# Checking Multiplication via Digit Sums

Last week a friend who is a fourth grade teacher came to me with a math problem.  The father of one of his students had showed him a trick for checking the result of a three-digit multiplication problem.  The father had learned the trick as a student himself, but he didn’t know why it worked.  My friend showed me the trick and asked if I had seen it before.  This post describes this check and explains why it works.

Suppose you want to multiply 231 $latex \times$ 243.  Working it out by hand, you get 56133.  Add the digits in the answer (5+6+1+3+3) to get 18.  Add the digits again to get 9.  Stop now that you have a single digit.

Alternatively, do this digit adding beforehand.  Adding the digits of 231 together, we get 6.  Adding the digits of 243 together, we get 9.  Multiply 6 $latex \times$ 9…

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## Author: mathtuition88

http://mathtuition88.com

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