Dividing Fractions by Whole Number
To divide fraction by whole number multiply denominator of the fraction by whole number, i.e. fraction $$$\frac{{n}}{{q}}$$$ divided by the whole number $$${m}$$$ is $$${\color{green}{{\frac{{n}}{{q}}\div{m}=\frac{{\frac{{n}}{{q}}}}{{m}}=\frac{{n}}{{{q}{m}}}}}}$$$.
After this you, possibly, need to reduce fraction.
Note! Rules for determining sign of the result are same as when dividing integers.
Example 1. Divide $$$\frac{{5}}{{12}}$$$ by 3.
$$$\frac{{\frac{{5}}{{12}}}}{{3}}=\frac{{5}}{{{12}\cdot{3}}}=\frac{{5}}{{36}}$$$.
Fraction is irreducible.
Answer: $$$\frac{{5}}{{36}}$$$.
Next example.
Example 2. Divide $$$\frac{{16}}{{5}}$$$ by 8.
$$$\frac{{\frac{{16}}{{5}}}}{{8}}=\frac{{16}}{{{5}\cdot{8}}}=\frac{{16}}{{40}}$$$.
Reduce fraction: $$$\frac{{16}}{{40}}=\frac{{2}}{{5}}$$$.
Answer: $$$\frac{{2}}{{5}}$$$.
Next example.
Example 3. Divide $$$\frac{{39}}{{7}}$$$ by 4.
$$$\frac{{\frac{{39}}{{7}}}}{{4}}=\frac{{39}}{{{7}\cdot{4}}}=\frac{{39}}{{28}}$$$.
Convert to mixed number if needed: $$$\frac{{39}}{{28}}={1}\frac{{11}}{{28}}$$$.
Answer: $$$\frac{{39}}{{28}}={1}\frac{{11}}{{28}}$$$.
Now, it is time to practice.
Exercise 1. Divide $$$\frac{{2}}{{5}}$$$ by 8.
Answer: $$$\frac{{1}}{{20}}$$$.
Next exercise.
Exercise 2. Divide $$$\frac{{90}}{{7}}$$$ by -3.
Answer: $$$-\frac{{30}}{{7}}=-{4}\frac{{2}}{{7}}$$$.
\Next example.
Exercise 3. Divide $$$-\frac{{21}}{{5}}$$$ by -5.
Answer: $$$\frac{{21}}{{25}}$$$.