Why is any number over itself equal to one?

Answer 1

In mathematics, when you place one number over another, with a small horizontal line between them, it means that you are to divide the one number by the other - the same as if you place the two numbers one after the other with a dividing sign between them. It is simply another way of expressing the same thing.

So if you have 5 things and you want to divide them equally among 5 people, you can only do this once. Each person gets one thing and then you have none left to divide. So 5 divided into 5 can only be done once.

Also, if you have 10 things to divide among 10 people, again you can only do this once before you run out. This, of course holds true for 12 and 12, or 125 and 125, or any number you choose, so long as the two numbers are the same.

So any quantity divided by the same number equals one.

However, if you have 10 things to divide among 5 people, now you can do this twice, since you can first give each person one thing, and then you can go around and give each person a second thing before you run out.

Vice-versa, if you have only 1 thing for 2 people, now each person gets only a half thing because you don't have enough to go around, and this is why 1 divided by 2 is the same as 1 over 2 or 1/2, which is referred to as a fraction.

It gets worse, but this will do for basic division and proper fractions.