So, I was explaining the special trick that lets you multiply by 11 to a brilliant math tutor of ours who hadn’t happened to encounter it before. It only works for some numbers, I pointed out, but it’s very quick for those. And, I added, there was probably a trick to get it to work for any number but I’d never actually tried to figure that out.
Of course the math tutor wandered back an hour later and showed me the REAL trick to multiplying by 11. So for no reason at all I will share this with you all, even though I know the need to multiply big numbers by 11 seldom arises for most of us.
1. Multiplying two-digit numbers by 11.
This trick can be illustrated thus: 11 x 72. Take the 7 and the 2 and spread them apart so there is space between them: 7 …. 2. Now add them together and drop that number in the middle. Voila, the answer is 792. This makes it practically as easy to multiply by 11 as 10.
Of course this only works if the two numbers sum to a one-digit number, but, as I showed the tutor, if you overshoot, you can carry the digit from the tens place. This is easier to illustrate than to explain, so: 11 x 84. Start by spreading out the 84: 8 …. 4. Add them. You get 12. Put the 2 in the middle and carry the 1 by adding it to the 8. The answer is 924.
It turns out there is a fairly simple pattern that will let you expand this trick to much bigger numbers.
2. Multiplying big numbers by 11.
This is easy to demonstrate with a pencil and paper, but may be tricky to type. But I’ll try.
11 x 6789. Spread out all the digits: 6 …. 7 ….8 …. 9.
Add each pair of numbers: 6 ..(13).. 7 ..(15).. 8 ..(17).. 9
We will work from back to front. Bring down the 9 in the back. Bring down the 7 from the 17. Add the 1 from the 17 to the 15 to get 16. Bring down the 6 from the 16 and add the one to the 13 to get 14. Bring down the 4 and add the one to the 6 from the front of the original number to get 7. Bring the 7 down and put it in the front of your answer.
This is your answer 11 x 6789 = 74,679
I personally can’t visualize the numbers well enough to actually do the big ones in my head, at least not very fast. I need a bit of paper and a pencil to do this quickly and easily. But, even in these days when every phone is also a calculator, it is still cool. If you have math-geeky kids, maybe they’ll enjoy this. It’s certainly a far cry from showing them that 3 x 11 = 33.