While I fully agree, I'd like to point out that reducing specifically to 0/0 = 0 is more generally useful (ie. maintains intuition) than x/0 = 0, which breaks i

While I fully agree, I'd like to point out that reducing specifically to 0/0 = 0 is more generally useful (ie. maintains intuition) than x/0 = 0, which breaks intuition. Given a/b = c, your intuition of finding c is to get a number such that c×b = a. c×0 = 0 has an infinite number of solutions, 0 being a particularly practical one. c×0 = 1 (and more generally a≠0) has no solution, especially in the reduced explanation of multiplication as taking integer multiples of a value. (Also note that having 0/0 = 0 maintains symmetry and continuity of the function y = 0/x.)