To multiply fractions, we simply have to multiply the numerators and denominators separately. However, if we have mixed fractions, we have to start by converting the mixed fraction to an improper fraction. Lastly, we simplify the final answer if possible.

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

## 10 Examples of multiplication of fractions

Each of the following examples of multiplication of fractions has its respective solution. These examples include multiplying fractions with whole numbers and with mixed fractions.

**EXAMPLE 1**

Multiply the fractions $latex \frac{4}{5}\times \frac{2}{3}$?

##### Solution

To multiply two fractions, we have to multiply the numerators and denominators separately.

Therefore, we can write the multiplication as follows:

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

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

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

$$=\frac{8}{15}$$

The fraction is already simplified.

**EXAMPLE **2

**EXAMPLE**

Solve the multiplication of fractions $latex \frac{5}{7}\times \frac{3}{2}$.

##### Solution

We can solve the multiplication of fractions by rewriting the fractions as follows:

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

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

Now, we solve the multiplications in the numerator and the denominator:

$$=\frac{15}{14}$$

We can simplify the fraction by writing it as a mixed fraction:

$$=1\frac{1}{14}$$

**EXAMPLE **3

**EXAMPLE**

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

##### Solution

In this case, we have a multiplication of three fractions. However, we can solve it in the same way. Thus, we write the multiplication as follows:

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

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

Now, we can solve the multiplications in the numerator and the denominator:

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

$$=\frac{5}{24}$$

The fraction is already simplified.

**EXAMPLE **4

**EXAMPLE**

Find the product of the multiplication of fractions $latex \frac{3}{4}\times \frac{4}{7} \times \frac{3}{5}$.

##### Solution

To solve this multiplication, we can write the fractions as follows:

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

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

Before multiplying, we can see that we have a 4 in the numerator and a 4 in the denominator. Therefore, we can simplify:

$$=\frac{3\times 1 \times 3}{1\times 7 \times 5}$$

Multiplying, we have:

$$=\frac{9}{35}$$

The fraction is already simplified.

**EXAMPLE **5

**EXAMPLE**

Solve the multiplication of fractions $latex \frac{2}{3}\times \frac{1}{4} \times 2$.

##### Solution

In this case, we have a multiplication of fractions with a whole number. Therefore, we can write as follows:

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

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

Then, we write the multiplication like this:

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

We can simplify both 2’s in the numerator with the 4 in the denominator:

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

Multiplying, we have:

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

**EXAMPLE **6

**EXAMPLE**

Find the product of the multiplication $latex 2\frac{3}{4}\times \frac{2}{5}$.

##### Solution

In this case, we have a mixed fraction. Therefore, we start by converting the mixed fraction to an improper fraction:

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

$$=\frac{11}{4}\times \frac{2}{5}$$

Now, we write the multiplication as follows:

$$\frac{11\times 2}{4 \times 5}$$

We can simplify the 2 in the numerator with the 4 in the denominator:

$$=\frac{11\times 1}{2 \times 5}$$

Multiplying, we have:

$$=\frac{11}{10}$$

We can write as a mixed fraction:

$$=1\frac{1}{10}$$

**EXAMPLE **7

**EXAMPLE**

Solve the multiplication $latex 2\frac{1}{3}\times 3\frac{1}{4}$.

##### Solution

We have a multiplication of mixed fractions, so we start by converting them to improper fractions:

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

$$=\frac{7}{3}\times \frac{13}{4}$$

Now, we write the multiplication as follows:

$$=\frac{7 \times 13}{3\times 4}$$

Multiplying, we have:

$$=\frac{91}{12}$$

Now, we can write as a mixed fraction:

$$=7\frac{7}{12}$$

**EXAMPLE **8

**EXAMPLE**

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

##### Solution

We start by writing the mixed fraction as an improper fraction:

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

$$=\frac{1}{5}\times \frac{7}{4}\times \frac{1}{2}$$

Now, we write the multiplication as follows:

$$=\frac{1\times 7 \times 1}{5\times 4\times 2}$$

Multiplying, we have:

$$=\frac{7}{40}$$

This fraction is already simplified.

**EXAMPLE **9

**EXAMPLE**

Solve the multiplication of fractions $latex 2\frac{2}{3}\times \frac{1}{3}\times 1\frac{5}{7}$.

##### Solution

Converting the mixed fractions to improper fractions, we have:

$$2\frac{2}{3}\times \frac{1}{3}\times 1\frac{5}{7}$$

$$=\frac{8}{3}\times \frac{1}{3}\times \frac{12}{7}$$

Now, we can write the multiplication as follows:

$$=\frac{8\times 1 \times 12}{3\times 3\times 7}$$

We can simplify the 12 in the numerator with the 3 in the denominator:

$$=\frac{8\times 1 \times 4}{1\times 3\times 7}$$

Multiplying, we have:

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

Writing as a mixed fraction, we have:

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

**EXAMPLE **10

**EXAMPLE**

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

##### Solution

We write the mixed fractions as improper fractions:

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

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

Now, we write the multiplication of fractions like this:

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

Simplifying the 5 in the numerator with the 5 in the denominator and the 9 in the numerator with the 3 in the denominator, we have:

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

Multiplying, we have:

$$=\frac{33}{4}$$

Writing as a mixed fraction, we have:

$$=8\frac{1}{4}$$

→ Multiplying Fractions Calculator

## 5 Multiplication of fractions practice problems

Test your knowledge about multiplying fractions by solving the following practice problems.

## See also

Interested in learning more about multiplying and dividing fractions? Take a look at these pages:

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