How to Multiply and Divide Fractions

Multiplying by a fraction means taking part of something. Half of $\frac{3}{4}$ is smaller than $\frac{3}{4}$ , so don't be surprised when a product gets smaller.

The method

To multiply, multiply the tops, then multiply the bottoms.
To divide, keep the first fraction, flip the second, and multiply.
Simplify your answer.

Worked examples

Multiply: $\frac{2}{3} \times \frac{3}{4}$

$\frac{2 \times 3}{3 \times 4} = \frac{6}{12}$

Simplify: $\frac{6}{12} = \frac{1}{2}$

Divide: $\frac{3}{4} \div \frac{2}{5}$

Flip the second fraction: $\frac{3}{4} \times \frac{5}{2}$

$\frac{15}{8}$ , which is $1 \frac{7}{8}$

Why flipping works: $3 \div \frac{1}{2}$

This asks how many halves fit in 3.

Each whole holds 2 halves, so 3 wholes hold 6.

That matches $3 \times 2 = 6$ .

Common mistake

$\frac{3}{4} \div \frac{2}{5} = \frac{4}{3} \times \frac{2}{5}$

Only the second fraction gets flipped. Flipping the first one gives $\frac{8}{15}$ instead of the correct $\frac{15}{8}$ .

Try it yourself

$\frac{2}{5} \times \frac{3}{4}$
Show answer
$\frac{3}{10}$
$\frac{5}{6} \div \frac{1}{3}$
Show answer
$\frac{5}{2}$ , or $2 \frac{1}{2}$
$4 \times \frac{3}{8}$
Show answer
$\frac{3}{2}$ , or $1 \frac{1}{2}$

Want to check your work? Open the free calculator

PreviousComparing fractions NextLong division

Want help with this?

Book a free consultation, and we'll help you make a plan.

Book a free consultation