2.6 Chapter Review
Review Exercises
Find Equivalent Fractions
In the following exercises, find three fractions equivalent to the given fraction. Show your work, using figures or algebra.
| 1. | 2. |
| 3. | 4. |
Simplify Fractions
In the following exercises, simplify.
| 5. | 6. |
| 7. | 8. |
| 9. | 10. |
| 11. | 12. |
Multiply Fractions
In the following exercises, multiply.
| 13. | 14. |
| 15. | 16. |
| 17. | 18. |
| 19. | 20. |
Divide Fractions
In the following exercises, divide.
| 21. ÷ | 22. ÷ |
| 23. ÷ | 24. ÷ |
| 25. ÷ | 26. ÷ |
| 27. ÷ | 28. ÷ |
| 29. ÷ | 30. ÷ |
| 31. | 32. |
| 33. | 34. |
| 35. | 36. |
Simplify Expressions Written with a Fraction Bar
In the following exercises, simplify.
| 37. | 38. |
| 39. | 40. |
| 41. | 42. |
| 43. | 44. |
| 45. | 46. |
| 47. | 48. |
Translate Phrases to Expressions with Fractions
In the following exercises, translate each English phrase into an algebraic expression.
| 49. the quotient of c and the sum of d and 9. | 50. the quotient of the difference of h and k, and . |
Add and Subtract Fractions with a Common Denominator
In the following exercises, add.
| 51. | 52. |
| 53. | 54. |
| 55. | 56. |
In the following exercises, subtract.
| 57. | 58. |
| 59. | 60. |
| 61. | 62. |
Add or Subtract Fractions with Different Denominators
In the following exercises, add or subtract.
| 63. | 64. |
| 65. | 66. |
| 67. | 68. |
| 69. | 70. |
| 71. | 72. |
| 73. | 74. |
Use the Order of Operations to Simplify Complex Fractions
In the following exercises, simplify.
| 75. | 76. |
| 77. | 78. |
Evaluate Variable Expressions with Fractions
In the following exercises, evaluate.
| 79. when a) b) |
80. when a) b) |
| 81. when and | 82. when and |
| 83. when |
84. when |
Name and Write Decimals
In the following exercises, write as a decimal.
| 85. Eight and three hundredths | 86. Nine and seven hundredths |
| 87. One thousandth | 88. Nine thousandths |
In the following exercises, name each decimal.
| 89. 7.8 | 90. 5.01 |
| 91. 0.005 | 92. 0.381 |
Round Decimals
In the following exercises, round each number to the nearest a) hundredth b) tenth c) whole number.
| 93. 5.7932 | 94. 3.6284 |
| 95. 12.4768 | 96. 25.8449 |
Add and Subtract Decimals
In the following exercises, add or subtract.
| 97. | 98. |
| 99. | 100. |
| 101. | 102. |
| 103. | 104. |
| 105. | 106. |
Multiply and Divide Decimals
In the following exercises, multiply.
| 107. | 108. |
| 109. | 110. |
| 111. | 112. |
In the following exercises, divide.
| 113. 0.15 ÷ 5 | 114. 0.27 ÷ 3 |
| 115. $8.49 ÷ 12 | 116. $16.99 ÷ 9 |
| 117. 12 ÷ 0.08 | 118. 5 ÷ 0.04 |
Convert Decimals and Fractions
In the following exercises, write each decimal as a fraction.
| 119. 0.08 | 120. 0.17 |
| 121. 0.425 | 122. 0.184 |
| 123. 1.75 | 124. 0.035 |
In the following exercises, convert each fraction to a decimal.
| 125. | 126. |
| 127. | 128. |
| 129. | 130. |
| 131. | 132. |
Identify Integers, Rational Numbers, Irrational Numbers, and Real Numbers
In the following exercises, write as the ratio of two integers.
| 133. a) 9 b) 8.47 | 134. a) b) 3.591 |
In the following exercises, list the a) rational numbers, b) irrational numbers.
| 135. | 136. |
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.
| 137. | 138. |
Locate Fractions on the Number Line
In the following exercises, locate the numbers on a number line.
