Multiplying Fractions

Related calculator: Fractions Calculator

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