By Michael Hartley
Elsewhere on this site, I gave some general times tables tips. On this page, let's have a closer look at the eleven times table. You can use this page to show your kids the hidden patterns in the eleven times table, and make it easier for them to learn. If you can somehow get you kids to find these patterns for themselves, they'll remember them much longer than if you simply point the patterns out to them. For the eleven times table, the most obvious patterns are hard not to spot, in fact!
I've put the eleven times table below. By the way, this site also has some free printable times table charts for you to download, including the 11 times table.
The first pattern, from 11x1 to 11x9, is very clear. The ones and tens digits are the same. 11 times 4 is forty-four, 11 times 8 is eighty-eight, 11 times 6 is sixty-six... 11 times blung is blungty-blung..., whatevr number 'blung' might be. The reason is very simple. 11 is 10+1, so 11 times (say) 7 is 10x7 plus 1x7, or 70+7.
For the next few rows in the table, the pattern is almost as simple.
There are similar patterns for numbers from 20 to 29, or 30 to 39, and so on. But this is enough for the 11 times table.
There's an interesting way to check if a number is divisible by 11. Let's try it on 11 times 35691, that is, 392601. The trick is to add together alternate digits. For example, for 392601, if we add 3+2+0, you get 5. On the other hand, if you add 9+6+1, you get 16. If the original number is a multiple of 11, the difference between these two sums will also be a multiple of 11. Try it! Which of these are multiples of 11?
Another fascinating fact about multiples of 11 follows
- Take any number.
- Write it forwards, then backwards.
- The result is a multiple of 11!
- I'll Take 4321
- Writing it forward and backwards, I get 43211234
- This is a multiple of 11 - in fact, 43211234 = 11 x 3928294...
By the way, numbers like this, that look the same backwards and forwards, are called palindromes. There are also palindromes that are not multiples of 11. Why not challenge your kids to try to find some?
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