Why does adding numbers these 2 ways give the same answer

[catta]

Thinks this is the same for any number/size of integers.
Why is the answer the same?

1. Add the integers
8 + 24 = 32
Then add the digits in the answer until you are left with a single digit
8 + 24 = 32; 3 + 2 = 5

2. Add the individual digits and keep going till you only have a single digit
(8 + 24)
8 + 2 + 4 = 14; 1 + 4 = 5

13 + 45 + 92 + 1269 = 1419; 1 + 4 + 1 + 9 = 15; 1 + 5 = 6
1+3+4+5+9+2+1+2+6+9 = 42; 4 + 2 = 6

 

[Dr.Peterson]

Thinks this is the same for any number/size of integers.
Why is the answer the same?

1. Add the integers
8 + 24 = 32
Then add the digits in the answer until you are left with a single digit
8 + 24 = 32; 3 + 2 = 5

2. Add the individual digits and keep going till you only have a single digit
(8 + 24)
8 + 2 + 4 = 14; 1 + 4 = 5

13 + 45 + 92 + 1269 = 1419; 1 + 4 + 1 + 9 = 15; 1 + 5 = 6
1+3+4+5+9+2+1+2+6+9 = 42; 4 + 2 = 6

This is called "casting out nines" (because 9 anywhere in the work doesn't affect the answer, and can be replaced with zero). The single-digit numbers you get are called "digital roots".

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