Why can you multiply by zero but not divide?

Question

Go easy on me.

In: Mathematics

Answer 1

Somebody already gave this answer, but I’ll give it a go:

x/0 is defined as the number y such that y*0 = x.

But y*0 is always zero. Thus if x is not 0, then x/0 is “undefined.” It’s not a number.

Now what about when x is 0?

0/0 is defined as the number z such that z*0 = 0.

But this is true for *any* number z. Thus 0/0 is “indeterminate.” It’s not a number.