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แผนการจัดการเรียนรู้ที่ 1 ตัวหารร่วมมากและตัวคุณร่วมน้อย

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แผนการจัดการเรียนรู้ที่ 1 ตัวหารร่วมมากและตัวคุณร่วมน้อย

  1. 1. 1 1 1 1 14 1 K-P-A : 1. 2. : 1. : 1 2. 3.
  2. 2. 4. 8 1 2 4 8 1. 20 1.1 , 1.2 1.3 20 1 2 4,5 10,20 3. 8 16 24 32 40
  3. 3. 4. “ ” 5. 6. 1.1 7. 8. 1.1 9. 18 39 10. – - 1. 1 2. 3. 1 1 4. 1.1 K-P-A
  4. 4. - K - - - 5 P - - - - - - 2 A 1 2. 3. 4. - 2
  5. 5. 5 1. 5 2. 3. 4. 26
  6. 6. 26 1.1 1 26 2 13
  7. 7. ………………………………………………………. 1 6 10 36 1 2 3 6 1 2 5 10 1 2 3 4 6 9 12 18 36 1 2 3 6 6 6 1 2 5 10 10 10 1 2 3 4 6 9 12 18 36 36 36 2 12 1 12 1 12 = 12 2 12 2 12 = 6 3 12 3 12 = 4 4 12 4 12 = 3 6 12 6 12 = 2 12 12 12 12 = 1 1 2 3 4 6 12 12
  8. 8. 1.1 1 1 1. 16 22 46 72 1 2 4 8 16 1 2 11 22 1 2 23 46 1 2 3 4 6 8 9 12 18 24 36 72 2. 87 = 1 3 29 87 (1) 7 = 1 7 (2) 9 = 1 3 9
  9. 9. (3) 24 = 1 2 3 4 6 8 12 24 (4) 35 = 1 5 7 35 (5) 100 = 1 2 4 10 25 50 100 1.1 1 1 1. 5 16 22 46 __________________________________________ __________________________________________ __________________________________________
  10. 10. 72 __________________________________________ 2. 5 87 = 1 3 29 87 1 7 = ______________________ 2 9 = ______________________ 3 24 = ______________________ 4 35 = ______________________ 5 100 = ______________________ ______________________________________________ ______ ___ ________
  11. 11. 2 1 1 1 14 1 2 “ ” “ ” 2 2 1 K-P-A : 1. 2. : 1 2 :
  12. 12. 2 “ ” “ ”  16  - 13 -  26  - 29 -  50  - 1. 1.1 2 2 1.2 1
  13. 13. 1.3 2 4 8 12 16 … 1.4 2 2. 10 19 23 36 404 523 724 396 1 001 1 236 3 993 3. 5. 2.1 6. 7. 8. " 5 64" 9. – 1. 1 2. 2.1
  14. 14. 3. 2.1 2.1 K-P-A - K - 2.1 - - 5 P - - - - 2.1 - 2 A - - - 2
  15. 15. - - 2.1
  16. 16. 2 1 2 “ ” “ ” 16 1 2 4 8 16 2 12 6 2 12 2 2  12  - 15 -  18  - 24  - 27 -  42  -
  17. 17. ______________________________________________ ______ ___ ________ 2.1 2 1 1.  “ ” “ ” 1  - 2 -  3 1 10 13 17 -  4 8 36 44  - 5 2 “ ”  2. 1
  18. 18. 2 3 3. 17 18 19 20 21 22 23 24 18 22,24 17 19 21 23 2.1 2 1 1.  “ ” “ ” 5
  19. 19. 1 2 3 1 10 13 17 4 8 36 44 5 2 “ ” 2. 3 1 ______________________ 2 ______________________ 3 ______________________ 3. 2 21 28 33 67 84 102 113 149 ______________________ ______________________
  20. 20. ______________________________________________ ______ ___ ______________ 3 1 1 1 14 1 1 1 K-P-A : 1. 2.
