A Math Trick for Multiplying by Eleven

(Last Updated On: June 1, 2018)

Multiplying by Eleven

Eleven is a Magic Number

Have you ever wanted to be able to perform basic arithmetic using only the raw power of your mind? Well, there are different tricks for different numbers, and one of the more basic calculations to get the hang of is the number eleven. Understanding this trick also makes it easier for you to perform other kinds of two-digit multiplication in your head. The premise behind the math is the same, but multiplying by eleven makes it very easy to see and understand the process.

To illustrate this math trick, let’s first take a look at the table below:

 27 x 11 = 297  43 x 11 = 473  63 x 11 = 693  32 x 11 = 352
x11 x11 x11 x11
 27 43 63 32
+270 +430 +630 +320
=297 =473 =693 =352

You’ve probably noticed by now that in each of these instance, the first and last digit of the result is identical to the number that is being multiplied by 11 (i.e. 27 x 11 = 297). That still leaves one question though – what about that middle number? It doesn’t come out of nowhere. The middle number is actually the sum of the first and second digit combined.

Let’s look again at the  27 x 11 = 297 example. Notice how 2 + 7 = 9? It’s that easy!

What to Do with Double-Digit Numbers?

“Ok, now wait a minute”, you say. “That’s all well and good when the two numbers don’t add up to a double-digit number, but what about the case of 67 x 11?”

You are very astute. 6 + 7 = 13, which throws a wrench into things, but the trick still works. Sort of. Here’s what happens.

Since the two digits (6+7) add up to 13, we obviously can’t stick the number 13 in the middle to get 6137. That would be very wrong, so we must do a little bit of fiddling.

In this instance, we’re going to keep the 3 and stick that in the middle again, so now we have 637 (which is also wrong). We’ve forgotten to carry the 1 over to the hundreds column. When we do that we get 737. Is that right? YES!

What About Three-Digit Numbers?

If you’re wondering about three-digit numbers, then you have a bright and curious mind. It’s a little trickier but the basic premise remains the same.

123 x 11 = 1353 or (1) 35 (3)

The first middle digit (in the hundreds place) is resolved by adding 1+2 to get 3, while the second middle digit is resolved by adding 2+3 or 5. So the first and last digits work exactly the way they did when resolving double digit numbers, but the middle numbers are resolved by adding the first two digits to get the first middle number in the sequence, and the last two numbers to get the second middle digit in the sequence. Got that?

Ok, what about 9-digit numbers…?

123456789 x 11 = 1358024679!

See, multiplying by eleven is easy, right? Now quiz yourself on multiplying by eleven and see what have you learned.

About the Author:

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Mark Heald is the Managing Editor of Sporcle.com. He enjoys spending time with his family, traveling, and bemoaning the fact the Sonics left Seattle.