The 9s

[T'senre]

I need to know what this is called and why it CONSTANTLY occurs in every equation. 9 added to any number. Add each number in original to itself. Them do the same to the result of the addition and they will ALWAYS match.

IE: 8,628,764+(9)=8,628,773
8+6+2+8+7+6+4=(17) and 8+6+2+8+7+7+3=(17)

 

[Dr.Peterson]

Search for "casting out nines".

The easiest explanation of why it works uses arithmetic modulo 9.

 

[Steven G]

Adding 9 is the same as adding 10 and subtracting 1. That is, the tens position goes up 1 and the units digit does down by 1 and the net result is 0

 

[lex]

Adding 9 is the same as adding 10 and subtracting 1. That is, the tens position goes up 1 and the units digit does down by 1 and the net result is 0

Need to allow for two other situations:
e.g. 793 + 9 = 802 and
e.g. 760 + 9 = 769