The 9s

T'senre

New member
Joined
Apr 10, 2021
Messages
1
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

Elite Member
Joined
Nov 12, 2017
Messages
11,514
Search for "casting out nines".

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

Jomo

Elite Member
Joined
Dec 30, 2014
Messages
10,556
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

Full Member
Joined
Mar 3, 2021
Messages
661
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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