Many languages have a “mod” or “%” operator that gives the remainder after division with truncation towards 0; for example C, C++, and Java, and probably C#, would say:
(-11)/5 = -2
(-11)%5 = -1
5*((-11)/5) + (-11)%5 = 5*(-2) + (-1) = -11.
Haskell’s quot and rem are intended to imitate this behaviour. I can imagine compatibility with the output of some C program might be desirable in some contrived situation.
Haskell’s div and mod, and subsequently Python’s / and %, follow the convention of mathematicians (at least number-theorists) in always truncating down division (not towards 0 — towards negative infinity) so that the remainder is always nonnegative. Thus in Python,
(-11)/5 = -3
(-11)%5 = 4
5*((-11)/5) + (-11)%5 = 5*(-3) + 4 = -11.
Haskell’s div and mod follow this behaviour.