  21. 21. : 1. : 4. 1 1 2,3,4,5,6,7 2 1 3 1 4 1 2 5 1 6 1 2 3 7 1 2,3,5, 1
  22. 22. 1. 1.1 1.2 2 2 3 5 7 1.3 2 2. 2 3. “ ” 4. 3 – 4 2 5. 1 1 1 1 “ ”
  23. 23. “ ” 6. 7. 3.1 7. 3.1 8. 1 2 3 9. 10. – 1. 1 2. 3.1 3. 3.1 3.1 K-P-A - K - 3.1 - - 5
  24. 24. P - - - - - 3.1 - 2 A - - - - - 2
  25. 25. 3 1 1 1 6 11 27 41 67 91 103 6 1 2 3 11 1 27 1 3 9 41 1 3.1
  26. 26. 3.1 67 1 91 1 7 13 103 1 11 41 67 103 1 1
  27. 27. 3 1 1. 1 100 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100
  28. 28. 3.1 3 1 1. 1 100 10 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90
  29. 29. 91 92 93 94 95 96 97 98 99 100 ______________________________________________ ______ ___ ______________ 4 1 1 1 14 1 “ ”
  30. 30. K-P-A : 1. 2. : 1 2 : 4. “ ” 20 26 32 38 42 1 2 4 5 10 20 1 2 13 26 1 2 4 8 16 32 1 2 19 38 1 2 3 6 7 14 42 2 5 2 13 2 2 19 2 3 7
  31. 31. 1. 2. - - 3. 4.1 4. “ ” 5. 6. 4.1 7. 8. - “ ”
  32. 32. 1. 1 2. 4.1 3. 4.1 4.1 K-P-A K - 4.1 - - 5 P - - - - 4.1 - 2
  33. 33. A - - - - - 2
  34. 34. 4.1 4 1 “ ” 20 26 32 38 42 1 2 4 5 10 20 1 2 13 26 1 2 4 8 16 32 1 2 19 38 1 2 3 6 7 14 42 2 5 2 13 2 2 19 2 3 7
  35. 35. 4.1 4 1 1. 17 37 46 1 17 1 37 1 2 17 37 2 46
  36. 36. 51 67 23 46 1 3 17 51 1 67 3 17 67 2. 1 18 = 2 3 2 27 = 3 3 35 = 5 7 4 40 = 2 5 5 70 = 2 5 7
  37. 37. 4.1 4 1 1. 5 17 37 46 51 67 ___________________ _ ___________________ _ ___________________ _ ___________________ _ ___________________ _ ____________________ ____________________ ____________________ ____________________ ____________________ 2. 5 1 18 = ______________________
  38. 38. 2 27 = ______________________ 3 35 = ______________________ 4 40 = ______________________ 5 70 = ______________________ ______________________________________________ ______ ___ _____ 5 1 1 1 14 1
  39. 39. K-P-A : 1. 2. : 1. : 4. 12 = 2 2 3 18 = 2 3 3 1 1 120 120
  40. 40. 2 60 2 3 20 2 3 2 10 2 3 2 2 5 120 = 2 2 2 3 5 2 2 360 2 ) 240 2 ) 120 2 ) 60 3 ) 30 3 ) 15 5 360 = 2 2 2 2 3 5 1. - 2 - 1 120 120
  41. 41. 2 60 2 2 30 2 2 2 15 2 2 2 3 5 240 = 2 2 2 3 5 2 180 2 ) 180 2 ) 90 3 ) 45 3 ) 15 5 180 = 2 2 3 3 5 3. 4. 5.1 5. 6. 5.1 7. 8. -
  42. 42. 1. 1 2. 5.1 3. 5.1 5.1 K-P-A - K - 5.1 - - 5
  43. 43. P - - - - - 5.1 - 2 A - - - - - 2
  44. 44. 5 1 12 = 2 2 3 18 = 2 3 3 1 1 240 5.1
  45. 45. 240 2 120 2 2 60 2 2 2 30 2 2 2 2 15 2 2 2 2 3 5 240 = 2 2 2 2 3 5 2 2 360 2 ) 360 2 ) 180 2 ) 90 3 ) 45 3 ) 15 5 360 = 2 2 2 3 3 5 5.1 5 1 1. 1 175
  46. 46. 175 5 35 5 5 7 175 = 5 5 7 2 196 196 2 98 2 2 49 2 2 7 7 196 = 2 2 7 7 2. 1 180 2 ) 180 2 ) 90 3 ) 45 3 ) 15 5 180 = 2 2 3 3 5 2 425 5 ) 425 5 ) 85 17 425 = 5 5 7
