You already know that multiplication is a fast way to add the same amount many times. The same trick works on a fraction: multiplying a fraction by a whole number just means adding that fraction to itself, over and over.

So 3 \times \frac{2}{5} means three lots of two-fifths:

Each two-fifths adds two more shaded parts, and the parts are still fifths the whole time — the size of a part never changes, only how many you have.

The shortcut

Adding the same fraction k times just stacks up its top number k times, while the bottom number stays put. So you can skip the repeated addition: multiply the numerator by the whole number, and keep the denominator.

For our example, 3 \times \frac{2}{5} = \frac{3 \times 2}{5} = \frac{6}{5} — exactly what the repeated addition gave. The denominator 5 is untouched because the pieces are still fifths; only the count of pieces grows.

See it built

Each bar below is one whole, split into the same number of equal parts. Watch one lot of the fraction get shaded in every bar — then count up all the shaded parts to see the new numerator. The denominator never moves. Step through it.

See it explained

Sal Khan multiplies fractions by whole numbers two different ways and shows they agree.