# How to Divide Fractions

We have already discussed addition and multiplication of fractions and what we have left are subtraction and division. In this post, we learn how to divide fractions.

To divide fractions, we must get the reciprocal of the divisor. This is just the same as swapping the numerator and the denominator. For example, the reciprocal of $\frac{2}{3}$ is $\frac{3}{2}$. After getting the reciprocal, just multiply the fractions.

Example 1 $\displaystyle \frac{3}{5} \div \frac{2}{3}$

Solution

First, we get the reciprocal of $\frac{2}{3}$, the divisor. This is $\frac{3}{2}$. Then, we multiply the fractions. $\displaystyle \frac{3}{5} \times \frac{3}{2} = \frac{9}{10}$

Answer: $\frac{9}{10}$

Example 2 $\displaystyle \frac{5}{6} \div \frac{10}{7}$

Solution

First, we get the reciprocal of $\frac{10}{7}$ which is $\frac{7}{10}$. Multiplying the fractions, we have $\displaystyle \frac{5}{6} \times \frac{7}{10} = \frac{35}{60}$

We reduce the answer to lowest terms by dividing both the numerator and denominator by 5 resulting to $\frac{7}{12}$.

Answer: $\frac{7}{12}$

Example 3 $\displaystyle 5 \frac{3}{4} \div \frac{4}{5}$

Solution

In dividing fractions, the dividend and the divisor must not be mixed fractions. Therefore, we need to convert the mixed fraction to improper fraction. To do this, we multiply $4$ by $5$ and then add $3$. The result becomes the numerator of the mixed fraction. So, the the equivalent of $5 \frac{3}{4}$ is $\frac{23}{4}$.

Multiplying the fractions, we have $\displaystyle \frac{23}{4} \times \frac{5}{4} = \frac{115}{16}$

We can convert the improper fraction to mixed form which is equal to $\displaystyle 7\frac{3}{16}$

Answer: $7 \frac{3}{16}$

Example 4 $\frac{7}{8} \div 4$.

Solution

If the divisor is a whole number, the reciprocal will be 1 “over” that number. In the given, the reciprocal of $4$ is $\frac{1}{4}$. After getting the reciprocal of the divisor, we multiply the two fractions: $\displaystyle \frac{7}{8} \times \frac{1}{4} = \frac{7}{32}$.

Answer: $\frac{7}{32}$ 