Tips In Arithmetic - Multiples Of 9

For all numbers that are a multiple of 9, the digits will add up to 9. For example 5,892,183 (9 x 654,687). Add up all the digits (5 + 8 + 9 + 2 + 1 + 8 + 3) and keep on adding until there is only one digit, which is 9.

You can easily demonstrate this algebraically for numbers up to 81:

9 = 10 - 1 X * (10 - 1) = 10 X - X

Re-write by adding and subtracting 10:

10X - 10 + (10 - X) Or 10(X - 1) + (10 - X) So the 10s digit is (X - 1) and the units digit is (10 - X). Add the digits together to (X - 1) + (10 - X) = 10 - 1 = 9

Can you extend this to larger numbers?

What about numbers in a different base?

If you can't remember your 9 times table you could multiply by 10 and subtract 9! For example: 7 x 9 = 70 - 7 = 63