Ok this sounds pathetic, and is, but I'm too embarrassed to ask anyone and google was not fruitful.
Say I want 11/5 and need to do it in my head.
What formula can I follow?
the general idea is this:
say we want to know m/n.
we first write m = qn + r, where q is the largest integer that "goes into m", when multiplying by n.
then m/n = (qn + r)/n = (qn)/n + r/n = q + r/n.
for example, say we want to know 43/7.
7*6 = 42, and 7*7 is 49, so q = 6. the remainder, r, is 1, so 43/7 = 6 and 1/7.