/tr>\n
169. a) \\(\\dfrac{1}{10}\\) b) \\(-\\dfrac{9}{4}\\)c)\\(\\dfrac{5}{3}\\)<\/td>\n171. 0<\/td>\n173. undefined<\/td>\n<\/tr>\n
175. 39<\/td>\n177. 57<\/td>\n179. 8<\/td>\n<\/tr>\n
181. \\(7x+63\\)<\/td>\n183. \\(-18m+3\\)<\/td>\n185. \\(5n-2\\)<\/td>\n<\/tr>\n
187. \\(-5a-13\\)<\/td>\n<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

Practice Test<\/h1>\n\n\n\n
1. Convert 1.85 to a fraction and simplify.<\/td>\n2.\u00a0Locate \\(\\dfrac{2}{3},-1.5\\), and \\(\\dfrac{9}{4}\\) on a number line.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n
\n\nIn the following exercises, simplify each expression.\n\n\n\n\n\n\n\n\n\n\n\n\n
3. \\(4+10\\left(3+9\\right)-{5}^{2}\\)<\/td>\n4.\u00a0\\(-85+42\\)<\/td>\n<\/tr>\n
5. \\(-19-25\\)<\/td>\n6. \\({\\left(-2\\right)}^{4}\\)<\/td>\n<\/tr>\n
7. \\(-5\\left(-9\\right)\\)\u00f7\\(15\\)<\/td>\n8. \\(\\dfrac{3}{8}\\cdot \\dfrac{11}{12}\\)<\/td>\n<\/tr>\n
9. \\(\\dfrac{4}{5}\\)\u00f7\\(\\dfrac{9}{20}\\)<\/td>\n10. \\(\\dfrac{12+3\\cdot 5}{15-6}\\)<\/td>\n<\/tr>\n
11. \\(\\dfrac{m}{7}+\\dfrac{10}{7}\\)<\/td>\n12. \\(\\dfrac{7}{12}-\\dfrac{3}{8}\\)<\/td>\n<\/tr>\n
13. \\(-5.8+\\left(-4.7\\right)\\)<\/td>\n14. \\(100-64.25\\)<\/td>\n<\/tr>\n
15. \\(\\left(0.07\\right)\\left(31.95\\right)\\)<\/td>\n16. 9 \u00f7 0.05<\/td>\n<\/tr>\n
17. \\(-14\\left(\\dfrac{5}{7}p\\right)\\)<\/td>\n18. \\(\\left(u+8\\right)-9\\)<\/td>\n<\/tr>\n
19. \\(6x+\\left(-4y\\right)+9x+8y\\)<\/td>\n20. \\(\\dfrac{0}{23}\\)<\/td>\n<\/tr>\n
21. \\(\\dfrac{75}{0}\\)<\/td>\n22. \\(-2\\left(13q-5\\right)\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n

Practice Test Answers<\/h1>\n
\n\n\n\n\n\n\n\n\n\n\n
1. \\(\\dfrac{37}{20}\\)<\/td>\n\"\"<\/td>\n3. 99<\/td>\n<\/tr>\n
4. \\(-43\\)<\/td>\n5. \\(-44\\)<\/td>\n6. \\(16\\)<\/td>\n<\/tr>\n
7.\u00a0 \\(3\\)<\/td>\n8. \\(\\dfrac{11}{32}\\)<\/td>\n9. \\(\\dfrac{16}{9}\\)<\/td>\n<\/tr>\n
10 \\(3\\)<\/td>\n11. \\(\\dfrac{m+10}{7}\\)<\/td>\n12. \\(\\dfrac{5}{24}\\)<\/td>\n<\/tr>\n
13. \\(-10.5\\)<\/td>\n14. 35.75<\/td>\n15. 2.2365<\/td>\n<\/tr>\n
16. \\(180\\)<\/td>\n17. \\(-10p\\)<\/td>\n18. \\(u -1\\)<\/td>\n<\/tr>\n
19. \\(15x+4y\\)<\/td>\n20. 0<\/td>\n21. undefined<\/td>\n<\/tr>\n
22. \\(-26q + 10\\)<\/td>\n<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>","rendered":"

