Dividing fractions

Dividing fractions has a reputation for being hard. It isn't — there's one trick that turns every division into a multiplication you already know how to do.

Flip and multiply

To divide by a fraction, flip the second one (swap its top and bottom) and multiply:

1/2 ÷ 1/4 → 1/2 × 4/1 = 4/2 = 2

The flipped fraction (4/1) is called the reciprocal. Divide becomes multiply, and the rest is the multiplying you just learned.

Why flipping works

"1/2 ÷ 1/4" is really asking: how many quarters fit in a half? A half is two quarters, so the answer is 2 — exactly what flip-and-multiply gave us.

Dividing by a small fraction gives a big answer, because lots of little pieces fit inside. That's why 1/2 ÷ 1/4 = 2, not 1/8.