Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I recall reading a website quite some time ago about the rules and exceptions of multiplication with regards to teaching children. For instance: The result of multiplying any number times 9 will have a result where the digits add to 9 (1x9=9, 2x9=18 so on, but breaks at 13). It was something like that -- there was a grid and there were about 8 'rules' and 5 'exceptions' that would let you multiply any integer under 13 by any other integer under 13 -- I think.

What's this technique called? Is it a good idea to teach kids multiplication with this technique?

share|cite|improve this question

These could be "divisibility tests" or "sanity checks". The one for $9$ in particular is a special case of "casting out $9$s".

I don't see why you say that it "breaks at 13": $9\times 13 = 117$, and $1+1+7=9$. What is true is that eventually you get numbers that add up to more than $9$, but if you repeat the process you will eventually get to $9$. For instance, $11\times 9 = 99$, and $9+9=18$, not $9$; however, if you repeat the process you get $1+8 = 9$.

Note that these rules don't actually teach multiplication, they just provide methods to check multiplication; they are also not definite tests: casting out nines does not detect all errors. For example, if you make the mistake of thinking that $9\times 9 = 18$, adding the digits to get $9$ will not disclose the error.

share|cite|improve this answer
After 10 the digits add up to 18 if you look at them right; here's another for-instance: when multiplying by 8, the first digit always increases by 1 and the 2nd digit always decreases by 2 (8, 16, 24, 32, 40, 48, 56...) except at 7 and 11. So there's an exception and rule. – jcollum Nov 15 '11 at 17:35
I'm looking for a technique to teach my kid the patterns in numbers, hoping that it will get him thinking about math instead of just memorizing the numbers. – jcollum Nov 15 '11 at 17:39
@jcollum: In my experience, that sort of things is better discovered by one-self than taught; otherwise, you are teaching him to memorize the pattern instead of memorizing the number, and you aren't really encouraging much, in my humble opinion. – Arturo Magidin Nov 15 '11 at 17:48
you were right about the 9's tho: 9 x 235 = 2115 which becomes 2 + 1 + 1 + 5 = 9. Wow. – jcollum Nov 15 '11 at 17:54
"Note that these rules don't actually teach multiplication" I couldn't possibly agree more. When teaching elementary mathematics, one should be seeking unity as much as possible. Taking the single concept of multiplication and breaking it into a dozen rules intended for memorization is about the worst thing you can do for a child. – Austin Mohr Nov 15 '11 at 19:54

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.