need help explaining.....

x/0 is undefined, including 0/0.

you can derive those from these properties:

n + 0 = n
n * 1 = n
a * (b + c) = (a * b) + (a * c)

since a * b = c implies a = c / b for non-zero b,
n * 1 = n implies n = n / 1 and
1 * n = n implies 1 = n / n for non-zero n

to show 0 / n = 0, you first need to show that
0 * n = 0

n * 1 = n implies 0 * 1 = 0
also, for any whole number a,
0 * (a + 1) = (0 * a) + (0 * 1) = (0 * a) + 0 = 0 * a
so if 0 * a = 0 then 0 * (a + 1) = 0
therefore, by mathematical induction, for any whole number n,
0 * n = 0

therefore, 0 * n = 0 implies 0 = 0 / n for non-zero n