Here is an even simpler way to see that you can't divide by zero.
Let x be a real number. and define y=x/0. By definition of division, we get 0y = x. The left hand side of this last equation equals 0 because of multiplication by zero. Thus this equation will be only true if x = 0. This means that for x ≠ 0, the expresson x/0 is automatically undefined.
In the special case of x = 0, the last equation, 0y = x holds true, for all real y. Therefore if we consider defining 0/0, we find that all real numbers work equally well. As a result, the expression 0/0 is called indeterminate. By themselves with no context, indeterminate numbers are undefined.
There are seven expressions total that are recognized as indeterminate:
0 / 0 ∞ / ∞ 0 · ∞ ∞ - ∞ ∞0 1∞ 00
You will learn them when you take calculus, as they arrise when taking limits.