ANSWERS A-13 Chapter 5 SECTION 5.1, PAGE 220 1. Theory 3. Zero 5. Composite 7. Divisor 9. Conjecture 11. 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97. 13. True 15. False. 36 is a multiple of 6. 17. True 19. True 21. True 23. True 25. True 27. 3 and 5 29. 2, 3, 4, 6, 8, and 9. 31. 2, 3, 4, 5, 6, 8, and 10. 33. 2 5 2 ⋅ 35. 2 3 5 3 ⋅ ⋅ 37. 2 167 3 ⋅ 39. 2 83 2 ⋅ 41. 6 43. 32 45. 60 47. 508 49. a) 5 b) 50 51. a) 4 b) 96 53. a) 15 b) 600 55. 30 days 57. 2 60, 3 40, 4 30, 5 24, 6 20, 8 15, × × × × × × 10 12, 12 10, 15 8, 20 6, 24 5, 30 4, × × × × × × 40 3, 60 2 × × 59. 35 cars 61. 30 trees 63. 30 days 65. a) Yes b) No c) No d) Yes 67. 17, 19, and 29, 31 69. 5, 17, and 257 are all prime. 71. A number is divisible by 14 if both 2 and 7 divide the number. 73. 6 75. 35 77. 30 79. Yes 81. No 83. a) 8 b) 384 85. a) 12 b) 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 87. For any three consecutive natural numbers, one of the numbers is divisible by 2 and another number is divisible by 3. Therefore, the product of the three numbers would be divisible by 6. 89. Yes 91. 8 233,9 333,10 235, 11 227,12 255,13 337, 14 257,15 357,16 277, 17 5 5 7,18 2 5 11,19 3 5 11, 20 2 7 11 = + + = + + = + + = + + = + + = + + = + + = + + = + + = + + = + + = + + = + + 93. a) 5, 7, 11, 13, 17, 19, 23, and 29 b) Every prime number greater than 3 differs by 1 from a multiple of 6. c) This conjecture should appear to be correct. SECTION 5.2, PAGE 232 Answer to Recreational Math box on page 228 0 4 4 4 4 = + − − 1 4 4 4 4 = + + 2 4 4 4 4 = ⋅ + 3 4 4 4 4 = + + 4 4 4 4 4 = − + 5 4 4 4 4 = ⋅ + 6 4 4 4 4 = + + 7 4 4 4 4 = + − 8 4 4 4 4 = + + − 9 4 4 4 4 = + + Other answers are possible. 1. Whole 3. a) Positive b) Negative 5. 2,489,000 7. 4,090,000,000 9. a) < b) < c) < d) > 11. 5 13. 3− 15. 5− 17. 2 19. 2− 21. 7− 23. 2− 25. 6− 27. 28 − 29. 36 31. 96 33. 60 − 35. 4 37. 1− 39. 7− 41. 15 − 43. a) 9 b) 8 45. a) 25 b) 25 − 47. a) 16 − b) 16 REVIEW EXERCISES, PAGE 209 1. 232 2. 42,053 3. 200,421 4. 1,214,330 5. 6. 7. 8. 9. 14 10. 142 11. 2437 12. 5759 13. LXXXIV 14. DCXCIII 15. MCMLXIV 16. VICDXCI 17. 32 18. 45 19. 267 20. 3429 21. 22. 23. 24. 25. 81 26. 548 27. 605 28. 3334 29. κβ 30. oψ γ 31. ωξζ 32. δσιθ ι 33. 191 34. 189 35. 3673 36. 7388 37. 38. 39. 40. 41. 48 42. 1367 43. 2521 44. 15,923 45. 46. 47. 48. 49. 39 50. 7 51. 28 52. 1244 53. 1552 54. 186 55. 1110011112 56. 130334 57. 33235 58. 7178 59. 32712 60. 1CF16 61. 11034 62. 1011112 63. 16612 64. 70F16 65. 121025 66. 124238 67. 1224 68. 1002 69. 9A612 70. 33245 71. 4508 72. CC116 73. 21336 74. 202234 75. 13145 76. 136328 77. 565612 78. 1D7616 79. 21 R1 3 3 80. 1304 81. 23 R1 5 5 82. 4336 83. 411 R1 6 6 84. 664 R2 8 8 85. 2875 86. 2875 87. 2875 CHAPTER TEST, PAGE 211 1. 1489 2. 1873 3. 8090 4. 969 5. 122,142 6. 2745 7. 8. o βυ ι f 9. 10. 11. MMDCCXLIX 12. 11 13. 1694 14. 1001002 15. B7A16 16. 110002 17. 20036 18. 2205 19. 980 20. 8428
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