Review Exercises<\/h1>\n

Find Equivalent Fractions<\/h2>\n

In the following exercises, find three fractions equivalent to the given fraction. Show your work, using figures or algebra.<\/p>\n\n\n\n\n
1. \"\dfrac{1}{4}\"<\/td>\n2. \"\dfrac{1}{3}\"<\/td>\n<\/tr>\n
3. \"\dfrac{5}{6}\"<\/td>\n4. \"\dfrac{2}{7}\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Simplify Fractions<\/h2>\n

In the following exercises, simplify.<\/p>\n\n\n\n\n\n\n
5. \"\dfrac{7}{21}\"<\/td>\n6. \"\dfrac{8}{24}\"<\/td>\n<\/tr>\n
7. \"\dfrac{15}{20}\"<\/td>\n8. \"\dfrac{12}{18}\"<\/td>\n<\/tr>\n
9. \"-\dfrac{168}{192}\"<\/td>\n10. \"-\dfrac{140}{224}\"<\/td>\n<\/tr>\n
11. \"\dfrac{11x}{11y}\"<\/td>\n12. \"\dfrac{15a}{15b}\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n

Multiply Fractions<\/h2>\n<\/div>\n

In the following exercises, multiply.<\/p>\n\n\n\n\n\n\n
13. \"\dfrac{2}{5}\cdot \dfrac{1}{3}\"<\/td>\n14. \"\dfrac{1}{2}\cdot \dfrac{3}{8}\"<\/td>\n<\/tr>\n
15. \"\dfrac{7}{12}(-\dfrac{8}{21})\"<\/td>\n16. \"\dfrac{5}{12}(-\dfrac{8}{15})\"<\/td>\n<\/tr>\n
17. \"-28p(-\dfrac{1}{4})\"<\/td>\n18. \"-51q(-\dfrac{1}{3})\"<\/td>\n<\/tr>\n
19. \"\dfrac{14}{5}(-15)\"<\/td>\n20. \"-1(-\dfrac{3}{8})\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n

Divide Fractions<\/h2>\n<\/div>\n

In the following exercises, divide.<\/p>\n\n\n\n\n\n\n\n
21. \"\dfrac{1}{2}\"\u00f7\"\dfrac{1}{4}\"<\/td>\n22. \"\dfrac{1}{2}\"\u00f7\"\dfrac{1}{8}\"<\/td>\n<\/tr>\n
23. \"-\dfrac{4}{5}\"\u00f7\"\dfrac{4}{7}\"<\/td>\n24. \"-\dfrac{3}{4}\"\u00f7\"\dfrac{3}{5}\"<\/td>\n<\/tr>\n
25. \"\dfrac{5}{8}\"\u00f7\"\dfrac{a}{10}\"<\/td>\n26. \"\dfrac{5}{6}\"\u00f7\"\dfrac{c}{15}\"<\/td>\n<\/tr>\n
27. \"\dfrac{7p}{12}\"\u00f7\"\dfrac{21p}{8}\"<\/td>\n28. \"\dfrac{5q}{12}\"\u00f7\"\dfrac{15q}{8}\"<\/td>\n<\/tr>\n
29. \"\dfrac{2}{5}\"\u00f7\"\left(-10\right)\"<\/td>\n30. \"-18\"\u00f7\"-\left(\dfrac{9}{2}\right)\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n
In the following exercises, simplify.<\/div>\n<\/div>\n\n\n\n\n\n
31. \"\dfrac{\dfrac{2}{3}}{\dfrac{8}{9}}\"<\/td>\n32. \"\dfrac{\dfrac{4}{5}}{\dfrac{8}{15}}\"<\/td>\n<\/tr>\n
33. \"\dfrac{-\dfrac{9}{10}}{3}\"<\/td>\n34. \"\dfrac{2}{\dfrac{5}{8}}\"<\/td>\n<\/tr>\n
35. \"\dfrac{\dfrac{r}{5}}{\dfrac{s}{3}}\"<\/td>\n36. \"\dfrac{-\dfrac{x}{6}}{-\dfrac{8}{9}}\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n