  47. 47. 5.1 5 1 1. 5 1 175 …………………………………………………………………………… …………………………………………………………………………… …………………………………………………………………………… …………………………………………………………………………… …………………………………………………………………………… …………………………………………………………………………… …………………………………………………………………………… …………………………………………………………………………… …………………………………………………………………………… …………………………………………………………………………… ……………………………………… 2 196 …………………………………………………………………………… …………………………………………………………………………… …………………………………………………………………………… …………………………………………………………………………… …………………………………………………………………………… …………………………………………………………………………… …………………………………………………………………………… ……………………………………………………………………………
  48. 48. …………………………………………………………………………… …………………………………………………………………………… ……………………………………… 2. 5 1 180 …………………………………………………………………………… …………………………………………………………………………… …………………………………………………………………………… …………………………………………………………………………… …………………………………………………………………………… …………………………………………………………………………… …………………………………………………………………………… …………………………………………………………………………… …………………………………………………………………………… …………………………………………………………………………… …………………………………………………………………………… …………………………………………………………………………… ……………………………………………… 2 425 …………………………………………………………………………… …………………………………………………………………………… …………………………………………………………………………… …………………………………………………………………………… ……………………………………………………………………………
  49. 49. …………………………………………………………………………… …………………………………………………………………………… …………………………………………………………………………… …………………………………………………………………………… …………………………………………………………………………… …………………………………………………………………………… …………………………………………………………………………… ……………………………………………… ______________________________________________ ______ ___ ___________ 6 1 1 1 14 1 4
  50. 50. K-P-A : 1. . 2. 3. : 1. : 4.
  51. 51. 1. . . . 1 . . . 36 60 36 1,2, 3,4, 6,9,12,18 36 60 1, 2, 3,4, 5,6, 10,12,15,20,30 60 36 60 1,2,3,4,6,12 36 60 12 . . . 36 60 12 12 2. . . . 2 . . . 24 36 24 36 24= 2 2 2 3 36= 2 2 3 3 24 36 2 2 3 24 36 2 2 3 = 12 . . . 24 36 12
  52. 52. 12 1. 2. 2 18 1, 2, 3, 6, 9 18 24 1, 2, 3, 4, 6, 8, 12 24 3. 18 24 18 24 1, 2, 3, 6 6 6 ( . . .) 18 24 4. . . . 4.1 . . . 1 . . . 16 24 16 1, 2, 4, 8 16 24 1, 2, 3, 4, 6, 8, 12 24 16 24 1, 2, 4 8
  53. 53. 16 24 8 . . . 16 24 8 8 4.2 . . . 2 . . . 24 30 24 30 24 = 2 2 2 3 30 = 2 3 5 24 30 2, 3 2 3 24 30 2 3 = 6 . . . 24 30 6 6 5. 2 3 2-3 6. 6.1 7. . . 8. . . . . 2
  54. 54. 9. 6.1 10. 11. - 1. 1 2. 6.1 3. 6.1 4. . . 6.1 K-P-A - K - 6.1 - - 5
  55. 55. P - - - - - 6.1 - 2 A - - - - - 2 * *
  56. 56. 6 1 1. . . . 1 . . . 15 20 15 1, 3, 5, 15 20 1, 2, 4, 5, 10 20 15 20 1, 5 15 20 5 . . . 15 20 5 5 2. . . . 6.1
  57. 57. 2 . . . 16 24 16 24 16 = 2 2 2 2 24 = 2 2 2 3 16 24 2 2 2 16 24 2 2 2 = 8 . . . 16 24 8 8 6.1 6 1 1.
