A Narrow Margin - Checking Multiplication via Digit Sums

[Xipe Totec]

Posted on December 27, 2011

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 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 7. Adding the digits of 243 together, we get 9. Multiply 7 times 9 to get 63, then add these digits to get 9. We got 9, just as we did before. And that’s the check: You have to get the same thing with either process.

This almost seems like magic, but there’s some interesting basic number theory going on here.

http://mikespivey.wordpress.com/2011/12/27/digit-sums/

[getting old in mke]

1. Made me smile

My grandmother taught me casting out nines, along with a grid method of multiplying back on a trip in 1964 or 1965. I had to prove it as an assignment during college. Hadn't thought of it in years. Thanks.

[Warpy]

2. Danger, Will Robinson! 2+3+1=6

However, the whole thing still works and I've been doing it for years.

[Xipe Totec]

3. The amazing thing, to me, is that my dad taught me this trick.

When I was in High School.

And he only had a 3rd grade formal education.

But he was Chief of the Watch on a gas drilling rig.

And supervisors, superintendents, and petroleum engineers looked to him and treated him with utmost respect.



That's him on the right, supervising the rig setup.

[Warpy]

4. That doesn't surprise me in the least

I remember a bank janitor with a less than grade school education who'd come to work early and read ten newspapers every day. He could converse intelligently on any subject.

I've also known people with post graduate degrees who never cracked a book once they'd left school who are among the most witless on the planet. My college professor grandpa once said most of his students graduated with the degree of A S S.