Simplify Expressions Written with a Fraction Bar<\/h2>\n<\/div>\n

In the following exercises, simplify.<\/p>\n\n\n\n\n\n\n\n\n
37. \"\dfrac{4+11}{8}\"<\/td>\n38. \"\dfrac{9+3}{7}\"<\/td>\n<\/tr>\n
39. \"\dfrac{30}{7-12}\"<\/td>\n40. \"\dfrac{15}{4-9}\"<\/td>\n<\/tr>\n
41. \"\dfrac{22-14}{19-13}\"<\/td>\n42. \"\dfrac{15+9}{18+12}\"<\/td>\n<\/tr>\n
43. \"\dfrac{5\cdot 8}{-10}\"<\/td>\n44. \"\dfrac{3\cdot 4}{-24}\"<\/td>\n<\/tr>\n
45. \"\dfrac{15\cdot 5-{5}^{2}}{2\cdot 10}\"<\/td>\n46. \"\dfrac{12 \cdot 9-{3}^{2}}{3\cdot 18}\"<\/td>\n<\/tr>\n
47. \"\dfrac{2+4\left(3\right)}{-3-{2}^{2}}\"<\/td>\n48. \"\dfrac{7+3\left(5\right)}{-2-{3}^{2}}\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n

Translate Phrases to Expressions with Fractions<\/h2>\n<\/div>\n

In the following exercises, translate each English phrase into an algebraic expression.<\/p>\n\n\n\n
49. the quotient of c<\/em> and the sum of d<\/em> and 9.<\/td>\n50. the quotient of the difference of h<\/em> and k<\/em>, and \"-5\".<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n

Add and Subtract Fractions with a Common Denominator<\/h2>\n<\/div>\n

In the following exercises, add.<\/p>\n\n\n\n\n\n
51. \"\dfrac{4}{9}+\dfrac{1}{9}\"<\/td>\n52. \"\dfrac{2}{9}+\dfrac{5}{9}\"<\/td>\n<\/tr>\n
53. \"\dfrac{y}{3}+\dfrac{2}{3}\"<\/td>\n54. \"\dfrac{7}{p}+\dfrac{9}{p}\"<\/td>\n<\/tr>\n
55. \"-\dfrac{1}{8}+\left(-\dfrac{3}{8}\right)\"<\/td>\n56. \"-\dfrac{1}{8}+\left(-\dfrac{5}{8}\right)\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n
\n

In the following exercises, subtract.<\/p>\n\n\n\n\n\n
57. \"\dfrac{4}{5}-\dfrac{1}{5}\"<\/td>\n58. \"\dfrac{4}{5}-\dfrac{3}{5}\"<\/td>\n<\/tr>\n
59. \"\dfrac{y}{17}-\dfrac{9}{17}\"<\/td>\n60. \"\dfrac{x}{19}-\dfrac{8}{19}\"<\/td>\n<\/tr>\n
61. \"-\dfrac{8}{d}-\dfrac{3}{d}\"<\/td>\n62. \"-\dfrac{7}{c}-\dfrac{7}{c}\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n
\n

Add or Subtract Fractions with Different Denominators<\/h2>\n<\/div>\n

In the following exercises, add or subtract.<\/p>\n\n\n\n\n\n\n\n\n
63. \"\dfrac{1}{3}+\dfrac{1}{5}\"<\/td>\n64. \"\dfrac{1}{4}+\dfrac{1}{5}\"<\/td>\n<\/tr>\n
65. \"\dfrac{1}{5}-\left(-\dfrac{1}{10}\right)\"<\/td>\n66. \"\dfrac{1}{2}-\left(-\dfrac{1}{6}\right)\"<\/td>\n<\/tr>\n
67. \"\dfrac{2}{3}+\dfrac{3}{4}\"<\/td>\n68. \"\dfrac{3}{4}+\dfrac{2}{5}\"<\/td>\n<\/tr>\n
69. \"\dfrac{11}{12}-\dfrac{3}{8}\"<\/td>\n70. \"\dfrac{5}{8}-\dfrac{7}{12}\"<\/td>\n<\/tr>\n
71. \"-\dfrac{9}{16}-\left(-\dfrac{4}{5}\right)\"<\/td>\n72. \"-\dfrac{7}{20}-\left(-\dfrac{5}{8}\right)\"<\/td>\n<\/tr>\n
73. \"1+\dfrac{5}{6}\"<\/td>\n74. \"1-\dfrac{5}{9}\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n

Use the Order of Operations to Simplify Complex Fractions<\/h2>\n<\/div>\n

In the following exercises, simplify.<\/p>\n\n\n\n\n
75. \"\dfrac{{\left(\dfrac{1}{5}\right)}^{2}}{2+{3}^{2}}\"<\/td>\n76. \"\dfrac{{\left(\dfrac{1}{3}\right)}^{2}}{5+{2}^{2}}\"<\/td>\n<\/tr>\n
77. \"\dfrac{\dfrac{2}{3}+\dfrac{1}{2}}{\dfrac{3}{4}-\dfrac{2}{3}}\"<\/td>\n78. \"\dfrac{\dfrac{3}{4}+\dfrac{1}{2}}{\dfrac{5}{6}-\dfrac{2}{3}}\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n

