# How to Divide Fractions – Step-by-step

To divide two or more fractions, we can multiply the first fraction by the reciprocal of the dividing fraction. Therefore, we flip the dividing fraction and change the sign from division to multiplication. Then, we multiply the numerator and denominator separately and simplify the resulting fraction if possible.

Here, we will learn to divide two or more fractions step by step. In addition, we will solve some practice problems in which we will apply these steps.

##### ARITHMETIC

Relevant for

Learning to divide two or more fractions step by step.

See steps

##### ARITHMETIC

Relevant for

Learning to divide two or more fractions step by step.

See steps

## Steps to divide fractions

To multiply fractions, we can follow the following steps.

Step 1: Take the reciprocal of the dividing fraction.

To take the reciprocal of a fraction, we simply have to flip the fraction. That is, we swap the numerator and the denominator.

Step 2: Change the division sign to multiplication.

Step 3: Multiply the numerators.

Step 4: Multiply the denominators.

Step 5: Simplify the final fraction if possible.

## Dividing fractions – Examples with answers

The steps to solve a division of fractions seen above are used to solve the following examples. Try to solve the problems yourself before looking at the solution.

### EXAMPLE 1

Solve the division of fractions $latex \frac{2}{3}\div \frac{1}{2}$.

Step 1: The dividing fraction is $latex \frac{1}{2}$. Its reciprocal is

$$\frac{2}{1}$$

Step 2: Writing the division as multiplication, we have:

$$\frac{2}{3}\div \frac{1}{2}$$

$$=\frac{2}{3}\times \frac{2}{1}$$

Step 3: Multiplying the numerators, we have:

$$=\frac{2\times 2}{3\times 1}$$

$$=\frac{4}{3\times 1}$$

Step 4: Multiplying the denominators, we have:

$$=\frac{4}{3}$$

Step 5: We can simplify by writing as a mixed fraction:

$$=1\frac{1}{3}$$

### EXAMPLE 2

Find the result of the division $latex \frac{5}{7}\div \frac{3}{5}$.

Step 1: The dividing fraction is $latex \frac{3}{5}$. Its reciprocal is

$$\frac{5}{3}$$

Step 2: We write the division as multiplication:

$$\frac{2}{3}\div \frac{3}{5}$$

$$=\frac{2}{3}\times \frac{5}{3}$$

Step 3: By multiplying the numerators, we have:

$$=\frac{2\times 5}{3\times 3}$$

$$=\frac{10}{3\times 3}$$

Step 4: By multiplying the denominators, we have:

$$=\frac{10}{9}$$

Step 5: Writing as a mixed fraction, we have:

$$=1\frac{1}{9}$$

### EXAMPLE 3

Solve the division of fractions $latex \frac{5}{6}\div \frac{3}{4}$.

Step 1: The reciprocal of the dividing fraction, $latex \frac{3}{4}$, is

$$\frac{4}{3}$$

Step 2: By changing the division sign to multiplication, we have:

$$\frac{5}{6}\div \frac{3}{4}$$

$$=\frac{5}{6}\times \frac{4}{3}$$

Step 3: Solving the multiplication of the numerators, we have:

$$=\frac{5\times 4}{6\times 3}$$

$$=\frac{20}{6\times 3}$$

Step 4: Solving the multiplication of the denominators, we have:

$$=\frac{20}{18}$$

Step 5: We can divide by 2 to simplify and write as a mixed fraction:

$$=\frac{10}{9}$$

$$=1\frac{1}{9}$$

### EXAMPLE 4

Solve the division of fractions $latex \frac{8}{9}\div \frac{4}{5}$.

Step 1: The dividing fraction is $latex \frac{4}{5}$. Its reciprocal is

$$\frac{5}{4}$$

Step 2: We use the reciprocal of the dividing fraction and write the division as multiplication:

$$\frac{8}{9}\div \frac{4}{5}$$

$$=\frac{8}{9}\times \frac{5}{4}$$

Step 3: Multiplying the numerators, we have:

$$=\frac{8\times 5}{9\times 4}$$

$$=\frac{40}{9\times 4}$$

Step 4: Multiplying the denominators, we have:

$$=\frac{40}{36}$$

Step 5: We simplify the fraction by dividing by 4 and write as a mixed fraction:

$$=\frac{10}{9}$$

$$=1\frac{1}{9}$$

### EXAMPLE 5

Find the result of the division $latex \frac{2}{3}\div \frac{4}{5}\div \frac{1}{2}$.

Step 1: We have two dividing fractions. The reciprocal of $latex \frac{4}{5}$ is $latex \frac{5}{4}$ and the reciprocal of $latex \frac{1}{2}$ is $latex \frac{2}{ 1}$.

Step 2: We use the reciprocals of the dividing fractions and write the division as multiplication:

$$\frac{2}{3}\div \frac{4}{5}\div \frac{1}{2}$$

$$=\frac{2}{3}\times \frac{5}{4}\times \frac{2}{1}$$

Step 3: By multiplying the numerators, we have:

$$=\frac{2\times 5 \times 2}{3\times 4 \times 1}$$

$$=\frac{20}{3\times 4 \times 1}$$

Step 4: By multiplying the denominators, we have:

$$=\frac{20}{12}$$

Step 5: We can simplify by dividing by 4 and writing as a mixed fraction:

$$=\frac{5}{3}$$

$$=1\frac{2}{3}$$

### EXAMPLE 6

Solve the division of fractions $latex \frac{3}{4}\div \frac{1}{2}\div \frac{5}{6}$.

Step 1: The reciprocal of $latex \frac{1}{2}$ is $latex \frac{2}{1}$ and the reciprocal of $latex \frac{5}{6}$ is $latex \frac{ 6}{5}$.

Step 2: Using the reciprocals of the dividing fractions and writing the division as multiplication, we have:

$$\frac{3}{4}\div \frac{1}{2}\div \frac{5}{6}$$

$$=\frac{3}{4}\times \frac{2}{1}\times \frac{6}{5}$$

Step 3: Multiplying the numerators, we have:

$$=\frac{3\times 2 \times 6}{4\times 1 \times 5}$$

$$=\frac{36}{4\times 1 \times 5}$$

Step 4: Multiplying the denominators, we have:

$$=\frac{36}{20}$$

Step 5: We can simplify by dividing by 4 and writing as a mixed fraction:

$$=\frac{9}{5}$$

$$=1\frac{4}{5}$$

## Dividing fractions – Practice problems

Apply everything you have learned about dividing fractions and solve the following practice problems.

#### Solve the division $latex 1\frac{2}{3}\div 2\frac{1}{4}$  