When we multiply a number by zero the answer is always zero, but when we divide a number by zero the answer is infinity.

The limit of didvidng any number by a smaller and smaller number is infinity.

BTW infinite is not a number.
And there are "infinities" of different "size".

When you multiply N by zero, zero means zero times N, thus zero.

When you divide N by M other than zero, you obtain M times equal fragments of N.
Then, when M is one (1) results in the same and whole N.

Dividing by zero is NOT really "valid" math operation (you may get logical fallacies by doing this, like "proving" that 0 = 1.

When you see something divided by zero, zero meaning (in that specific case while not in others) should be "a non zero quantity as small as you can sucesively make it be.
Thus more and more (no limit) "replicas" of the "divided" number.

Just like infinity (each kind of infinity) means the opposite reciprocal, no limit to make it grow, once and again.

It would require a smarter man than I to answer this question.

I refuse to think about it.

Simple arithmetic