CHAPTER 2 Operations with Rational Numbers and Introduction to Real Numbers
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. \div |
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. |