Why dividing by zero is undefined?

Answer 1

Try this on your calculator
5/.01 = ..
5/.00001 =
5/.0000001 =

notice I am making my divisor smaller and smaller, almost zero and what is happening to your answer?

The closer my divisor gets to zero, the larger the answer.
So when I could actually divide by zero, then the answer should be infinitely large
which of course is not a number, thus we call it "undefined"

Answer 2

Or, consider this. Suppose 4/0 = x for some value of x.

To clear the fraction, we get 4 = 0*x

But 0 times any number is zero. So, there is no possible value of x for which 0*x = 4. (Or any other nonzero value)