  58. 58. 20 45 20 1, 2, 4, 5, 10 20 45 1, 3, 5, 9, 15 45 20 45 1, 5 20 45 5 . . . 20 45 5 5 2 25 60 25 1, 5 25 60 1, 2, 3, 4, 5 6 10, 12, 15, 20 30 60 25 60 1, 5 25 60 5 . . . 25 60 5 5 2 = 3 7 105 = 3 5 7 = 21
  59. 59. = = = = 105 = = = 5 =
  60. 60. 6.1 6 1 1. 20 45 2 ……………………………………………………………………… ………………… ……………………………………………………………………… ………………… ……………………………………………………………………… …………………
  61. 61. ……………………………………………………………………… ………………… ……………………………………………………………………… ………………… 2 25 60 2 ……………………………………………………………………… ………………… ……………………………………………………………………… ………………… ……………………………………………………………………… ………………… ……………………………………………………………………… ………………… ……………………………………………………………………… ………………… ……………………………………………………………………… ………………… 2 2 ……………………………………………………………………… ………………… ……………………………………………………………………… …………………
  62. 62. ……………………………………………………………………… ………………… ……………………………………………………………………… ………………… ……………………………………………………………………… ………………… 2 ……………………………………………………………………… ………………… ……………………………………………………………………… ………………… ……………………………………………………………………… ………………… ……………………………………………………………………… ………………… ……………………………………………………………………… ………………… ……………………………………………………………………… ………………… 2 ……………………………………………………………………… ………………… ……………………………………………………………………… …………………
  63. 63. ……………………………………………………………………… ………………… ……………………………………………………………………… ………………… ……………………………………………………………………… ………………… ……………………………………………………………………… ………………… ______________________________________________ ______ ___ ___________
  64. 64. 7 1 1 1 14 1 4
  65. 65. K-P-A : : 1. : 4. . . . . . . 27, 36 45 3 ) 27 36 45 3 ) 9 12 15 3 4 5
  66. 66. . . . 27, 36 45 3 3 = 9 9 1. . . 2. 3-4 3. 1 . . . 12, 24 60 2 ) 12 24 60 2 ) 6 12 30 3 ) 3 6 15 1 3 5 . . . 12, 24 60 2 2 3 = 12 12 2 . . . 12, 18 24 2 ) 12 18 24 3 ) 6 9 12 2 3 4 . . . 12, 24 60 2 3 = 6 6
  67. 67. 4. 4.1 3 4.2 3 4.3 5. 2-3 6. . . 7. 5 7.1 . . . 7.1 . . . 8. . . 9. -
  68. 68. 1. 1 2. 7.1 . . . 3. 7.1 . . . 7.1 . . . K-P-A - K - 7.1 . . . - - 5
  69. 69. P - - - - - 7.1 . . . - 2 A - - - - - 2
  70. 70. 7 1 . . . 7.1 . . .
  71. 71. 1 . . . 27, 36 45 3 ) 27 36 45 3 ) 9 12 15 3 4 5 . . . 27, 36 45 3 3 = 9 9 2 . . . 12, 18 24 2 ) 12 18 24 3 ) 6 9 12 2 3 4 . . . 12, 24 60 2 3 = 6 6
  72. 72. 7.1 . . . 7 1 1 2 ) 28 80 2 ) 14 40 7 20 = 3 ) 36 54 63 3 ) 12 18 21 2 ) 4 6 7 2 3 7 = 3 18 78 18 78
  73. 73. 2) 18 54 78 3 ) 9 27 39 3 9 13 15 78 2 =6 6 7.1 . . . 7 1 1. 2 ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… ……………………………………………………………………… ……………………
  74. 74. ……………………………………………………………………… …………………… 4 ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… 3 15 78 4 ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… ……………………………………………………………………… …………………..
  75. 75. ……………………………………………………………………… ………………….. ……………………………………………………………………… …………………….. ______________________________________________ ______ ___ ___________ 8 1 1 1 14 1 4
  76. 76. K-P-A : : 1. : 4. 45 126 1 45 126 2 36 45 9 36 4 36 0 1 126 45 = 2 36 2 1 36 45 36 =1 9
  77. 77. 3 2 9 36 36 9 = 4 0 45 126 9 1. 1 3 - . . - - 2. . . 3. 2 1 210 385 1 210 385 1 175 210 35 175 5 175 0 1 385 210 = 1 175
  78. 78. 2 1 175 210 175 = 1 35 3 2 35 175 175 35 = 5 0 210 385 35 2 78 90 6 78 90 1 72 78 6 12 2 12 0 78 90 6 4. 3 - 5 5. . . 6. 8.1 8.1 7. 1 . .