Evaluate Variable Expressions with Fractions<\/h2>\n<\/div>\n

In the following exercises, evaluate.<\/p>\n\n\n\n\n\n
79. \"x+\dfrac{1}{2}\" when
\na) \"x=-\dfrac{1}{8}\"
\nb) \"x=-\dfrac{1}{2}\"<\/td>\n		80. \"x+\dfrac{2}{3}\" when
\na) \"x=-\dfrac{1}{6}\"
\nb) \"x=-\dfrac{5}{3}\"<\/td>\n<\/tr>\n
81. \"4{p}^{2}q\" when \"p=-\dfrac{1}{2}\" and \"q=\dfrac{5}{9}\"<\/td>\n82. \"5{m}^{2}n\" when \"m=-\dfrac{2}{5}\" and \"n=\dfrac{1}{3}\"<\/td>\n<\/tr>\n
83. \"\dfrac{u+v}{w}\" when
\n\"u=-4,v=-8,w=2\"<\/td>\n		84. \"\dfrac{m+n}{p}\" when
\n\"m=-6,n=-2,p=4\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n

\u00a0Name and Write Decimals<\/h2>\n<\/div>\n

In the following exercises, write as a decimal.<\/p>\n\n\n\n\n
85. Eight and three hundredths<\/td>\n86. Nine and seven hundredths<\/td>\n<\/tr>\n
87. One thousandth<\/td>\n88. Nine thousandths<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n
\n

In the following exercises, name each decimal.<\/p>\n\n\n\n\n
89. 7.8<\/td>\n90. 5.01<\/td>\n<\/tr>\n
91. 0.005<\/td>\n92. 0.381<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n
\n
\n

Round Decimals<\/h2>\n<\/div>\n<\/div>\n

In the following exercises, round each number to the nearest a) hundredth b) tenth c) whole number.<\/p>\n\n\n\n\n
93. 5.7932<\/td>\n94. 3.6284<\/td>\n<\/tr>\n
95. 12.4768<\/td>\n96. 25.8449<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n
\n

Add and Subtract Decimals<\/h2>\n<\/div>\n<\/div>\n

In the following exercises, add or subtract.<\/p>\n\n\n\n\n\n\n\n
97. \"18.37+9.36\"<\/td>\n98. \"256.37-85.49\"<\/td>\n<\/tr>\n
99. \"15.35-20.88\"<\/td>\n100. \"37.5+12.23\"<\/td>\n<\/tr>\n
101. \"-4.2+\left(-9.3\right)\"<\/td>\n102. \"-8.6+\left(-8.6\right)\"<\/td>\n<\/tr>\n
103. \"100-64.2\"<\/td>\n104. \"100-65.83\"<\/td>\n<\/tr>\n
105. \"2.51+40\"<\/td>\n106. \"9.38+60\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n
\n

Multiply and Divide Decimals<\/h2>\n<\/div>\n<\/div>\n

In the following exercises, multiply.<\/p>\n\n\n\n\n\n
107. \"\left(0.3\right)\left(0.4\right)\"<\/td>\n108. \"\left(0.6\right)\left(0.7\right)\"<\/td>\n<\/tr>\n
109. \"\left(8.52\right)\left(3.14\right)\"<\/td>\n110. \"\left(5.32\right)\left(4.86\right)\"<\/td>\n<\/tr>\n
111. \"\left(0.09\right)\left(24.78\right)\"<\/td>\n112. \"\left(0.04\right)\left(36.89\right)\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n
\n

In the following exercises, divide.<\/p>\n\n\n\n\n\n
113. 0.15 \u00f7 5<\/td>\n114. 0.27 \u00f7 3<\/td>\n<\/tr>\n
115. $8.49 \u00f7 12<\/td>\n116. $16.99 \u00f7 9<\/td>\n<\/tr>\n
117. 12 \u00f7 0.08<\/td>\n118. 5 \u00f7 0.04<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n
\n
\n

