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)

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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)

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Search for "casting out nines".

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

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

Need to allow for two other situations: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

e.g. 793 + 9 = 802 and

e.g. 760 + 9 = 769