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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   Dividing a repeating 6-digit number by 13,
                then by 11

  1. Select a 3-digit number.
  2. Repeat these digits to make a 6-digit number.
  3. Divide these 6 digits by 13, then by 11.
  4. The answer is 7 times the first three digits!

   Example:

  1. If the 3-digit number selected is 231:
  2. The 6-digit number is 231231.
  3. Divide by 13, then by 11:
    7 x 231 = 1400 + 210 + 7 = 1617.
  4. So 231231 divided by 13, then 11 is 1617.

   See the pattern?

  1. If the 3-digit number selected is 412:
  2. The 6-digit number is 412412.
  3. Divide by 13, then by 11:
    7 x 412 = 2800 + 70 + 14 = 2884.
  4. So 412412 divided by 13, then 11 is 2884.

Remember to multiply left to right and add in increments. Then you will be able to give these answers quickly and accurately.


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17 June 1996
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