Division by Zero

What do you get when you divide a number by 0? Is the answer 0? Well, not really. The only thing you get when you try to divide a number by 0 is a headache. Let's find out why.

In order to understand what happens when you try to divide a number by 0, we must first recall the fact that division can be seen as reverse multiplication. For example:

  • 28 ÷ 7 = 4 can be rewritten as 7 x 4 = 28
  • 15 ÷ 3 = 5 can be rewritten as 3 x 5 = 15

However, what happens when you try to divide by zero? Let's see:

  • 36 ÷ 0 = ? can be rewritten as 0 x ? = 36.

Can you think of a number that can be substituted for the "?" above? There is no number that you can multiply by 0 to get 36, since any number multiplied by 0 would equal to 0. This is why you can't divide by zero. We say that the answer to our problem is “undefined”.

  • 36 ÷ 0 = undefined.
  • 13 ÷ 0 = undefined.
  • 4 ÷ 0 = undefined.

So far we have seen what happens when you try to divide by zero. What about dividing zero by any number? Well, this is much easier, since in this case the answer will always be zero. Let's look at some examples:

  • 0 ÷ 7 = 0 since the problem can be rewritten as 0 x 7 = 0
  • 0 ÷ 3 = 0 since the problem can be rewritten as 0 x 3 = 0
  • 0 ÷ 41 = 0 since the problem can be rewritten as 0 x 41 = 0

In other words, 0 divided by any number is 0, but any number divided by 0 is undefined.