Why can’t we divide a number by zero?

Let’s start with a very simple example. If we want to divide 8 oranges by zero people, how many oranges will they get? It is not possible to do this calculation since the question itself does not make any sense. There is no person to give oranges to.

According to the mathematical point of view, we can look at the division as a set of successive subtractions. For instance, if we have to divide 8 by 2, we can successively subtract 8 by 2. We can do that subtraction 4 times and there will be nothing left. So, 8 divided by 2 equals 4 and the remainder is 0. But, let’s talk about the case of the oranges again. If I have 8 and I successively subtract it by 0, I won’t reach anything, even if I do that operation again and again.

The division is the, mathematically speaking, inverse operation of multiplication ad so, when I do the operation 8 divided by 2, what I really want is to find out what is the number that multiplied by 2 equals 8. But if I try to divide number by zero, I won’t succeed since there is not any number that multiplied by zero equals 8.

But if we divide a number by zero, won’t it be infinite?

This question leads us to the theory of limits and we aren’t actually dividing by zero. What we are doing is dividing by a number which is really close to zero. Therefore, we are saying that in a division, the smaller the divisor is with regard to the dividend, the bigger the quotient will be. The closer we are to zero, the bigger the result of the division will be. We call infinite to that big result. However, I call your attention to the fact that: the infinite is not a number!

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