> It is also unclear why multiplication and division have different difficulties, when dividing by n is equal to multiplying by 1/n.

Well sure, but once you multiply by 1/n you leave N (or Z) and enter Q, and I suspect that's what makes it more difficult because Q is just a much more complex structure because it formally consists of equivalence relations. In fact it's easy to divide an integer x by an integer y, it's just x/y ... the problem is that we usually want the fraction in lowest terms, though.