o.O Confusion strikes the number theory layman

At first, I thought it might involve modulo 9 arithmetic, because it involves summing the digits of a number and the result being 9. But I'm not so sure now, since the process is different (involving subtracting a resulting value from the original), and that not all two digit numbers are multiples of 9.

This kind of math with summing the digits and finding patterns has always interested me. I've found many basic patterns, but as to this problem, I'm clueless :P Then again, I am not a number theorist, much less a mathematician.

Either I did it wrong, or I've found a counter example.

I chose the number 428, it has more than 1 digit (WOW! 3 digits to be exact!). I added its digits, 4+2+8 and I got 14. I have to add the digits again since it's not yet a single digit, 1+4 is 5. Now I subtract this 5 from my original number 428, until I get a single digit. This number, according to my calculations, is 8. Not 9. Did I do it wrong? (as a matter of fact, I think there are several more counter examples, but I'm probably doing it wrong)