multiply by 11 you can carry any number up to 9. This method is easy and fun.
A simple check
Here is a simple check for multiplication by 11 problems. The problem isn’t completed until we have
checked it.
Let’s check our first problem:
Write an X under every second digit of the answer, beginning from the right-hand end of the number.
The calculation will now look like this:
Add the digits with the X under them:
1 + 5 = 6
Add the digits without the X:
3 + 3 = 6
If the answer is correct, the answers will be the same, have a difference of 11, or a difference of a
multiple of 11, such as 22, 33, 44 or 55. Both added to 6, so our answer is correct. This is also a test to
see if a number can be evenly divided by 11.
Let’s check the second problem:
Add the digits with the X under them:
5 + 8 = 13
Add the digits without the X:
1 + 1 = 2
To find the difference between 13 and 2, we take the smaller number from the larger number:
13 − 2 = 11
If the difference is 0, 11, 22, 33, 44, 55, 66, etc., then the answer is correct. We have a difference of
11, so our answer is correct.
Note to parents and teachers
I often ask students in my classes to make up their own numbers to multiply by 11 and see how big a difference they can get. The
larger the number they are multiplying, the greater the difference is likely to be. Let your students try for a new record.
Children will multiply a 700-digit number by 11 in their attempt to set a new record. While they are trying for a new world record,
they are improving their basic addition skills and checking their work as they go.Multiplying by multiples of 11
What are factors? We read about factors in Chapter 6. We found that it is easy to multiply by 20 because
2 and 10 are factors of 20, and it is easy to multiply by both 2 and 10.
It is easy to multiply by 22 because 22 is 2 times 11, and it is easy to multiply by both 2 and 11.
It is easy to multiply by 33 because 33 is 3 times 11, and it is easy to multiply by both 3 and 11.
Whenever you have to multiply any number by a multiple of 11 — such as 22 (2 × 11), 33 (3 × 11) or
44 (4 × 11) — you can combine the use of factors and the shortcut for multiplication by 11. For