  79. 79. 8. - 1. 1 2. 8.1 3. 8.1 8.1 K-P-A - K - 8.1 - P - - - - - 8.1 A -
  80. 80. - - -
  81. 81. 8 1 45 126 1 45 126 2 36 90 9 36 4 36 0 1 126 45 = 2 36 2 1 36 45 36 =1 9 3 2 9 36 36 9 = 4 0 45 126 9 8.1
  82. 82. 8.1 2 78 90 6 78 90 1 72 78 6 12 2 12 0 78 90 6 8 1 1 1 85 136 1 85 136 1 51 85 34 51 1
  83. 83. 34 34 17 85 136 17 2 105 195 1 105 195 1 90 85 15 90 6 90 0 105 195 15 3 255 795 8 255 795 3 240 765 15 30 2 30 0 255 795 15 8.1
  84. 84. 8 1 1 1 85 136 2 ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… 2 105 195 4 ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… ……………………………………………………………………… ……………………
  85. 85. ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… 3 255 795 4 ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… ……………………………………………………………………… ………………… ……………………………………………………………………… ………………… …………………………………………………………………………… ……………
  86. 86. ______________________________________________ ______ ___ ___________ 9 1 1 1 14 1 4 K-P-A :
  87. 87. . . . : 1. : 4. 1 15 23 31 1 2 3 15 1 15-1 14 23 2 23-2 21 31 3 31-3 28 14 21 28 14 21 28 . . . 14 21 28 7 ) 14 21 28 2 3 4 . . . 14 21 28 7
  88. 88. 15 23 31 1 2 3 7 7 2 108 84 . . . 84 108 . . . 84 108 3 ) 84 108 4 ) 28 96 7 24 . . . 84 108 3 4 = 12 108 84 12108 1284 = 9 7 9 7 1. . . . 2. . . .
  89. 89. 2 - 3 1 1,504 1,697 1 1,697 1 (1,697 - 1) 1,696 1,504 1,697 1 . . . 1,504 1,696 . . . 1,504 1,696 2 ) 1,504 1,696 2 ) 752 848 2 ) 376 424 2 ) 188 212 2 ) 94 106 47 53 . . . 1,504 1,696 2 2 2 2 2 = 32 1,504 1,697 1 32 32 2 875,1 315
  90. 90. . . . 315 1,875 . . . 315 1,875 3 ) 3151,875 5 ) 105 625 21 125 . . . 315 1,875 3 5 = 15 875,1 315 15875,1 15315 = 125 21 125 21 3. 9.1 4. 3 – 4 “ 63 90 ” . . . 63 90 63 = 3 3 7 90 = 3 3 2 5
  91. 91. . . . 63 90 3 3 = 9 9 63 9 = 7 90 9 = 10 9 9 7 10 = 70 9 70 5. . . 6. 9.1
  92. 92. 7. . . 8. - 1. 1 2. 9.1 3. 9.1 9.1 K-P-A - K - 9.1 - - 5 P - - - - 9.1 - 2
  93. 93. - A - - - - - 2
  94. 94. 9 1 1 15 23 31 1 2 3 15 1 15-1 14 23 2 23-2 21 31 3 31-3 28 14 21 28 14 21 28 . . . 14 21 28 9.1
  95. 95. 7 ) 14 21 28 2 3 4 . . . 14 21 28 7 15 23 31 1 2 3 7 7 2 108 84 . . . 84 108 . . . 84 108 3 ) 84 108 4 ) 28 96 7 24 . . . 84 108 3 4 = 12 108 84 12108 1284 = 9 7 9 7 9.1 9 1
  96. 96. 1. 252 108 . . . 108 252 3 ) 108 252 4) 36 84 3) 9 21 3 7 . . . 108 252 3 4 3 = 36 252 108 7 3 36252 36108 7 3 160 80 70 2 ) 160 80 70 5) 80 40 35 16 8 7 160 80 70 2 5 = 10 10 10 160 = 16 10 80 = 8 10 70 = 7
  97. 97. 16 + 8 + 7 = 31 31 9.1 9 1 1. 252 108 5 ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… ……………………………………………………………………… ……………………
  98. 98. ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… 160 80 70 5 ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… ……………………………………………………………………… ……………………
  99. 99. ……………………………………………………………………… …………………… ……………………………………………………………………… …………… ______________________________________________ ______ ___ __________ 10 1 1 1 14 1 3
