The world of mathematics is a truly beautiful place. Everything is neat, everything is provable, everything is logical, everything makes perfect sense. It’s a self-contained universe where everything fits together perfectly: no wonder that, for many people, it holds such appeal.
One of the expressions of that beauty is the existence of strange and unexpected patterns that seem to emerge from the ether - and it turns out there’s one that you could have learned back in infant school, but almost certainly didn’t.
It concerns that bane of your school life: learning your multiplication tables. There was no way round it: you just had to boringly chant them over and over again until they stuck in your head.
But it turns out that for the eleven times table - a tricky one once you get beyond 9 x 11 - there is an extremely neat hack that enables you to look like a little bit of a genius.
It’s very, very simple: to multiply any 2 digit number by 11, simply add the two digits together and place it between those 2 digits. That’s it.
Here are some examples:
25 x 11 = 275 -> that is 2(2+5)5
36 x 11 = 396 -> 3(3+6)6
If the sum of the two digits is greater than 9, simply add 1 to the first digit. For example:
89 x 11 = 979
But what if you want to up the ante and multiply a 3-digit number by 11? Easy, for a genius like you.
You need to keep the outer 2 digits where they are, and then put 2 digits in between them, made up of the sum of digit 1 and 2, and the sum of digit 2 and 3. Sounds a little complicated perhaps, but take a look at the examples and you’ll see it’s very straightforward.
253 x 11 = 2783 -> 2(2+5)(5+3)3
118 x 11 = 1298 -> 1(1+1)(1+8)8
If the sum of digits 1 and 2 is greater than 9, you need to add a 1 to the front. For example,
754 x 11 = 8294
And if the sum of digits 2 and 3 is greater than 9, you need to add 1 to digit 2 of your new number. For example:
357 x 11 = 3927
And if the sum of digits 1 and 2, and 2 and 3 are greater than 9, you need to do both. For example:
789 x 11 = 8679
What about multiplying by 111?
62 x 111 = 6882
51 x 111 = 5661
It’s similar, but with the middle digit doubled - although it gets a little tricky when the sums start going over 9, involving some adding 1s to digits 1 and 2 of your new number, as this final example shows:
79 x 111 = 8769
See, who said Maths wasn’t fun?
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