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