  100. 100. K-P-A : 1. 2. 3. : 1. : 4. 2, 4, 6, 8, 10, 12, 14, 16, 18,… 2 3, 6, 9, 12, 15, 18,… 3 6, 12, 18,... 2 3 6,12,18,... 2 3 2 3
  101. 101. . . . 2 3 . . . 2 3 6 . . . . . . 1 . . . 8 12 8, 16, 24, 32, 40, 48,… 8 12, 24, 36, 48,… 12 24, 48, ... 8 12 24 8 12 . . . 8 12 24 24 2 . . . 6, 20 30 6, 20 30 6 = 2 3 20 = 2 2 5 30 = 2 3 5 6, 20 30 6, 20 30 2 2 3 5 = 60 . . . 6, 20 30 60
  102. 102. 60 1. . . . . 2. 2 2, 4, 6, 8, 10, ... 2, 4, 6, 8, 10, ... 2 3, 4, 5 2, 4, 6, 8, 10, 12, 14, 16, 18, ... 2 3, 6, 9, 12, 15, 18, 21, 24, 27 ... 3 4, 8, 12, 16, 20, 24, 28, 32, ... 4 3. 2 3 6, 12, 18, ... 2 3 6, 12, 18, ... 2 3 2 3 ( . . .) . . . 2 3 6 . . . 3 4 2 4 4. . . . 2 . . . 2 - 3
  103. 103. 1 . . . 6 15 6 15 6 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, ... 15 15, 30, 45, 60, ... 6 15 30, 60, ... 6 15 30 . . . 6 15 30 30 5. . . . 5.1 . . . 4.4 . . . . . . 6 15 6 = 2 3 15 = 3 5 . . . 6 15 6 15 6 15 . . . 6 15 3 2 5 = 30 5.2 2 3 . . . 2 - 3
  104. 104. 6. . . . 7. 10.1 . . . 10.1 . . . 8. . . 9. - 1. 1 2. 10.1 . . . 3. 10.1 . . . 4. . . 10.1 . . . K-P-A
  105. 105. - K - 10.1 . . . - - 5 P - - - - - 10.1 . . . - 2 A - - - - - 2
  106. 106. * 2 3 3 “ ” *
  107. 107. 10 1 2, 4, 6, 8, 10, 12, 14, 16, 18,… 2 3, 6, 9, 12, 15, 18,… 3 6, 12, 18,... 2 3 6,12,18,... 2 3 2 3 . . . 2 3 . . . 2 3 6 10.1 . . .
  108. 108. . . . . . . 1 . . . 8 12 8, 16, 24, 32, 40, 48,… 8 12, 24, 36, 48,… 12 24, 48, ... 8 12 24 8 12 . . . 8 12 24 24 2
  109. 109. . . . 6, 20 30 6, 20 30 6 = 2 3 20 = 2 2 5 30 = 2 3 5 6, 20 30 6, 20 30 2 2 3 5 = 60 . . . 6, 20 30 60 60
  110. 110. 10.1 . . . 10 1 1. 1 . . . 4 6 4, 8, 12, 16, 20, 24, 28 32 36 … 4 6, 12, 18, 24, 30 36 42 … 6 12, 24, 36 ... 4 6 12 4 6 . . . 4 6 12 12
  111. 111. 2 . . . 9 18 9, 18, 27, 36, 45 … 9 18, 36 54 … 18 18, 36 ... 9 18 18 9 18 . . . 9 18 18 18 2. = 2 3 7 105 = 3 5 7 = = = = =
  112. 112. = = = 350
  113. 113. 10.1 . . . 10 1 1. 1 . . . 4 6 2 ………………………………………………………………………… ………………… ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… ……………………………………………………………………… ……………………
  114. 114. 2 . . . 9 18 2 ………………………………………………………………………… ………………… ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… 2. 2 ………………………………………………………………………… ………………… ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… ……………………………………………………………………… ……………………
  115. 115. ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… 2 ………………………………………………………………………… ………………… ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… 2 ………………………………………………………………………… …………………
  116. 116. ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… ……………………………………………………………………… …………… ……………………………………………………………………… …………………… ______________________________________________ ______ ___ ___________
  117. 117. 11 1 1 1 14 1 3 K-P-A : : 1.
