The strange thing about one half is that it requires you to have had a whole first.
You can't have one half of nothing. Before there's a half, there has to be a thing — a cake, a day, an apple, a kingdom — and then the thing has to be divided, and then the division has to be equal, and only then do you have a half. One half is what's left when you've taken something apart the right way.
This is different from one. You don't need to know anything before you can have one. You just need something. One stone. One cloud. One thought that won't stop repeating. One is the beginning of counting. You can count to one without knowing what comes next.
But to get to one half, you have to pass through one, then you have to understand that one can be opened up, like a house with rooms inside. Numbers have rooms.
The rooms can be very small. One tenth. One hundredth. One thousandth. The room gets smaller the bigger the bottom number gets. This feels wrong at first. Three should be bigger than two, so one third should be bigger than one half. But one third is smaller. The room gets smaller as the number below gets bigger because that number is counting the rooms, and the more rooms there are, the less space each one gets.
Mathematicians call the number on top the numerator — the namer. It names how many rooms you have. The number on the bottom is the denominator — the one who names the whole, the one who decides how small each room is.
The denominator is not trying to confuse you. It's just doing a different job than you thought.
A cake cut into eight pieces: the denominator decided the piece-size. If you have three pieces, the numerator names how many. Three eighths. The denominator made you a smaller world, and the numerator tells you where you stand in it.
The world can be made smaller. You can still know your place. That's fractions.