Convert Decimals and Fractions<\/h2>\n<\/div>\n<\/div>\n

In the following exercises, write each decimal as a fraction.<\/p>\n\n\n\n\n\n
119. 0.08<\/td>\n120. 0.17<\/td>\n<\/tr>\n
121. 0.425<\/td>\n122. 0.184<\/td>\n<\/tr>\n
123. 1.75<\/td>\n124. 0.035<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n
\n

In the following exercises, convert each fraction to a decimal.<\/p>\n\n\n\n\n\n\n
125. \"\dfrac{2}{5}\"<\/td>\n126. \"\dfrac{4}{5}\"<\/td>\n<\/tr>\n
127. \"-\dfrac{3}{8}\"<\/td>\n128. \"-\dfrac{5}{8}\"<\/td>\n<\/tr>\n
129. \"\dfrac{5}{9}\"<\/td>\n130. \"\dfrac{2}{9}\"<\/td>\n<\/tr>\n
131. \"\dfrac{1}{2}+6.5\"<\/td>\n132. \"\dfrac{1}{4}+10.75\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n

Identify Integers, Rational Numbers, Irrational Numbers, and Real Numbers<\/h2>\n

In the following exercises, write as the ratio of two integers.<\/p>\n\n\n\n
133. a) 9 b) 8.47<\/td>\n134. a) \"-15\"b) 3.591<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n
\n

In the following exercises, list the a) rational numbers, b) irrational numbers.<\/p>\n\n\n\n
135. \"0.84,0.79132\text{…},1.\stackrel{\text{-}}{3}\"<\/td>\n136. \"2.3\stackrel{\text{-}}{8},0.572,4.93814\text{…}\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n
\n
\n

In the following exercises, list the a) whole numbers, b) integers, c) rational numbers, d) irrational numbers, e) real numbers for each set of numbers.<\/p>\n\n\n\n
137. \"-4,0,\dfrac{5}{6} ,17 ,5.2537\text{…}\"<\/td>\n138. \"-2, 0.\stackrel{\text{-}}{36},\dfrac{13}{3},6.9152\text{…},10\dfrac{1}{2}\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n
\n
\n

Locate Fractions on the Number Line<\/h2>\n<\/div>\n<\/div>\n

In the following exercises, locate the numbers on a number line.<\/p>\n\n\n\n\n
139. \"\dfrac{2}{3},\dfrac{5}{4},\dfrac{12}{5}\"<\/td>\n140. \"\dfrac{1}{3},\dfrac{7}{4},\dfrac{13}{5}\"<\/td>\n<\/tr>\n
141. \"2\dfrac{1}{3},-2\dfrac{1}{3}\"<\/td>\n142. \"1\dfrac{3}{5},-1\dfrac{3}{5}\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

In the following exercises, order each of the following pairs of numbers, using < or >.<\/p>\n

\n
\n\n\n\n\n
143. \"-1\" ___ \"-\dfrac{1}{8}\"<\/td>\n144. \"-3\dfrac{1}{4}\"___ \"-4\"<\/td>\n<\/tr>\n
145. \"-\dfrac{7}{9}\" ___ \"-\dfrac{4}{9}\"<\/td>\n146. \"-2\" ___ \"-\dfrac{19}{8}\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Locate Decimals on the Number Line<\/h2>\n<\/div>\n<\/div>\n

In the following exercises, locate on the number line.<\/p>\n\n\n\n\n
147. 0.3<\/td>\n148. -0.2<\/td>\n<\/tr>\n
149. -2.5<\/td>\n150. 2.7<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n
\n

In the following exercises, order each of the following pairs of numbers, using < or >.<\/p>\n\n\n\n\n
151. 0.9 ___ 0.6<\/td>\n152. 0.7 ___ 0.8<\/td>\n<\/tr>\n
153. -0.6 ___ -0.59<\/td>\n154. -0.27 ___ -0.3<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n
\n

Use the Commutative and Associative Properties<\/h2>\n<\/div>\n

In the following exercises, use the Associative Property to simplify.<\/p>\n\n\n\n\n
155. \"-12\left(4m\right)\"<\/td>\n156. \"30\left(\dfrac{5}{6}q\right)\"<\/td>\n<\/tr>\n
157. \"\left(a+16\right)+31\"<\/td>\n158. \"\left(c+0.2\right)+0.7\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n
\n

