The Secret of Multiplying by 11

The Math Trick: For Kids

Multiplying by 11 is probably one of the most famous mental math shortcuts.  If you have not heard of it, this math trick requires you to memorize three simple steps. To get the product of any 2-digit number multiplied by 11, for example 25 × 11, here are the steps.

Step 1: Copy the ones digit of the multiplier and make it the ones digit of the product.

In the example below, we copy 5 from 25 which is the multiplier and make it the ones digit of the product (see first figure). 

Step 2: Add the ones and tens digit of the multiplier and make it the tens digit of the product.

We add 2 and 5 and make 7 the tens digit of the product.

 

multiplying by 11

 

Step 3: Copy the tens digit and make it hundreds digit of the product.

In the example, we copy 2 from 25 and make it the hundreds digit of the product. 

So, the final answer is 275. I call this rule copy-add-copy. 

It is possible that in step 2, the sum of the ones and tens digit of the multiplier is more than 10, so we have to carry over. For example, if we want to multiply 87 by 11, first, we copy 7, which is the ones digit of the product.

multiplying by 11 a

 

In step 2, we add 8 and 7, and the sum is 15. Since its more than 10, we make 5 the tens digit of the product (see figure above), and carry over 1 to the hundreds digit.

In step 3, before we copy the tens digit and make it the hundreds digit of the product, we have a carry over of 1, so we add it making the hundreds digit 9.

Therefore, in summary, we have the digits of the product.

ones digit: 7

tens digit: 5 (5 in 15 = 8 + 7)

hundreds digit: 9 = 8 + 1.

Therefore, the correct answer is 957.

This math trick seems complicated when you read it, but with short practice, you can perform it using mental calculations. Remember: Practice makes perfect.

The Secret: For Smart Kids

The secret behind the trick is the alignment when multiplying vertically.  Notice that when we multiply by 11, we are actually multiply by 1 and by 10 by distributive property. That is, 25(11) = 25(10 + 1). Observe how this works in the vertical multiplication below.

multiplying by 11 b

Click image to enlarge

 

Step 1 above comes from the fact that the ones digit of multiplier is always aligned with 0 (e.g. 5 and 0 in 25 and 250)..

Step 2 is the alignment of the ones digit of the multiplier and the tens digit of the product of the multiplier and 10 (e.g. 8 and 7 in 87 and 870 respectively).

Step 3 is the tens digit of the multiplier (added to 1 if the sum of step 2 is more than 10).

Now that you know the secrets of multiplying by 11, it’s time for you to share it to your friends.

3 thoughts on “The Secret of Multiplying by 11

  1. Pingback: Squaring Numbers Ending in 5

  2. Pingback: Mental Math Shortcut on Multiplying by 5 - Math Tricks for Kids

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