Introduction to Fraction Multiplication

The product of two fractions is obtained by multiplying the numerators and then multiplying the denominators of the fractions to get the product fraction. If any simplification or cross cancelling is required, it is done and fraction is written 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.
• If required, we simplify the fraction so obtained and reduce it to the lowest terms.

Example

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

Solution

Step 1:

We multiply the numerators on the top and denominators on the bottom as follows.

$\frac{2}{3}$ × $\frac{5}{7}$ = $\frac{(2 × 5)}{(3 × 7)}$ = $\frac{10}{21}$

Step 2:

Since no number other than 1 evenly divides both 10 and 21, this is the answer in simplest form.

$\frac{2}{3}$ × $\frac{5}{7}$ = $\frac{10}{21}$

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

Solution

Step 1:

We multiply the numerators on the top and denominators on the bottom as follows.

$\frac{2}{7}$ × $\frac{9}{5}$ = $\frac{(2 × 9)}{(7 × 5)}$ = $\frac{18}{35}$

Step 2:

Since no number other than 1 evenly divides both 18 and 35, this is the answer in simplest form.

$\frac{2}{7}$ × $\frac{9}{5}$ = $\frac{18}{35}$

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

Solution

Step 1:

We multiply the numerators on the top and denominators on the bottom as follows.

$\frac{4}{5}$ × $\frac{8}{9}$ = 4 × $\frac{8}{(5 × 9)}$ = $\frac{32}{45}$

Step 2:

Since no number other than 1 evenly divides both 32 and 45, this is the answer in simplest form.

$\frac{4}{5}$ × $\frac{8}{9}$ = $\frac{32}{45}$