# Multiplication of 3 Fractions

The product of three fractions is obtained by multiplying the numerators and then multiplying the denominators of the three fractions to get the product fraction. If any simplification or cross cancelling is required, it is done and fraction obtained is in lowest terms. The following three steps are followed in fraction multiplication.

• We multiply the top numbers or numerators
• We multiply the bottom numbers or denominators
• We simplify the fraction so obtained if required

Example

Multiply $\frac{2}{3}$ × $\frac{5}{7}$ × $\frac{8}{9}$

Solution

Step 1:

We multiply the numerators at the top and denominators at the bottom of all three fractions as follows.

$\frac{2}{3}$ × $\frac{5}{7}$ × $\frac{8}{9}$

= $\frac{(2 × 5 × 8)}{(3 × 7 × 9)}$ = $\frac{80}{189}$

Step 2:

The highest common factor of 80 and 189 is 1

So, $\frac{2}{3}$ × $\frac{5}{7}$ × $\frac{8}{9}$ = $\frac{80}{189}$

Multiply $\frac{2}{5}$ × $\frac{15}{8}$ × $\frac{4}{5}$

### Solution

Step 1:

First Multiply $\frac{2}{5}$ × $\frac{15}{8}$

Multiply the numerators and denominators of both fractions as follows.

$\frac{2}{5}$ × $\frac{15}{8}$ = $\frac{(2 × 15)}{(5 × 8)}$ = $\frac{30}{40}$

Step 2:

Simplifying

$\frac{30}{40}$ = $\frac{3}{4}$

So $\frac{2}{5}$ × $\frac{15}{8}$ = $\frac{3}{4}$

Step 3:

Now $\frac{2}{5}$ × $\frac{15}{8}$ × $\frac{4}{5}$ = $\frac{3}{4}$ × $\frac{4}{5}$ = $\frac{3}{5}$.

So, $\frac{2}{5}$ × $\frac{15}{8}$ × $\frac{4}{5}$ = $\frac{2}{5}$.

Multiply $\frac{3}{4}$ × $\frac{8}{9}$ × $\frac{5}{7}$

### Solution

Step 1:

Multiply the numerators at the top and denominators at the bottom of all three fractions as follows.

$\frac{3}{4}$ × $\frac{8}{9}$ × $\frac{5}{7}$

= $\frac{(3 × 8 × 5)}{(4 × 9 × 7)}$ = $\frac{120}{252}$

Step 2:

The highest common factor of 120 and 252 is 12

$\frac{(120÷12)}{(252÷12)}$ = $\frac{10}{21}$

Step 3:

So, $\frac{3}{4}$ × $\frac{8}{9}$ × $\frac{5}{7}$ = $\frac{10}{21}$