  118. 118. : 4. 1 15 21 42 75 3 ) 1521 42 75 5 ) 5 7 14 25 7 ) 1 7 14 5 1 1 2 5 . . . 15 21 42 75 3 5 7 2 5 = 1 050 1 050 2 9 12 16 3 ) 912 16 2 ) 3 4 16 2 ) 3 2 8 3 1 4 . . . 9 12 16 3 2 2 3 4 = 144 144
  119. 119. 1. . . . . . . 2. . . . 2.1 . . . 18, 30 36 2.2 . . . . . . 1 18 30 36 2 ) 183036 3 ) 915 18 3 ) 3 5 6 1 5 2 . . . 18, 30 36 2 3 3 1 5 2 =180 180 2.3 . . . 2 1 . . . 24 40 ( 120) 2 . . . 28, 35 42 ( 420)
  120. 120. 3. . . . . . . 4. 3-4 11.1 . . . 11.1 . . . 5. . . 6. - 1. 1 2. 11.1 . . . 3. 11.1 . . . 11.1 . . . K-P-A - K - - - 5
  121. 121. 11.1 . . . P - - - - - 11.1 . . . - 2 A - - - - - 2
  122. 122. 11 1 1 15 21 42 75 3 ) 1521 42 75 5 ) 5 7 14 25 7 ) 1 7 14 5 1 1 2 5 . . . 15 21 42 75 3 5 7 2 5 = 1 050 1 050 2 9 12 16 3 ) 912 16 2 ) 3 4 16 2 ) 3 2 8 3 1 4 . . . 9 12 16 3 2 2 3 4 = 144 144 11.1 . . .
  123. 123. 11.1 . . . 11 1 1. 1 12 18 20 24 2 ) 1218 20 24 2 ) 6 9 10 12 3 ) 3 9 5 6 1 3 5 2 12 18 20 24 2 2 3 3 5 2 = 360 360
  124. 124. 11.1 . . . 2 15 25 60 75 3 ) 15 25 60 75 5 ) 5 25 20 25 5) 1 5 4 5 1 1 4 1 15 25 60 75 3 5 5 = 600 600 3 24 36 48 60 84 2 ) 2436 48 60 84 2 ) 1218 24 30 42 2) 6 9 12 15 21 3) 3 9 6 15 21 1 3 2 5 7 24 36 48 60 84 2 2 2 3 3 2 5 7 = 5 040 5 040 11 1
  125. 125. 1. 1 12 18 20 24 2 ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… 2 15 25 60 75 4 ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… ……………………………………………………………………… ……………………
  126. 126. ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… 3 24 36 48 60 84 4 ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… ……………………………………………………………………… ………… ……………………………………………………………………… ………… ……………………………………………………………………… ………… ……………………………………………………………………… ………… ______________________________________________ ______ ___ _________
  127. 127. 12 1 1 1 14 1 3 K-P-A : . . . : 1. :
  128. 128. 4. 1 15 4 12 5 8 5 . . . 8, 12 15 120 120 15 4 12 5 8 5 = 815 84 1012 105 158 155 = 30 4 30 24 30 5 = 120 32 120 50 120 75 = 120 325075 = 120 3225 = 120 57 = 40 19 40 19 2 6 8 10
  129. 129. 6 8 10 6 8 10 120 120 120 1. . . . 2. . . . 2 - 3 1 15 2 5 4 - 6 1 . . . 5, 15 6 30 30 15 2 5 4 6 1 = 215 22 65 64 56 51 = 30 4 30 24 30 5 = 30 424 30 5
  130. 130. = 30 5 30 28 = 30 23 30 23 2 10, 20 30 . . . 10, 20 30 2 ) 10 2030 5 ) 5 1015 1 2 3 . . . 10, 20 30 2 5 2 3 = 60 60 1 1 3. 3-4 2 * 108, 54, 45 18 8 108, 54, 45 18 108, 54, 45 18 . . . . . . 108, 54, 45 18
  131. 131. 3 ) 108544518 3 ) 361815 6 3 ) 12 6 5 2 2 ) 4 2 5 2 2 1 5 1 . . . 108, 54, 45 18 3 3 3 2 2 5 = 540 108, 54, 45 18 540 108, 54, 45 18 8 540 + 8 = 548 548 4. . . 5. 12.1 12.1 6. 7. -
  132. 132. 1. 1 2. 12.1 3. 12.1 12.1 K-P-A - K - 12.1 - - 5 P - - - - - 12.1 - 2
  133. 133. A - - - - - 2
  134. 134. 12 1 1 15 4 12 5 8 5 . . . 8, 12 15 120 12.1
  135. 135. 120 15 4 12 5 8 5 = 815 84 1012 105 158 155 = 30 4 30 24 30 5 = 120 32 120 50 120 75 = 120 325075 = 120 3225 = 120 57 = 40 19 40 19 2 6 8 10 6 8 10 6 8 10 120 120 120 12.1
  136. 136. 12 1 1. . 1 30 7 5 2 3 4 . . . 3, 5 30 30 30 30 7 5 2 3 4 = 30 7 65 62 103 104 = 30 4 30 24 30 5 = 30 7 30 12 30 40 = 30 71240 = 30 35 = 6 7 6 7
  137. 137. 2 8 5 10 9 15 7 . . . 8, 10 15 120 120 8 5 10 9 15 7 = 158 155 1210 129 815 87 = 30 4 30 24 30 5 = 120 75 120 108 120 56 = 120 7510856 = 120 3356 = 120 89 120 89 3 9 12 20 9 12 20
  138. 138. 2 ) 9 1220 2) 9 610 3) 9 3 5 3 1 5 . . . 9, 12 20 2 2 3 3 5 = 180 180 180 12.1 12 1 1. . 1 30 7 5 2 3 4 3 ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… ……………………………………………………………………… ……………………
  139. 139. ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… 2 8 5 10 9 15 7 3 ……………………………………………………………………… …………………… ……………………………………………………………………… ……………………
  140. 140. ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… 3 9 12 20
  141. 141. 4 ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… ……………………………………………………………………… ……………………
  142. 142. ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… ……………………………………………………………………… …………………… ……………………………………………………………………… ……………………
  143. 143. ______________________________________________ _ ________ _________ 13 1 1 1 14 1 “ ”
  144. 144. K-P-A : 1. : 1. : 4. x y a x y b x y 1. “ ” a b = x y
