246 CHAPTER 5 Number Theory and the Real Number System 15. 95 125 19 25 16. 13 221 1 17 In Exercises 17–22, convert each mixed number to an improper fraction. 17. 3 5 8 29 8 18. 4 2 5 22 5 19. −5 3 4 − 23 4 20. −7 1 5 − 36 5 21. −4 15 16 − 79 16 22. 11 9 16 185 16 In Exercises 23–28, convert each improper fraction to a mixed number. 23. 19 8 2 3 8 24. 25 4 6 1 4 25. − 32 3 −10 2 3 26. − 157 12 −13 1 12 27. − 878 15 −58 8 15 28. 1028 21 48 20 21 In Exercises 29–32, write the number of inches indicated by the arrows as an improper fraction and as a mixed number. 29. 1 2 3 3 2 , 1 1 2 30. 1 2 3 9 8 , 1 1 8 31. 1 2 3 15 8 , 1 7 8 32. 1 2 3 9 4 , 2 1 4 In Exercises 33– 40, express each rational number as terminating or repeating decimal number. 33. 3 5 0.6 34. 5 8 0.625 35. 1 3 0.3 36. 1 6 0.16 37. 3 8 0.375 38. 23 7 3.285714 39. 13 6 2.16 40. 115 15 7.6 In Exercises 41–48, express each terminating decimal number as a quotient of two integers. Reduce the quotient to lowest terms. 41. 0.6 = 6 10 3 5 42. 0.13 13 100 43. 0.175 = 175 1000 7 40 44. 0.375 = 375 1000 3 8 45. 0.295 = 295 1000 59 200 46. 0.251 251 1000 47. 0.0131 131 10,000 48. 0.2345 = 2345 10,000 469 2000 In Exercises 49–56, express each repeating decimal number as a quotient of two integers. Reduce the quotient to lowest terms. 49. 0.1 1 9 50. 0.8 8 9 51. 0.9 = 1 1 1 52. 0.23 23 99 53. 1.36 15 11 54. 0.135 5 37 55. 2.05 37 18 56. 2.49 5 2 In Exercises 57– 66, perform the indicated operation and reduce your answer to lowest terms. 57. ⋅ 2 9 18 19 4 19 58. ⋅ 3 7 18 21 18 49 59. ⎛ − ⎝⎜ ⎞ ⎠⎟ ⎛ − ⎝⎜ ⎞ ⎠⎟ 3 8 16 15 2 5 60. ⎛ − ⎝⎜ ⎞ ⎠⎟ ÷ 3 5 10 21 − 63 50 61. ÷ 7 8 8 7 49 64 62. ÷ 3 7 3 7 1 63. ⋅ ÷ 3 5 4 7 1 3 36 35 64. ÷ ⋅ 4 7 4 5 1 7 5 49 65. ⎛ − ⎝⎜ ⎞ ⎠⎟ ⎛ ⎝⎜ ⎞ ⎠⎟ ⎡ ⎣⎢ ⎤ ⎦⎥ ÷ ⎛ − ⎝⎜ ⎞ ⎠⎟ 2 3 5 8 7 16 20 21 66. ⋅ ⎛ ⎝⎜ ⎞ ⎠⎟ ÷ ⎛ ⋅ ⎝⎜ ⎞ ⎠⎟ 7 15 5 8 7 9 5 2 3 20 In Exercises 67–76, perform the indicated operation and reduce your answer to lowest terms. 67. + 1 5 2 5 3 5 68. − 9 13 5 13 4 13 69. + 1 5 2 3 13 15 70. − 7 8 1 6 17 24 71. + 1 2 11 5 22 1 9 22 72. + 2 3 14 8 21 2 25 42 73. + + 1 12 1 48 1 72 17 144 74. + + 3 5 7 15 9 75 89 75 75. − − 1 30 3 40 7 50 − 109 600 76. − − 4 25 9 100 7 40 − 21 200
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