Dividing Fractions by Whole Number

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