When two fractions have the same denominator, the pieces are all the same size. Adding them is then easy: you are just counting pieces. Keep the denominator the same and add the numerators together.

Three eighths plus two eighths is five eighths — three pieces and two more pieces make five pieces, and each piece is still an eighth. The bottom number tells you the size of the pieces, and that size never changes, so it stays put.

The rule

In general, for any two fractions sharing a denominator n:

Subtraction works exactly the same way — same-size pieces, so take the numerators apart and keep the denominator:

Only the top changes; the bottom is the size of the slice and rides along unchanged.

See it built

One bar cut into equal pieces. First we shade \frac{3}{8} in one colour, then \frac{2}{8} more in another. The shaded pieces simply add up — the bottom number never moves. Step through it.

See it explained

Sal Khan adds fractions that already share a denominator, just by adding the tops.

What if the bottoms are different?

This easy trick only works when the denominators match — the pieces have to be the same size before you can count them together. If the bottoms differ, first rewrite the fractions using equivalent fractions so they share a denominator, and then add as above. That is the next step.