  145. 145. 2. 2 1 30 42 2 30 42 3. 2 30 42 1 2 4. 1 12 40 12 = 2 2 3 40 = 2 2 2 5 12 40 2 2 =4 12 40 2 2 2 3 5 =120 4 120 = 480 12 40 = 480 2 . . . 24 36 2 ) 24 36 2 ) 12 18 3 ) 6 9 2 3 . . . 32 64 2 2 3 =12 32 64 2 2 2 3 3 = 72
  146. 146. 12 72 = 864 24 36 = 864 3 5 195 15 m 5 195 15 m = 5 195 m = 15 1955 m = 65 65 65 5. x y a x y b x y a b = x y
  147. 147. 6. 13.1 13.1 7. 8. - 1. 1 2. 13.1 3. 13.1 13.1 K-P-A - K - - -
  148. 148. 13.1 5 P - - - - - 13.1 - 2 A - - - - - 2
  149. 149. 13.1 13 1 1 18 48 18 = 2 3 3 48 = 2 2 2 2 3 18 48 2 3 =6 18 48 2 2 2 2 3 3 =144 6 144 = 864 18 48 = 864 2 . . . 27 45 3 ) 27 45 3 ) 9 15 3 5 . . . 27 45 3 3 = 9
  150. 150. 13.1 27 45 3 3 3 5 = 135 9 135 = 1 215 27 45 = 1 215 3 4 168 24 m 4 168 24 m = 4 168 m = 24 1684 m = 28 28 28 13 1 1. 1 25 105 5 525 2 625 2 625 2 36 18 108 1 944 1 944
  151. 151. 54 3 20 48 4 240 960 960 4 40 80 40 80 3 200 3 200 5 50 75 25 150 3 750 3 750 1.1 x y a x y b x y a b = x y 2. 12 72 24 a 12 72 24 a = 12 72 a = 24 7212 a = 36
  152. 152. 36 36 13.1 13 1 1. 5 1 25 105 2 36 54 3 20 48 4 40 80 5 50 75 1.1 ...................................... .......................................................................................................... .......................................................................................................... ..........................................................................................................
  153. 153. .......................................................................................................... .......................................................................................................... .......................................................................................................... .......................................................................................................... .......................................................................................................... .......................................................................................................... .................................................................................................... 2. 12 72 24 5 .......................................................................................................... .......................................................................................................... .......................................................................................................... .......................................................................................................... .......................................................................................................... .......................................................................................................... .......................................................................................................... .......................................................................................................... .......................................................................................................... .......................................................................................................... .......................................................................................................... .......................................................................................................... .......................................................................................................... ..........................................................................................................
  154. 154. .......................................................................................................... ................................................ ______________________________________________ ______ ___ _________ 14 1 1 1 14 1 K-P-A : 1. 50 2. : 1.
  155. 155. : 4. 1. 2. 30 3. 4. 1. 1 2. - K-P-A
  156. 156. K - - - 50 P - - - - - - 2 A - - - - - 2
  157. 157. 21101 1 14

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