Dividing Fractions by Whole Number

Related calculator: Fractions Calculator

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: $$$-\frac{{30}}{{7}}=-{4}\frac{{2}}{{7}}$$$.

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Next example.

Exercise 3. Divide $$$-\frac{{21}}{{5}}$$$ by -5.

Answer: $$$\frac{{21}}{{25}}$$$.