Dividing Fractions

In a Nutshell

To divide by a fraction, flip it and multiply. Keep, change, flip.

Dividing by a fraction asks "how many of that fraction fit into this amount?" The trick is to turn the division into a multiplication by using the reciprocal.

The reciprocal of a fraction is that fraction flipped upside down. The reciprocal of 23\frac{2}{3} is 32\frac{3}{2}.

ab÷cd=ab×dc\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}

The fraction bar below can help you see how many smaller pieces fit inside the shaded region.

See it: how many fit inside?

Fraction division — how many fit inside? A shaded bar represents the dividend fraction. A smaller measuring piece slides along the bar, counting how many times it fits, demonstrating that dividing by a fraction gives the same answer as flipping and multiplying.
Try:

Press Measure to watch the smaller fraction piece slide along the shaded bar, counting how many times it fits. The count is the same answer you get from "flip and multiply" — try each example to see for yourself.

Watch it work

Question 1: Work out 34÷2\frac{3}{4} \div 2.

Question 2: Work out 23÷45\frac{2}{3} \div \frac{4}{5}.

Have a go

Q1. Work out 12÷3\frac{1}{2} \div 3.

Q2. Work out 35÷12\frac{3}{5} \div \frac{1}{2}.

Q3. Work out 56÷23\frac{5}{6} \div \frac{2}{3}.

Q4. A ribbon is 45\frac{4}{5} of a metre long. It is cut into pieces that are each 110\frac{1}{10} of a metre. How many pieces are there?