Numerical digit
Casting out nines

Casting out nines is a procedure for checking arithmetic done by hand. To describe it, let f (x) {\displaystyle f(x)} represent the digital root of x {\displaystyle x}, as described above. Casting out nines makes use of the fact that if A + B = C {\displaystyle A+B=C}, then f (f (A) + f (B)) = f (C) {\displaystyle f(f(A)+f(B))=f(C)}. In the process of casting out nines, both sides of the latter equation are computed, and if they are not equal, the original addition must have been faulty.
punctuation:no_comma, combination:two_responses, startend:end_checker