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 3)

  1. Choose a 2-digit number.
  2. Select a number either 3 smaller or 3 larger.
  3. Add 1 to the smaller number, then square.
  4. Subtract one from the smaller number.
  5. Add this to the square.

   Example:

  1. If the first number is 27, choose 24 as the second number.
  2. Add 1 to the smaller number: 24 + 1 = 25.
  3. Square this number: 25 x 25 = 625.
  4. Subtract one from the smaller number: 24 - 1 = 23.
  5. Add this to the square: 625 + 23 = 648.
  6. So 27 x 24 = 648.

   See the pattern?

  1. If the first number is 34, choose 31 as the second number.
  2. Add 1 to the smaller number: 31 + 1 = 32.
  3. Square this number: 32 x 32 = 1024.
  4. Subtract one from the smaller number: 31 - 1 = 30.
  5. Add this to the square: 1024 + 30 = 1054.
  6. So 34 x 31 = 1054.

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


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22 April 1996
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