| 139. | 140. |
| 141. | 142. |
In the following exercises, order each of the following pairs of numbers, using < or >.
| 143. ___ | 144. ___ |
| 145. ___ | 146. ___ |
Locate Decimals on the Number Line
In the following exercises, locate on the number line.
| 147. 0.3 | 148. -0.2 |
| 149. -2.5 | 150. 2.7 |
In the following exercises, order each of the following pairs of numbers, using < or >.
| 151. 0.9 ___ 0.6 | 152. 0.7 ___ 0.8 |
| 153. -0.6 ___ -0.59 | 154. -0.27 ___ -0.3 |
Use the Commutative and Associative Properties
In the following exercises, use the Associative Property to simplify.
| 155. | 156. |
| 157. | 158. |
In the following exercises, simplify.
| 159. | 160. |
| 161. | 162. |
| 163. | 164. |
| 165. | 166. |
Use the Identity and Inverse Properties of Addition and Multiplication
In the following exercises, find the additive inverse of each number.
|
167. a) |
168. a) b) c) d) |
In the following exercises, find the multiplicative inverse of each number.
| 169. a) 10 b) c) 0.6 | 170. a) b) c) 2.1 |
Use the Properties of Zero
In the following exercises, simplify.
| 171. | 172. |
| 173. | 174. |
In the following exercises, simplify.
| 175. | 176. |
| 177. | 178. |
| 179. | 180. |
Simplify Expressions Using the Distributive Property
In the following exercises, simplify using the Distributive Property.
| 181. | 182. |
| 183. | 184. |
| 185. | 186. |
| 187. | 188. |
Review Exercise Answers
| 1. answers may vary | 3. answers may vary | 5. |
| 7. | 9. | 11. |
| 13. | 15. | 17. |
| 19. | 21. 2 | 23. |
| 25. | 27. | 29. |
| 31. | 33. | 35. |
| 37. | 39. | 41. |
| 43. | 45. | 47. |
| 49. | 51. | 53. |
| 55. | 57. | 59. |
| 61. | 63. | 65. |
| 67. | 69. | 71. |
| 73. | 75. | 77. 14 |
| 79. a) b) 0 | 81. | 83. |
| 85. 8.03 | 87. 0.001 | 89. seven and eight tenths |
| 91. five thousandths | 93. a) 5.79 b) 5.8 c) 6 | 95. a) 12.48 b) 12.5 c) 12 |
| 97. 27.73 | 99. −5.53 | 101. −13.5 |
| 103. 35.8 | 105. 42.51 | 107. 0.12 |
| 109. 26.7528 | 111. 2.2302 | 113. 0.03 |
| 115. $0.71 | 117. 150 | 119. |
| 121. | 123. | 125. 0.4 |
| 127. | 129. | 131. 7 |
| 133. a) b) |
135. a) b) ,
|
137. a) 0, 17 b) -4,0,17 c) d) e) |
| 139. | 141. | 143. < |
| 145. > | 147. | 149. |
| 151. > | 153. > | 155. |
| 157. | 159. 37 | 161. |
| 163. | 165. | 167. a) b) c) 14 d) |
| 169. a) b) c) | 171. 0 | 173. undefined |
| 175. 39 | 177. 57 | 179. 8 |
| 181. | 183. | 185. |
| 187. |
Practice Test
| 1. Convert 1.85 to a fraction and simplify. | 2. Locate , and on a number line. |
In the following exercises, simplify each expression.
| 3. | 4. |
| 5. | 6. |
| 7. ÷ | 8. |
| 9. ÷ | 10. |
| 11. | 12. |
| 13. | 14. |
| 15. | 16. 9 ÷ 0.05 |
| 17. | 18. |
| 19. | 20. |
| 21. | 22. |
Practice Test Answers
| 1. | 3. 99 | |
| 4. | 5. | 6. |
| 7. | 8. | 9. |
| 10 | 11. | 12. |
| 13. | 14. 35.75 | 15. 2.2365 |
| 16. | 17. | 18. |
| 19. | 20. 0 | 21. undefined |
| 22. |