Casting out nines

Summary

Casting out nines is a method to check a computation with integers by the remainders modulo $9$. It uses the fact that a natural number is congruent modulo $9$ to the sum of its decimal digits. To check $a \cdot b = c$, one compares the digit sum of $c$ with the product of the digit sums of $a$ and $b$, all modulo $9$. The same works for sums and differences.