sum of two equal digit numbers vs. sum of those digits

Question

if I take 5688+6984=12672 then sum the result 1+2+6+7+2=18 then sum that result 1+8=9. vs. this. same digits from above. 5+6+8+8+6+9+8+4=54 then sum that result 5+4=9. using this method where the original two are always the same length, four digits in this example, and always re-summing down to one digit, the result is always the same. Is this significant at all??? than you.

Answer 1

Hint : A number is divisible by $9$ if and only if the sum of its digits is divisible by $9$.