A fraction is what you get when you take a whole and split it into equal parts, then keep some of them. The word "equal" is the heart of it: the pieces must all be the same size, or it isn't a fair fraction.

We write a fraction as one number stacked over another:

The bottom number, n, is the denominator — it says how many equal parts the whole was split into. The top number, m, is the numerator — it says how many of those parts we take. So \frac{3}{4} means three of four equal parts.

Splitting a whole into equal parts is really just division — sharing the whole out fairly — so a fraction and a division are two views of the same idea.

See it built

Watch a whole bar get split into equal parts, then some of them shaded. The denominator counts the slices the bar is cut into; the numerator counts the shaded slices. Step through it.

See it explained

Sal Khan splits up wholes into equal pieces to build fractions from scratch.