It couldn’t be easier.
You may have heard of the simple trick for multiplying a two digit number before — add the two digits together and simply stick that new number between them — but you can use a modified version of this trick to multiply a number with as many digits as you like by 11.
Let’s take a look at a few examples using the simple, 2-digit, version of this trick:
21 x 11
2 + 1= 3, so 2 x 11 = 231
45 x 11
4 + 5 = 9, so 45 x 11 = 495
Why does that work? Well, it all comes down to long division:
| | 4 | 5 |
| x | 1 | 1 |
___________________________________________
| | 4 | 5 |
| 4 | 5 | - |
___________________________________________
| 4 | 9 | 5 |
As you can see, when 45 is multiplied by the “10” digit of 11, it is offset one place to the right, so the 4 and 5 get added together.
How might this work for a longer number? Let’s take 4235 as an example.
| | 4 | 2 | 3 | 5 |
| x | | | 1 | 1 |
___________________________________________
| | 4 | 2 | 3 | 5 |
| 4 | 2 | 3 | 5 | - |
___________________________________________
| 4 | 6 | 5 | 8 | 5 |
4…Take the first digit from the left of the number you are multiplying by 11 and write it down. In this case, that’s “4.”
Then, add the first and second digits together:
46…
Then add the second and third digits together:
465…
Continuing with the same method, we get:
46585
The final digit simply corresponds to the last digit in the original number.
This method gets a tiny bit more complicated if the digits add up to a number larger than 10, but you just have to remember to carry.
For example, for 392, you’d write 3 down:
3…
Then add 3 + 9 to get 12. So, you’d write down the “2” and carry the “1” to the “3” that you already have written down.
42…
Then, when you add 9 + 2 = 11 you have to carry again, so you get:
431…
When you write the last digit down, you end up with: 4312.
This might take a little bit of practice, but it could save you lots of time in the long run!
