BEATCALC:  Beat the Calculator!

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Back to Calculation Tips & Tricks
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From the BEATCALC mailing list:
a weekly service from B. Lee Clay, archived here by the Math Forum.
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   Multiplying two 2-digit numbers
            (difference of 6)

  1. Choose a 2-digit number.
  2. Select a number either 6 smaller or 6 larger.
  3. Find the middle number of the two (the average).
  4. Square this middle number.
  5. Subtract 9 from this square.

   Example:

  1. If the first number is 78, choose 72 as the second number.
  2. The middle number (the average) is 75.
  3. Square this middle number: 75 x 75 = 5625. (Remember how to square a 2-digit number ending in 5?)
  4. Subtract 9 from this square: 5625 - 9 = 5616.
  5. So 78 x 72 = 5616.

   See the pattern?

  1. If the first number is 31, choose 37 as the second number.
  2. The middle number (the average) is 34.
  3. Square this middle number: 34 x 34 = 1156. (Remember how to square a 2-digit number ending in 4?)
  4. Subtract 9 from this square: 1156 - 9 = 1147.
  5. So 31 x 37 = 1147.

    Choose the second number that will give you the easier square, and use your square shortcuts. Practice!


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2 December 1996
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