In the following exercises, simplify.<\/p>\n\n\n\n\n\n\n
159. \"6y+37+\left(-6y\right)\"<\/td>\n160. \"\dfrac{1}{4}+\dfrac{11}{15}+\left(-\dfrac{1}{4}\right)\"<\/td>\n<\/tr>\n
161. \"\dfrac{14}{11}\cdot \dfrac{35}{9}\cdot \dfrac{14}{11}\"<\/td>\n162. \"-18\cdot 15 \cdot \dfrac{2}{9}\"<\/td>\n<\/tr>\n
163. \"\left(\dfrac{7}{12}+\dfrac{4}{5}\right)+\dfrac{1}{5}\"<\/td>\n164. \"\left(3.98d+0.75d\right)+1.25d\"<\/td>\n<\/tr>\n
165. \"11x+8y+16x+15y\"<\/td>\n166. \"52m+\left(-20n\right)+\left(-18m\right)+\left(-5n\right)\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n
\n
\n

Use the Identity and Inverse Properties of Addition and Multiplication<\/h2>\n<\/div>\n<\/div>\n

In the following exercises, find the additive inverse of each number.<\/p>\n\n\n\n
\n

167.<\/p>\n

a) \"\dfrac{1}{3}\"
\nb) \"5.1\"
\nc) \"-14\"
\nd) \"-\dfrac{8}{5}\"<\/td>\n

168.
\na) \"-\dfrac{7}{8}\"
\nb) \"-0.03\"
\nc) \"17\"
\nd) \"\dfrac{12}{5}\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n
\n

In the following exercises, find the multiplicative inverse of each number.<\/p>\n\n\n\n
169. a) 10 b) \"-\dfrac{4}{9}\" c) 0.6<\/td>\n170. a) \"-\dfrac{9}{2}\" b) \"-7\" c) 2.1<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n
\n
\n

Use the Properties of Zero<\/h2>\n<\/div>\n<\/div>\n

In the following exercises, simplify.<\/p>\n\n\n\n\n
171. \"83\cdot 0\"<\/td>\n172. \"\dfrac{0}{9}\"<\/td>\n<\/tr>\n
173. \"\dfrac{5}{0}\"<\/td>\n174. \"0\"\\div \"\dfrac{2}{3}\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n
\n

In the following exercises, simplify.<\/p>\n\n\n\n\n\n
175. \"43+39+\left(-43\right)\"<\/td>\n176. \"\left(n+6.75\right)+0.25\"<\/td>\n<\/tr>\n
177. \"\dfrac{5}{13}\cdot 57 \cdot \dfrac{13}{5}\"<\/td>\n178. \"\dfrac{1}{6}\cdot17\cdot12\"<\/td>\n<\/tr>\n
179. \"\dfrac{2}{3}\cdot 28 \cdot \dfrac{3}{7}\"<\/td>\n180. \"9\left(6x-11\right)+15\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n
\n

