Why is a Number divided by 0 undefined?

There are two answers that I am aware of to this question. (If anyone else knows any other answer to this question, please let me know by posting a comment).

The first is a pretty easy explanation. First of all we want to distinguish between indeterminate and the undefined. Indeterminate means that we cannot determine the answer because there are too many answers to the question. (an example would be 0/0.) Because we know that division is the opposite of multiplication, we can use multiplication to get our answer. 0/0 means:

___ x 0 = 0 The answer to this question is ANYTHING. Any number times 0 is 0. So that is why it is indeterminate.

On the other hand, there is also the undefined. We can apply the same rule-- multiplication being the inverse of division to find our answer. 0 x ____ = a

"a" stands for a constant-- any constant, may it be 6, or 7, or 1, or 2..... but not 0. You cannot times 0 by any number and get a constant a. This is the simple reason why we cannot divide by zero.

Now for the more complex reasoning..... 1/0 could be infinity or negative infinity. If we divide 1 by a tiny positive number, the answer will be a big positive number. If we divide 1 by a tiny negative number, the answer will be a big negative number. In other words, as our denominator gets closer to 0 from the right we're going to infinity, as it gets closer to 0 from the left, we're going to negative infinity. That's why we let 1/0 be undefined. This concept is explored in Algebra with asymptotes, and in Calculus with the idea of Limits in more detail.

Julie Code