# Multiplying fractions

Home -> Tutorials -> Multiplying fractions

A fraction represents a part of a whole. It is made up of an integer numerator (the top number) and a non-zero integer denominator (the bottom number).

## To multiply two fractions:

1. Multiply the numerators.
2. Multiply the denominators.
3. Reduce the resultant fraction to its lowest terms.

For all real numbers a, b, c, d (b≠0,d≠0)

### Example1:

Find: $\frac{1}{2} \times \frac{2}{5}$

### Solution:

Step1:

Multiply the numerators and denominators

$\frac{1}{2} \times \frac{2}{5} = \frac{1 \times 2}{2 \times 5} = \frac{2}{10}$

Step2:

Simplify the fraction

$\frac{2}{10} = \frac{1}{5}$

Answer: $\frac{1}{5}$

### Example2:

Find: $\frac{8}{9} \times \frac{3}{4}$

### Solution:

Step1:

Multiply the numerators and denominators

$\frac{8}{9} \times \frac{3}{4} = \frac{8 \times 3}{9 \times 4}$

Step2:

Divide out common factors

$\frac{8 \times 3}{9 \times 4} = \frac{ 2 \times 1}{3 \times 1}$

Step3:

Simplify the fraction

$\frac{ 2 \times 1}{3 \times 1} = \frac{2}{3}$

Answer: $\frac{2}{3}$