If you've ever tried to divide a number by zero on a calculator, you know that the calculator will return an 'error'. Why does it do this? Why can't you divide by zero?

Here is a typical division question. Six divides by two exactly three times. Nothing mysterious about that! But have you thought about why this works?
The obvious reason is because two times three is six. Notice the pattern. What you were dividing by must multiply with your answer to give the original number.

Now let's try dividing by zero. Whatever the answer is, we'll call it X for now. If this question has an answer at all, then 0 times X must equal 6.

What could the value of X be? What number can you multiply by zero, and get an answer of six?

Of course, nothing will work. There is no number you can multiply by zero, and get six.
It's impossible!

This means that the question "six divided by zero" cannot possibly have an answer.

One way of stating this is to say that 'dividing by zero is impossible'. This means that the answer is 'no answer'. The answer can also be described as 'undefined', because no such answer exists.

The answer isn't zero. There isn't an answer.

There's another way of looking at division by zero, that also makes sense:

Let's try dividing six by various numbers that get smaller and smaller, and look at what happens as we get closer and closer to zero on the bottom.

As the number we're dividing by gets smaller and smaller, the answer gets bigger and bigger. That should seem reasonable.

When we divide six by a very tiny number, the answer is really big.

Can you see the pattern? The closer the bottom number gets to zero, the closer the answer gets to infinity.

In fact, it is quite correct to say that dividing by zero gives infinity. But 'infinity' is not a number!
So this is just another way of saying that division by zero does not have an answer we can write.

That's why your calculator says 'error' when you try to divide by zero!

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