CHAPTER 2 Operations with Rational Numbers and Introduction to Real Numbers

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. ÷
In the following exercises, simplify.
 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

 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

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) b) c) d) 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

 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.