**Find a check digit for a number**

Any number—no matter how many digits long it is—can be turned into a single digit number by adding together all the digits of the number, and repeatedly doing this each time the resulting number has more than a single digit.

The number 233 ➔ 2 + 3 + 3 = 8

8 is the check digit for 233

7720 ➔ 7 + 7 + 2 + 0 = 16 ➔ 1 + 6 = 7

7 is the check digit for 7720

The number 233 ➔ 2 + 3 + 3 = 8

8 is the check digit for 233

7720 ➔ 7 + 7 + 2 + 0 = 16 ➔ 1 + 6 = 7

7 is the check digit for 7720

## Casting out 9's to check your calculations

**Multiplication - Casting out 9's to check our calculations**

45

__x12__

540

find the check digit for the two factors and the answer (cast out any 9's and change them to 0)

45 ➔ 4 + 5 = 9 (cast out the 9) = 0

12 ➔ 1 + 2 = 3

540 ➔ 5 + 4 + 0 = 9 (cast out the 9) = 0

Multiply the factors check digits 0 x 3 = 0

If the factors match the answers check digit then the answer is probably right,

If they don't match then the answer is definitely wrong!

32

__x14__

448

find the check digit for the two factors and the answer (cast out any 9's and change them to 0)

32 ➔ 3 + 2 = 5

14 ➔ 1 + 4 = 5

448 ➔ 4 + 4 + 8 = 16 (change into single digit) ➔ 1 + 6 =

**7**

Multiply the factors check digits 5 x 5 = 25 (change into single digit) ➔ 2 + 5 =

**7**

If the factors match the answers check digit then the answer is probably right,

If they don't match then the answer is definitely wrong!

**Subtraction - checking our calculations**

35

__-12__

23

find the check digit for the two factors

**and**the answer (cast out any 9's and change them to 0)

35 ➔ 3 + 5 = 8

__12 ➔ 1 + 2 = 3__

23 ➔ 2 + 3 = 5

Subtract the two check numbers from the problem 8 - 3 = 5 (if the number is negative add 9) ➔ -1 + 9 = 8

Do the two answers match? Do the two answers match? If yes then the answer is probably right,

If they don't match then the answer is definitely wrong!

23

__-15__

8

find the check digit for the two factors

**and**the answer (cast out any 9's and change them to 0)

22 ➔ 2 + 2 = 4

__14 ➔ 1 + 4 = 5__

8 = 8

subtract the top number from the bottom 4 - 5 = -1 (if the number is negative add 9) ➔ -1 + 9 = 8

Do the two answers match? If yes then the answer is probably right,

If they don't match then the answer is definitely wrong!