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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