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From B. Lee Clay


 Squaring Numbers

 Multiplying Numbers

 Dividing Numbers

  1. any by 0.125
  2. 2 digits by 1 1/9
  3. 2 digits by 1 1/8
  4. 2 digits by 1 1/7
  5. 2 digits by 1 1/6
  6. 2 digits by 1 1/5
  7. 2 digits by 1 1/4
  8. 2 digits by 1 2/7
  9. 2 digits by 1 1/3
  10. 2 digits by 1 2/5
  11. 2 digits by 1 3/7
  12. 2 digits by 1 1/2
  13. 2 digits by 1 3/5
  14. 2 digits by 1 2/3
  15. 2 digits by 1 3/4
  16. 2 digits by 1 4/5
  17. 2 digits by 2 2/9
  18. 2 digits by 2 1/4
  19. 2 digits by 2 1/3
  20. 2,3 digits by 2 1/2
  21. 2 digits by 2 2/3
  22. 2 digits by 2 6/7
  23. 2 digits by 3 1/8
  24. 2,3 digits by 3 1/3
  25. 2 digits by 3 1/2
  26. 2 digits by 3 4/7
  27. 2 digits by 4 1/6
  28. 2 digits by 4 2/7
  29. 2 digits by 4 4/9
  30. 2 digits by 4 1/2
  31. 2 digits by 5
  32. 2 digits by 5 5/7
  33. 2 digits by 6 1/4
  34. 2 digits by 6 2/3
  35. 2 digits by 7 1/7
  36. 2 digits by 7 1/2
  37. 2 digits by 8 1/3
  38. 2 digits by 8 4/7
  39. 2 digits by 12 1/2
  40. 2 digits by 15
  41. 2,3 digits by 16 2/3
  42. 2,3 digits by 25
  43. 2,3 digits by 33 1/3
  44. 2,3 digits by 35
  45. 2 digits by 37 1/2
  46. 2 digits by 40
  47. 2 digits by 45
  48. 2 digits by 50
  49. 2 digits by 62 1/2
  50. 2 digits by 66 2/3
  51. 2,3 digits by 75
  52. 2 digits by 83 1/3
  53. 2 digits by 87 1/2
  54. 2 digits by 125
  55. 2 digits by 166 2/3
  56. 2 digits by 250
  57. 2,3 digits by 333 1/3
  58. 2 digits by 375
  59. 2 digits by 625
  60. 2 digits by 875
  61. 3 digits rep./37+41
  62. 6 digits rep. by 15873
  63. 6 digits rep. by 7, then 13
  64. 6 digits rep. by 13, then 11
  65. 6 digits rep. by 7,11,13, subtract 101
  66. 6 digits rep. by 37037 x 5
  67. mixed numbers by 2
  68. diff. of squares of 2 consec. 2-digit numbers
  69. diff. of squares of 2 different 2-digit numbers
  70. sqrt of squares of 2-digit numbers ending in 1
  71. sqrt of perfect squares ending in 5

 Adding Numbers

 Subtracting Numbers

 Finding Percents

Calculation
Practice Exercises

Full List



   Find the difference of the squares of two
               different 2-digit numbers

  1. Select two consecutive 2-digit numbers, one not more than 10 larger than the other (experts need not use this limitation).
  2. Subtract the smaller number from the larger.
  3. Add the two numbers.
  4. Multiply the first answer by the second.

   Examples:

  1. If 71 and 64 are selected:
  2. 71 - 64 = 7.
  3. 71 + 64 = 135
    (Add left to right: 71 + 64 = 71 + 60 + 4 = 131 + 4 = 135)
  4. Multiply these results: 7 × 135 = 945
    (Multiply left to right: 7 × 135 = 7 × (100+30+5) =
    700 + 210 + 35 = 910 + 35 = 945)
  5. So the difference of the squares of 71 and 64 is 945.

   See the pattern?

  1. If 27 and 36 are selected:
  2. 36 - 27 = 9.
  3. 36 + 27 = 63
    (Think: 27 + 30 + 6 = 57 + 6 = 63)
  4. Multiply these results: 9 × 63 = 567
    (Think: 9 × (60+3) = 540 + 27 = 567)
  5. So the difference of the squares of 27 and 36 is 567.

Practice multiplying and adding from left to right and this will become an easy but impressive mental math feat.


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20 January 1996
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