To solve a division of fractions, we have to take the reciprocal of the dividing fraction and write the division as multiplication. Then, we multiply the numerators and denominators separately. Finally, we simplify the result if possible.

Here, we will look at 10 examples of division of fractions with answers. In addition, you will be able to test your skills with some practice problems.

## 10 Examples of division of fractions with examples

The following examples include division of simple fractions, division of mixed fractions, and division of fractions by whole numbers. Each of the examples has a detailed solution.

**EXAMPLE 1**

Divide the fractions $latex \frac{4}{5}\div \frac{2}{3}$.

##### Solution

To divide two fractions, we have to find the reciprocal of the dividing fraction and write the division as multiplication.

Therefore, considering that the reciprocal of $latex \frac{2}{3}$ is $latex \frac{3}{2}$, we have:

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

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

Now, we solve the multiplication by writing as follows:

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

Simplifying the 4 in the numerator with the 2 in the denominator, we have:

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

Solving the multiplication, we have:

$$=\frac{6}{5}$$

We can simplify by writing as a mixed number:

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

**EXAMPLE **2

**EXAMPLE**

Solve the division of fractions $latex \frac{5}{7}\div \frac{3}{2}$.

##### Solution

The reciprocal of $latex \frac{3}{2}$ is $latex \frac{2}{3}$. Then, we can write the division of fractions as multiplication:

$$\frac{5}{7}\div \frac{3}{2}$$

$$=\frac{5}{7}\times \frac{2}{3}$$

Now, we write the multiplication as follows:

$$=\frac{5 \times 2}{7 \times 3}$$

Solving the multiplications in the numerator and denominator, we have:

$$=\frac{10}{21}$$

The fraction is already simplified.

**EXAMPLE **3

**EXAMPLE**

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

##### Solution

The reciprocal of $latex \frac{4}{5}$ is $latex \frac{5}{4}$. Then, we use that reciprocal to write the division as multiplication:

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

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

Now, we can write as follows:

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

We can simplify the 8 in the numerator with the 4 in the denominator:

$$=\frac{2 \times 5}{9 \times 1}$$

Solving the multiplication, we have:

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

Writing as a mixed number, we have:

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

**EXAMPLE **4

**EXAMPLE**

Find the result of dividing the fractions $latex \frac{9}{11}\div \frac{4}{7}$.

##### Solution

Considering that the reciprocal of $latex \frac{4}{7}$ is $latex \frac{7}{5}$, we can write it as follows:

$$\frac{9}{11}\div \frac{4}{7}$$

$$=\frac{9}{11}\times \frac{7}{4}$$

Now, we write the multiplication like this:

$$=\frac{9 \times 7}{11 \times 4}$$

Solving the multiplications in the numerator and denominator, we have:

$$=\frac{63}{44}$$

We can simplify by writing as a mixed number:

$$=1\frac{19}{44}$$

**EXAMPLE **5

**EXAMPLE**

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

##### Solution

In this case, we have an integer in the division. We can solve this problem by writing the whole number as a fraction. Therefore, we have:

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

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

Now, we convert the divisions to multiplication by taking the reciprocal of the dividing fractions:

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

We can write the multiplication as follows:

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

Simplifying the 2 in the numerator with the 2 in the denominator, we have:

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

Solving the multiplication, we have:

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

Writing as a mixed number, we have:

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

**EXAMPLE **6

**EXAMPLE**

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

##### Solution

Here, we have a mixed fraction. To solve the division, we have to start by converting the mixed fraction to an improper fraction. Therefore, we have:

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

$$=\frac{7}{4}\div \frac{2}{5}$$

Writing multiplication as division, we have:

$$=\frac{7}{4}\times \frac{5}{2}$$

Now, we solve the multiplication by writing as follows:

$$=\frac{7 \times 5}{4 \times 2}$$

$$=\frac{35}{8}$$

Writing as a mixed number, we have:

$$=4\frac{3}{8}$$

**EXAMPLE **7

**EXAMPLE**

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

##### Solution

We start by converting both mixed fractions to improper fractions. Therefore, we have:

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

$$=\frac{8}{3}\div \frac{7}{4}$$

Writing the division as multiplication, we have:

$$\frac{8}{3}\div \frac{7}{4}$$

$$=\frac{8}{3}\times \frac{4}{7}$$

We solve the multiplication as follows:

$$=\frac{8 \times 4}{3 \times 7}$$

$$=\frac{32}{21}$$

We can simplify by writing as a mixed number:

$$=1\frac{11}{21}$$

**EXAMPLE **8

**EXAMPLE**

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

##### Solution

In this case, we have a division of three fractions, but the process used is the same. Therefore, we write division as multiplication:

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

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

Now, we solve the multiplication by writing as follows:

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

Simplifying the 3 in the numerator with the 3 in the denominator, we have:

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

Solving the multiplications of the numerator and the denominator, we have:

$$=\frac{8}{5}$$

We can simplify by writing as a mixed number:

$$=1\frac{3}{5}$$

**EXAMPLE **9

**EXAMPLE**

Solve the division of fractions $latex \frac{6}{7}\div \frac{5}{3}\div \frac{3}{4}$.

##### Solution

We use the reciprocals of the divisor fractions to write division as multiplication:

$$\frac{6}{7}\div \frac{5}{3}\div \frac{3}{4}$$

$$=\frac{6}{7}\times \frac{3}{5} \times \frac{4}{3}$$

We write multiplication as follows:

$$=\frac{6 \times 3 \times 4}{7 \times 5 \times 3}$$

Simplifying the 3 in the numerator with the 3 in the denominator, we have:

$$=\frac{6 \times 1 \times 4}{7 \times 5 \times 1}$$

Solving the multiplications of the numerator and the denominator, we have:

$$=\frac{24}{35}$$

**EXAMPLE **10

**EXAMPLE**

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

##### Solution

We start by converting the mixed fractions to improper fractions:

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

$$=\frac{11}{4}\div \frac{5}{3}\div \frac{9}{5}$$

Writing division as multiplication, we have:

$$=\frac{11}{4}\times \frac{3}{5}\times \frac{5}{9}$$

Now, we solve the multiplication by writing as follows:

$$=\frac{11 \times 3 \times 5}{4 \times 5 \times 9}$$

We can simplify the 5 in the numerator with the 5 in the denominator and the 3 in the numerator with the 9 in the denominator:

$$=\frac{11 \times 1 \times 1}{4 \times 1 \times 3}$$

Solving the multiplication, we have:

$$=\frac{11}{12}$$

→ Dividing Fractions Calculator

## 5 Dividing fractions practice problems

Test your skills in dividing fractions by solving the following practice problems.

## See also

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