Multiplying larger numbers by 11
There is a very simple way to multiply any number by 11. Let’s take the example of 123 × 11.
We would write the problem like this:
We write a zero in front of the number we are multiplying. You will see why in a moment. Beginning
with the units digit, add each digit to the digit on its right. In this case, add 3 to the digit on its right.
There is no digit on its right, so add nothing:
3 + 0 = 3
Write 3 as the last digit of your answer. Your calculation should look like this:Now go to the 2. Three is the digit on the right of the 2:
2 + 3 = 5
Write 5 as the next digit of your answer. Your calculation should now look like this:Continue the same way:
1 + 2 = 3
0 + 1 = 1
Here is the finished calculation:If we hadn’t written the 0 in front of the number to be multiplied, we might have forgotten the final
step.
This is an easy method for multiplying by 11. The strategy develops your addition skills while you
are using the method as a shortcut.
Let’s try another problem. This time we will have to carry digits. The only digit you can carry using
this method is 1.
Let’s try this example:
471 × 11
We write the problem like this:
We add the units digit to the digit on its right. There is no digit to the right, so 1 plus nothing is 1.
Write down 1 below the 1. Now add the 7 to the 1 on its right:
7 + 1 = 8
Write the 8 as the next digit of the answer. Your working so far should look like this:The next steps are:
4 + 7 = 11
Write 1 and carry 1. Add the next digits:
0 + 4 + 1 (carried) = 5
Write the 5, and the calculation is complete. Here is the finished calculation:That was easy. The highest digit we can carry using this method is 1. Using the standard method to