Dividing by Zero

Don't divide by zero or this could happen! Just kidding.

In truth:

Dividing by Zero is undefined.

Dividing

To see why, let us look at what is meant by "division":

12 Chocolates		12 Chocolates Divided by 3

So they get 4 each: 12/3 = 4

Dividing by Zero

Now, let us try dividing the 12 chocolates among zero people, how much does each person get?

Does that question even make sense? No, of course it doesn't.

You can't share among zero people, and you can't divide by 0.

Another Good Reason

After dividing, can you multiply to get back again?

But multiplying by 0 gives 0, so that won't work.

Once again, dividing by zero gives us difficulties!

Imagine You Could Divide by Zero

Okay, let us imagine you can divide by zero, and see what happens.

That means that things like ¹/₀ and ⁰/₀ should behave like normal numbers.

Try Multiplying By Zero

So let us try using our new "numbers".

For example, we know that zero times any number is zero:

So that should also be true for ¹/₀:

0 × (¹/₀) = 0

But we could also rearrange it a little like this:

0 × (¹/₀) = (⁰/₀) × 1 = 1

(Remember, we are assuming that you can divide by zero, so 0/0 should work the same as 5/5, which equals 1).

Arrggh! If you multiply ¹/₀ by zero you could get 0 or 1.

In fact you can't have both possibilites, so we cannot define ¹/₀ to be a number.

So it is undefined.

In conclusion:

When you try to divide by zero, things stop making sense

That is all.

But Wait ...

There is a special method where you get closer and closer to zero ... just read Limits (An Introduction) to find out more.