Multiplying Fractions

In a Nutshell

Multiply the tops, multiply the bottoms, then simplify. No common denominator needed.

When you multiply two fractions, you are finding a fraction of another fraction. Think of it as shading part of a part.

The rule is beautifully simple. For any two fractions:

ab×cd=a×cb×d\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}

The area model below makes this visible. Rows represent the first fraction and columns represent the second. The dark overlap is the answer.

Fraction area model for multiplication A rectangle divided into rows and columns. Shaded rows represent the first fraction and shaded columns represent the second. The overlapping cells show the product of the two fractions.

Change the fractions using the drop-downs. The dark cells show the product. Count them against the total to check the answer.

Watch it work

Question: Work out 23×35\frac{2}{3} \times \frac{3}{5}. Give your answer in its simplest form.

Have a go

Q1. Work out 12×34\frac{1}{2} \times \frac{3}{4}.

Q2. Work out 25×56\frac{2}{5} \times \frac{5}{6}. Simplify your answer.

Q3. Work out 34×23\frac{3}{4} \times \frac{2}{3}.

Q4. Work out 112×231\frac{1}{2} \times \frac{2}{3}. Give your answer as a mixed number.