Chapter 8
MULTIPLICATION BY 11
Everyone knows it is easy to multiply by 11. If you want to multiply 4 by 11, you simply repeat the digit
for the answer, 44. If you multiply 6 by 11 you get 66. What answer do you get if you multiply 9 by 11?
Easy, 99.
Did you know it is just as easy to multiply two-digit numbers by 11?
Multiplying a two-digit number by 11
To multiply 14 by 11 you simply add the digits of the number, 1 + 4 = 5, and place the answer in
between the digits for the answer, in this case giving you 154.
Let’s try another: 23 × 11.
2 + 3 = 5
Answer: 253
These calculations are easy to do in your head. If somebody asks you to multiply 72 by 11 you could
immediately say, ‘Seven hundred and ninety-two.’
Test yourself
Here are some to try for yourself. Multiply the following numbers by 11 in your head:
42, 53, 21, 25, 36, 62
The answers are: 462, 583, 231, 275, 396 and 682.
They were easy, weren’t they?
What happens if the digits add to 10 or more? It is not difficult — you simply carry the 1 (tens digit)
to the first digit. For example, if you were multiplying 84 by 11 you would add 8 + 4 = 12, put the 2
between the digits and add the 1 to the 8 to get 924.
If you were asked to multiply 84 by 11 in your head, you would see that 8 plus 4 is more than 10, so
you could add the 1 you are carrying first and say, ‘Nine hundred . . .’, before you even add 8 plus 4.
When you add 8 and 4 to get 12, you take the 2 for the middle digit, followed by the remaining 4, so
you would say ‘. . . and twenty- . . . four.’
Let’s try another. To multiply 28 by 11 you would add 2 and 8 to get 10. You add the carried 1 to the
2 and say, ‘Three hundred and . . .’. Two plus 8 is 10, so the middle digit is 0. The final digit remains 8,
so you say, ‘Three hundred and . . . eight.’
How would we multiply 95 by 11?
Nine plus 5 is 14. We add 1 to the 9 to get 10. We work with 10 the same as we would with a single-
digit number. Ten is the first part of our answer, 4 is the middle digit and 5 remains the final digit. We
say, ‘One thousand and . . . forty-five.’ We could also just say ‘Ten . . . forty-five.’
Practise some problems for yourself and see how quickly you can call out the answer. You will be
surprised how fast you can call them out.
This approach also applies to numbers such as 22 and 33. Twenty-two is 2 times 11. To multiply 17
by 22, you would multiply 17 by 2 to get 34, then by 11 using the shortcut, to get 374. Easy.