Multiplying Fractions

To multiply fractions multiply separately numerators and separately denominators: ${\color{green}{{\frac{{a}}{{b}}\cdot\frac{{c}}{{d}}=\frac{{{a}{c}}}{{{b}{d}}}}}}$ .

After this you, possibly, need to reduce a fraction.

Note! Rules for determining sign of the result are same as when multiplying integers.

Example 1. Find $\frac{{4}}{{5}}\cdot\frac{{7}}{{8}}$ .

$\frac{{4}}{{5}}\cdot\frac{{7}}{{8}}=\frac{{{4}\cdot{7}}}{{{5}\cdot{8}}}=\frac{{28}}{{40}}$ .

Now, reduce fraction: $\frac{{28}}{{40}}=\frac{{7}}{{10}}$ .

Answer: $\frac{{7}}{{10}}$ .

Next example.

Example 2. Find $\frac{{16}}{{5}}\cdot\frac{{9}}{{11}}$ .

$\frac{{16}}{{5}}\cdot\frac{{9}}{{11}}=\frac{{{16}\cdot{9}}}{{{5}\cdot{11}}}=\frac{{144}}{{55}}$ .

Fraction is irreducible, so we can just convert it to mixed number: $\frac{{144}}{{55}}={2}\frac{{34}}{{55}}$ .

Answer: $\frac{{144}}{{55}}={2}\frac{{34}}{{55}}$ .

Next example.

Example 3. Find $\frac{{9}}{{2}}\cdot\frac{{5}}{{3}}$ .

$\frac{{9}}{{2}}\cdot\frac{{5}}{{3}}=\frac{{{9}\cdot{5}}}{{{2}\cdot{3}}}=\frac{{45}}{{6}}$ .

Now, reduce fraction: $\frac{{45}}{{6}}=\frac{{15}}{{2}}$ .

Convert to mixed number: $\frac{{15}}{{2}}={7}\frac{{1}}{{2}}$ .

Answer: $\frac{{15}}{{2}}={7}\frac{{1}}{{2}}$ .

Now, it is time to practice.

Exercise 1. Find $\frac{{2}}{{5}}\cdot\frac{{3}}{{7}}$ .

Answer: $\frac{{6}}{{35}}$ .

Next exercise.

Exercise 2. Find $\frac{{9}}{{7}}\cdot\frac{{2}}{{3}}$ .

Answer: $\frac{{6}}{{7}}$ .

Next example.

Exercise 3. Find $\frac{{19}}{{2}}\cdot\frac{{18}}{{5}}$ .

Answer: $\frac{{171}}{{5}}={34}\frac{{1}}{{5}}$ .