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tomodan
Nov 3rd, 2006, 04:20 AM
Hi, new to the forums and I am trying to resolve a dispute that has arrisen at work. Can anyone point me to the mathmatical proof for the following:

If you:

Take any two digit number (eg 38)

sum the two digits from this number (3+8 = 11)

Subtract the result from the origional number (38-11 = 27)

The answer will always be a multiple of 9.

Can someone show me why this is always the case?

Much appreciated.

jeroen79
Nov 3rd, 2006, 04:37 AM
The multiple will always be the first digit.

(10a+b) - (a+b) = 9x
10a+b - a-b = 9x
10a - a = 9x
9a = 9x
a = x