Have you ever seen someone multiply huge numbers by 11, in their head, in a matter of seconds?

Curious how they do it?

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Multiplication by 11 is easy! To multiply by a 2-digit number add the two digits and place the sum in between! 57 x 11 = 627 <-- you need to carry the 1!

This rule also works for 3 or 4 digit numbers as well as higher. The key to remember is to carry when needed.

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Some examples :

237 x 11 =

25(2+3)10(3+7)TEN CARRIES7

Here, 2 and 7 are placed as the far ends of the number which will be our answer.

Next, we add the adjascent digits one after another, carrying when necessary.

After, placing 2 at the first digit's place, we add the first two adjascent numbers, this time it's 2 + 3 which equals 5. 5 will be our second digit.

Next, we continue the process with the next two, 3 and 7. 3 + 7 equals 10. This is the case where we must carry the ten over to the next digit place by adding 1 ( Refresh yourself on carrying rules if necessary, it's all you need to know) The 5 in hundreds place becomes 6 because of the 3+7 carry over.

Now our answer sequence is almost done. So far we have 260_
The zero is present because of remainder zero from the carry.
For our last digit, we just bring down the 7 from the original number just like we did for the first digit, 2.

Giving us the answer 2607.

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Let's try something bigger, more impressive:

We will a 4 digit number.. let's say 7443

7(7+4=11(carry))(4+4=8 )(4+3=7)3

7 changes to 8 from carry

81873 is our answer after doing the basic arithmetic.

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One more, let do a BIG one! One in the millions!

4,072,231 x 11

Remember your rules and it's just the same, just longer. Don't let the numbers scare you!
And like a genius you know the answer is..

44,794,541

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Have fun with this and see how large you can go! It's a great way to work out your mind.

Thanks for listening~

You may appreciate the trick of easily rendering 27ths as decimals. 1/27 = 0.037, recurring. Very simple, and because 3 x 37 = 111, everything else is a breeze.

Not only that, we should also see that 1/37 = 0.027, recurring, as well, so we can make quite a few good approximations of what decimal fractions might turn out to be as rational fractions.

Also, if you haven't before, check out how this might apply to Life Sciences in Space Research, vol.3, p.10 (Oct. 2014)