[HELP]Modulus Operator Workings

Question

How does the modulus operator work on a math perspective.
Also how is that math different on the computer

Answer 1

% (Modulo) means the remainder of the quotient, Math isn't different from computers to real life, maybe it wasn't teached

Answer 2

In mathematics you'd have a definition/proposition like this:

Given two integers a,d, where d is not zero, there are unique integers q,r, such that
a = qd + r and 0≤r<abs(d).
Then a%d is defined to be r.

Of course you'd have to proof existence and uniqueness of r and q, to be sure r is well defined this way. This result/idea generalises, but I'm not going to go into details there.

If you are only dealing with ints, the modulus is consistent with the mathematical version.