Dividing Fractions

Related calculator: Fractions Calculator

To divide fraction by a fraction multiply numerator of the first fraction by the denominator of the second fraction and denominator of the first fraction by the numerator of the second fraction, i.e. $$${\color{green}{{\frac{{a}}{{b}}\div\frac{{c}}{{d}}=\frac{{\frac{{a}}{{b}}}}{{\frac{{c}}{{d}}}}=\frac{{{a}{d}}}{{{b}{c}}}}}}$$$.

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 $$$\frac{{11}}{{7}}$$$.

$$$\frac{{\color{blue}{{{5}}}}}{{\color{red}{{{12}}}}}\div\frac{{\color{red}{{{11}}}}}{{\color{blue}{{{7}}}}}=\frac{{{5}\cdot{7}}}{{{12}\cdot{11}}}=\frac{{35}}{{132}}$$$.

Fraction is irreducible.

Answer: $$$\frac{{35}}{{132}}$$$.

Next example.

Example 2. Divide $$$\frac{{16}}{{11}}$$$ by $$$\frac{{8}}{{3}}$$$.

$$$\frac{{\frac{{\color{blue}{{{16}}}}}{{\color{red}{{{11}}}}}}}{{\frac{{\color{red}{{{8}}}}}{{\color{blue}{{{3}}}}}}}=\frac{{{16}\cdot{3}}}{{{11}\cdot{8}}}=\frac{{48}}{{88}}$$$.

Reduce fraction: $$$\frac{{48}}{{88}}=\frac{{6}}{{11}}$$$.

Answer: $$$\frac{{6}}{{11}}$$$.

Next example.

Example 3. Divide $$$\frac{{39}}{{7}}$$$ by $$$\frac{{5}}{{2}}$$$.

$$$\frac{{\frac{{39}}{{7}}}}{{\frac{{5}}{{2}}}}=\frac{{{39}\cdot{2}}}{{{5}\cdot{7}}}=\frac{{78}}{{35}}$$$.

Convert to mixed number if needed: $$$\frac{{78}}{{35}}={2}\frac{{8}}{{35}}$$$.

Answer: $$$\frac{{78}}{{35}}={2}\frac{{8}}{{35}}$$$.

Now, it is time to practice.

Exercise 1. Divide $$$\frac{{2}}{{5}}$$$ by $$$\frac{{1}}{{12}}$$$.

Answer: $$$\frac{{24}}{{5}}={4}\frac{{4}}{{5}}$$$.

Next exercise.

Exercise 2. Divide 15 by $$$-\frac{{5}}{{7}}$$$.

Answer: -21. Hint: $$${15}=\frac{{15}}{{1}}$$$.

Last exercise.

Exercise 3. Divide $$$-\frac{{21}}{{5}}$$$ by $$$-\frac{{35}}{{4}}$$$.

Answer: $$$\frac{{12}}{{25}}$$$.