Sometimes in math class, we were told rules, like “we cannot divide by 0”, but did not go through the understanding for why these rules are true. Usually these rules are not arbitrary – they are completely natural, just as natural as the law of gravitation, or the way light travels faster than sound.
Yet we are not always taught the reasoning behind these laws in math, so we forget them or think they are only true because the teacher said they were true.
So today, I am going to try to correct that, and explain why it does not make any sense to “divide by 0”.
Let’s take a pizza for a first example. We can divide it into 2: that would leave it in 2 pieces. We can divide it into 3 as well, leaving it in 3 pieces.
We could divide it into 10, or 100, or even – if our knife was sharp enough – into 1,000 pieces.
We can even divide it into 1: that would just leave the original piece.
But can we take the pizza, and divide it into 0 groups?
Another example: if we have a class of 24 students. We can take the original class and divide it into 2 groups (each with 12).
We could also divide it into 3 groups, or 4 groups. We can’t divide it evenly into 5 groups: one of the groups would be unbalanced.
We could in fact divide it into any number of groups, up to 24 – but since the students are whole, we can’t divide them into more than 24 groups.
But can we take the students, and divide them into 0 groups?
Here’s a third example. Suppose we have a large bucket full of water, and a collection of 10 smaller buckets. We can “divide” the water in the large bucket by 10, by pouring it evenly into the smaller buckets.
We can even find 100 smaller buckets, or 1,000, and divide the original bucket into 100, or 1,000. But is any way we can take 0 smaller buckets – ie: no smaller buckets – and divide the water in the original bucket?
In each case, it makes no sense to even talk about dividing a group of people, or a pizza, or a large bucket of water, into 0 pieces or groups or smaller buckets.
That’s the underlying reasoning behind why we say “dividing by 0” makes no sense, absolutely no sense.
Does that make sense?