Why when multiplying any number by 9?

Question

Mathematics

The bottom line is this: when multiplying any number by 9, the sum of all subsequent digits adds up to 9. This is not the case with the rest of the numbers. Give the formula if you pray)

Answer 1

It seems that you are talking about checking for divisibility...
www.cleverstudents.ru/divisibility/divisibility_ru...

Answer 2

This is a sign that numbers are divisible by 9. If the sum of the digits in a number is divisible by 9, then the number is divisible by 9. The proof is simple.

a = an*10^n + ... + a1*10 + a0 (где аk - цифра числа а) = 
an*(9..n-1 раз..9 + 1) + ... + a1*(9 + 1) + a0 =
an*9..n-1 раз..9 + an + ... + a1*9 + a1 + a0 =
9*(an*1..n-1 раз..1 +...+a2*11 + a1*1) + (an + ... +a2 + a1 + a0)

Thus, the original number a was divided into two terms, one of which is divisible by 9, and the second is the sum of the digits of the number a. Therefore, a is divisible by 9 if and only if the sum of its digits is divisible by 9. QED
I seem to have answered a slightly more general question.