Ask HN: Mathematicians, Why 9 cancels out in an addition of digits?

1 pointrokhayakebe4 comments

I was playing with additions and it seems that 9 cancels itself out (Sorry, nobody thought me this in elementary algebra, or I forgot) when continuously adding all the digits in a number in order to reach one final one-digit number.

Example:

92. 9+2=11 -> 1+1=2. So just remove the 9 and you have 2

989. 17+9 -> 8 + 9 => 1 + 7 = 8. So just leave out the 9s.

94968594892 -> 9+4+9+6+8+5+9+4+8+9+2 = 73 -> 7+3 = 10 -> 1+0 =1

Remove the 9s

4+6+8+5+4+8+2 = 37 -> 3+7 = 1

So why do the smallest one digit number (0) and the largest one digit number (9) both cancel out in such additions?

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