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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   Multiply the sum and difference of a 2-
                  and a 1-digit number

  1. Choose a two-digit multiple of 10 and a single-digit number (1-9).
  2. Add the two numbers
  3. Find their difference (subtract the smaller from the larger).
  4. Multiply the sum and the difference by squaring the two numbers and finding the difference.

   Example:

  1. If the numbers selected are 80 and 3:
  2. Add the numbers: 80 + 3 = 83.
  3. Subtract 3 from 80: 80 - 3 = 77.
  4. 80 x 80 - 3 x 3 = 6400 - 9 = 6391.
  5. So 83 x 77 = 6391.

   See the pattern?

  1. If the numbers selected are 60 and 8:
  2. Add the numbers: 60 + 8 = 68.
  3. Subtract 8 from 60: 60 - 8 = 52.
  4. 60 x 60 - 8 x 8 = 3600 - 64 = 3536.
  5. So 68 x 52 = 3536.

Practice and you will be able to multiply sums and differences quickly and accurately.


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9 September 1996
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