The 9s

T'senre

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Apr 10, 2021
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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)
 
Search for "casting out nines".

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