Simplify Expressions Using the Distributive Property<\/h2>\n<\/div>\n

In the following exercises, simplify using the Distributive Property.<\/p>\n\n\n\n\n\n\n
181. \"7\left(x+9\right)\"<\/td>\n182. \"9\left(u-4\right)\"<\/td>\n<\/tr>\n
183. \"-3\left(6m-1\right)\"<\/td>\n184. \"-8\left(-7a-12\right)\"<\/td>\n<\/tr>\n
185. \"\dfrac{1}{3}\left(15n-6\right)\"<\/td>\n186. \"\left(y+10\right)\cdot p\"<\/td>\n<\/tr>\n
187. \"\left(a-4\right)-\left(6a+9\right)\"<\/td>\n188. \"4\left(x+3\right)-8\left(x-7\right)\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Review Exercise Answers<\/h1>\n
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
1. \"\dfrac{2}{8},\dfrac{3}{12},\dfrac{4}{16}\" answers may vary<\/td>\n3. \"\dfrac{10}{12},\dfrac{15}{18},\dfrac{20}{24}\" answers may vary<\/td>\n5. \"\dfrac{1}{3}\"<\/td>\n<\/tr>\n
7. \"\dfrac{3}{4}\"<\/td>\n9. \"-\dfrac{7}{8}\"<\/td>\n11. \"\dfrac{x}{y}\"<\/td>\n<\/tr>\n
13. \"\dfrac{2}{15}\"<\/td>\n15. \"-\dfrac{2}{9}\"<\/td>\n17. \"7p\"<\/td>\n<\/tr>\n
19. \"-42\"<\/td>\n21. 2<\/td>\n23. \"-\dfrac{7}{5}\"<\/td>\n<\/tr>\n
25. \"\dfrac{25}{4a}\"<\/td>\n27. \"\dfrac{2}{9}\"<\/td>\n29. \"-\dfrac{1}{25}\"<\/td>\n<\/tr>\n
31. \"\dfrac{3}{4}\"<\/td>\n33. \"-\dfrac{3}{10}\"<\/td>\n35. \"\dfrac{3r}{5s}\"<\/td>\n<\/tr>\n
37. \"\dfrac{15}{8}\"<\/td>\n39. \"-6\"<\/td>\n41. \"\dfrac{4}{3}\"<\/td>\n<\/tr>\n
43. \"-4\"<\/td>\n45. \"\dfrac{5}{21}\"<\/td>\n47. \"-2\"<\/td>\n<\/tr>\n
49. \"\dfrac{c}{d+9}\"<\/td>\n51. \"\dfrac{5}{9}\"<\/td>\n53. \"\dfrac{y+2}{3}\"<\/td>\n<\/tr>\n
55. \"-\dfrac{1}{2}\"<\/td>\n57. \"\dfrac{3}{5}\"<\/td>\n59. \"\dfrac{y-9}{17}\"<\/td>\n<\/tr>\n
61. \"-\dfrac{11}{d}\"<\/td>\n63. \"\dfrac{8}{15}\"<\/td>\n65. \"\dfrac{3}{10}\"<\/td>\n<\/tr>\n
67. \"\dfrac{17}{12}\"<\/td>\n69. \"\dfrac{13}{24}\"<\/td>\n71. \"\dfrac{19}{80}\"<\/td>\n<\/tr>\n
73. \"\dfrac{11}{6}\"<\/td>\n75. \"\dfrac{1}{275}\"<\/td>\n77. 14<\/td>\n<\/tr>\n
79. a) \"\dfrac{3}{8}\" b) 0<\/td>\n81. \"\dfrac{5}{9}\"<\/td>\n83. \"-6\"<\/td>\n<\/tr>\n
85. 8.03<\/td>\n87. 0.001<\/td>\n89. seven and eight tenths<\/td>\n<\/tr>\n
91. five thousandths<\/td>\n93. a) 5.79 b) 5.8 c) 6<\/td>\n95. a) 12.48 b) 12.5 c) 12<\/td>\n<\/tr>\n
97. 27.73<\/td>\n99. \u22125.53<\/td>\n101. \u221213.5<\/td>\n<\/tr>\n
103. 35.8<\/td>\n105. 42.51<\/td>\n107. 0.12<\/td>\n<\/tr>\n
109. 26.7528<\/td>\n111. 2.2302<\/td>\n113. 0.03<\/td>\n<\/tr>\n
115. $0.71<\/td>\n117. 150<\/td>\n119. \"\dfrac{2}{25}\"<\/td>\n<\/tr>\n
121. \"\dfrac{17}{40}\"<\/td>\n123. \"\dfrac{7}{4}\"<\/td>\n125. 0.4<\/td>\n<\/tr>\n
127. \"-0.375\"<\/td>\n129. \"0.\stackrel{\text{-}}{5}\"<\/td>\n131. 7<\/td>\n<\/tr>\n
133. a) \"\dfrac{9}{1}\" b) \"\dfrac{847}{100}\"<\/td>\n\n
<\/div>\n
135. a) \"0.84,1.\stackrel{\text{-}}{3}\" b) \"0.79132\text{…}\",<\/div>\n<\/td>\n
137. a) 0, 17 b) -4,0,17 c) \"-4,0,\dfrac{5}{6},17\" d) \"5.2537\text{…}\" e) \"-4,0,17,\dfrac{5}{6}, 5.2537\text{…}\"<\/td>\n<\/tr>\n
139. \"This<\/span><\/td>\n141. \"This<\/span><\/td>\n143. <<\/td>\n<\/tr>\n
145. ><\/td>\n147. \"This<\/span><\/td>\n149. \"This<\/span><\/td>\n<\/tr>\n
<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
151. ><\/td>\n153. ><\/td>\n155. \"-48m\"<\/td>\n<\/tr>\n
157. \"a+47\"<\/td>\n159. 37<\/td>\n161. \"\dfrac{35}{9}\"<\/td>\n<\/tr>\n
163. \"1\dfrac{7}{12}\"<\/td>\n165. \"27x+23y\"<\/td>\n167. a) \"-\dfrac{1}{3}\" b) \"-5.1\" c) 14 d) \"\dfrac{8}{5}\"<\/td>\n<\/tr>\n
169. a) \"\dfrac{1}{10}\" b) \"-\dfrac{9}{4}\"c)\"\dfrac{5}{3}\"<\/td>\n171. 0<\/td>\n173. undefined<\/td>\n<\/tr>\n
175. 39<\/td>\n177. 57<\/td>\n179. 8<\/td>\n<\/tr>\n
181. \"7x+63\"<\/td>\n183. \"-18m+3\"<\/td>\n185. \"5n-2\"<\/td>\n<\/tr>\n
187. \"-5a-13\"<\/td>\n<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

