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 4)

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

   Example:

  1. If the first number is 63, choose 67 as the second number.
  2. The middle number (the average) is 65.
  3. Square this middle number: 65 x 65 = 4225. (Remember how to square a 2-digit number ending in 5?)
  4. Subtract 4 from this square: 4225 - 4 = 4221.
  5. So 63 x 67 = 4221.

   See the pattern?

  1. If the first number is 38, choose 42 as the second number.
  2. The middle number (the average) is 40.
  3. Square this middle number: 40 x 40 = 1600.
  4. Subtract 4 from this square: 1600 - 4 = 1596.
  5. So 38 x 42 = 1596.

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


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29 July 1996
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