A-14 ANSWERS 115. a) 1 1 or 1 b) 0.9 c) 1 3 2 3 1, 0.3 0.6 0.9 + = + = d) 0.9 1 = SECTION 5.4, PAGE 256 1. Irrational 3. Radicand 5. Itself 7. Rationalized 9. Rational 11. Irrational 13. Irrational 15. Rational 17. Rational 19. 0 21. 5 23. 6− 25. 10 − 27. Rational, integer 29. Irrational 31. Rational 33. Rational 35. Irrational 37. 2 7 39. 3 6 41. 3 7 43. 2 21 45. 7 6 47. 4 3 3 7 − − 49. 13 3 − 51. 4 3 53. 9 55. 3 7 57. 2 59. 3 61. 7 7 63. 6 3 65. 2 15 3 67. 15 3 69. Between 6 and 6.5; 37 6.08. ≈ 71. Between 9.5 and 10; 97 9.85. ≈ 73. Between 13 and 13.5; 170 13.04. ≈ 75. a) 2.5 sec b) 5 sec c) 7.5 sec d) 10 sec 77. a) 34.3 inches b) 36.0 inches c) 37.5 inches d) 38.9 inches 79. False. c may be a rational number or an irrational number for a composite number c. (For example, 25 is a rational number; 8 is an irrational number.) 81. True 83. False. The product of a rational number and an irrational number may be a rational number or an irrational number. The product of 0 and an irrational number is 0, which is a rational number. The product of a nonzero rational number and an irrational number is always an irrational number. 85. ( ) 0 π π + − = 87. 2 3 6 ⋅ = 89. 2 1.414 ≠ since 2 is irrational and 1.414 is rational. 91. No. π is irrational; it cannot equal 22 7 or 3.14, both of which are rational. 93. 49 4 9, 36 23,6 6 ⋅ = ⋅ = ⋅ = 95. a) Rational. 0.04 0.2, = which is a rational number. b) Irrational 0.7 0.8366600265 . = … Since the decimal number is not a terminating or a repeating decimal number, this number is an irrational number 97. a) (44 4) 4 11 ÷ ÷ = b) (44 4) 4 13 ÷ + = c) 4 4 4 4 14 + + + = d) 4(4 4) 4 18; + + = Other answers are possible. SECTION 5.5, PAGE 263 Answer to Recreational Math box on page 260 163 123 71 22 4 24 24 2 4 1 3 1 3 4 3 2 1 1 4 2 2 3 4 1. Real 3. Closed 5. Commutative 7. Associative 9. Yes 11. No 13. Yes 15. Yes 17. Yes 19. Yes 49. a) 64 − b) 64 − 51. 1− 53. 12 55. 12 57. 75 − 59. 1 61. 1100 feet under water 63. 65,233 ft 65. a) 11 hours b) 2 hours c) 14 hours d) 15 hours 67. True 69. False; the difference of two negative integers may be a positive integer, a negative integer, or zero. 71. True 73. True 75. False; the sum of a positive integer and a negative integer may be a positive integer, a negative integer, or zero. 77. Division by zero is undefined because a x 0 = always leads to a false statement. 79. 1− 81. 01234567891 +−++−+−−+= 82. a) 4 4 4 4 12, 4 4 4 4 15, 4 4 4 4 16, ⎛ − ⎝⎜ ⎞ ⎠⎟ = ⋅ − = ⋅ ⋅ = 4 4 4 4 17, 4 4 4 4 20 ⋅ + = ⎛ + ⎝⎜ ⎞ ⎠⎟ = b) 44 4 4 10 − = SECTION 5.3, PAGE 245 1. Integers 3. Denominator 5. Improper 7. Repeating 9. Ten-thousandths 11. 2 5 13. 4 9 15. 19 25 17. 29 8 19. 23 4 − 21. 79 16 − 23. 2 3 8 25. 10 2 3 − 27. 58 8 15 − 29. 3 2 , 1 1 2 31. 15 8 , 1 7 8 33. 0.6 35. 0.3 37. 0.375 39. 2.16 41. 6 10 3 5 = 43. 175 1000 7 40 = 45. 295 1000 59 200 = 47. 131 10,000 49. 1 9 51. 1 1 1 = 53. 15 11 55. 37 18 57. 4 19 59. 2 5 61. 49 64 63. 36 35 65. 20 21 67. 3 5 69. 13 15 71. 1 9 22 73. 17 144 75. 109 600 − 77. 11 14 79. 1 24 − 81. 13 30 83. 1 40 − 85. 7 32 87. 53 77 89. 11 10 91. a) 10 1 5 7 3 5 − b) 2 3 5 93. a) 14 8 5 8 × b) 120 3 4 in. 95. a) 71 5 8 69 7 8 − b) 1 3 4 in. 97. a) 1 1 2 2 5 − ⎛ + ⎝⎜ ⎞ ⎠⎟ b) 1 10 99. a) 4 1 2 30 1 4 24 1 8 + + b) 58 7 8 in. 101. a) 1 49 60 , 2 48 60 , 9 6 60 , 6 3 60 , 2 9 60 , 22 60 b) 22 17 60 hours; 22 hours 17 minutes 103. 26 5 32 in. 105. a) 29 3 16 in. b) 33 in. c) 32 3 4 in. 107. 0.215 109. 2.1755 − 111. 1 2 113. 11 200
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