Maths test

[little_monkey]

I will prove that for every multiple of 9, the sum of its digit is 9.

To prove that, I will assume that the sum of its digit is 9, and prove that number must be a multiple of 9.

I will demonstrate for a two digit number ( proof is the same for any number of digits, but longer)

Let T be the digit for the tens, U be the digit for the units.

Assumption:

(1) T + U = 9

or (2) U = 9 - T

(3) The number is N = 10 x T + U

Substitute (2) into (3)

(4) N = 10 x T + ( 9 - T) = 9 x (T +1) , which is always a multiple of 9

Therefore, the sum of the digit of a multiple of 9 is always 9.

QED