Practice Test<\/h1>\n\n\n\n
1. Convert 1.85 to a fraction and simplify.<\/td>\n2.\u00a0Locate \"\dfrac{2}{3},-1.5\", and \"\dfrac{9}{4}\" on a number line.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n
\n

In the following exercises, simplify each expression.<\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n
3. \"4+10\left(3+9\right)-{5}^{2}\"<\/td>\n4.\u00a0\"-85+42\"<\/td>\n<\/tr>\n
5. \"-19-25\"<\/td>\n6. \"{\left(-2\right)}^{4}\"<\/td>\n<\/tr>\n
7. \"-5\left(-9\right)\"\u00f7\"15\"<\/td>\n8. \"\dfrac{3}{8}\cdot \dfrac{11}{12}\"<\/td>\n<\/tr>\n
9. \"\dfrac{4}{5}\"\u00f7\"\dfrac{9}{20}\"<\/td>\n10. \"\dfrac{12+3\cdot 5}{15-6}\"<\/td>\n<\/tr>\n
11. \"\dfrac{m}{7}+\dfrac{10}{7}\"<\/td>\n12. \"\dfrac{7}{12}-\dfrac{3}{8}\"<\/td>\n<\/tr>\n
13. \"-5.8+\left(-4.7\right)\"<\/td>\n14. \"100-64.25\"<\/td>\n<\/tr>\n
15. \"\left(0.07\right)\left(31.95\right)\"<\/td>\n16. 9 \u00f7 0.05<\/td>\n<\/tr>\n
17. \"-14\left(\dfrac{5}{7}p\right)\"<\/td>\n18. \"\left(u+8\right)-9\"<\/td>\n<\/tr>\n
19. \"6x+\left(-4y\right)+9x+8y\"<\/td>\n20. \"\dfrac{0}{23}\"<\/td>\n<\/tr>\n
21. \"\dfrac{75}{0}\"<\/td>\n22. \"-2\left(13q-5\right)\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n

Practice Test Answers<\/h1>\n
\n\n\n\n\n\n\n\n\n\n\n
1. \"\dfrac{37}{20}\"<\/td>\n\"\"<\/td>\n3. 99<\/td>\n<\/tr>\n
4. \"-43\"<\/td>\n5. \"-44\"<\/td>\n6. \"16\"<\/td>\n<\/tr>\n
7.\u00a0 \"3\"<\/td>\n8. \"\dfrac{11}{32}\"<\/td>\n9. \"\dfrac{16}{9}\"<\/td>\n<\/tr>\n
10 \"3\"<\/td>\n11. \"\dfrac{m+10}{7}\"<\/td>\n12. \"\dfrac{5}{24}\"<\/td>\n<\/tr>\n
13. \"-10.5\"<\/td>\n14. 35.75<\/td>\n15. 2.2365<\/td>\n<\/tr>\n
16. \"180\"<\/td>\n17. \"-10p\"<\/td>\n18. \"u -1\"<\/td>\n<\/tr>\n
19. \"15x+4y\"<\/td>\n20. 0<\/td>\n21. undefined<\/td>\n<\/tr>\n
22. \"-26q + 10\"<\/td>\n<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n","protected":false},"author":90,"menu_order":6,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-395","chapter","type-chapter","status-publish","hentry"],"part":251,"_links":{"self":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters\/395","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/users\/90"}],"version-history":[{"count":1,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters\/395\/revisions"}],"predecessor-version":[{"id":396,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters\/395\/revisions\/396"}],"part":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/parts\/251"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters\/395\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/media?parent=395"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=395"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/contributor?post=395"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/license?post=395"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}