How to Multiply Fractions – Step-by-step

To multiply two or more fractions, we simply have to multiply the numerators and denominators separately. However, if we have whole numbers or mixed fractions, we convert them to improper fractions before multiplying. Finally, we simplify the resulting fraction if possible.

Here, we will learn how to multiply fractions step by step. We will look at some examples in which we will apply these steps to solve the multiplication of fractions.

ARITHMETIC

Relevant for

Learning to multiply two or more fractions.

See steps

ARITHMETIC

Relevant for

Learning to multiply two or more fractions.

See steps

Steps to multiply fractions

To multiply fractions, we can follow the following steps:

Step 1: Convert mixed fractions or whole numbers to improper fractions, if any.

If we have whole numbers, we simply write 1 as the denominator. If we have mixed fractions, we multiply the whole number by the denominator and add the result to the numerator.

Step 2: Multiply the numerators.

Step 3: Multiply the denominators.

Step 4: Simplify the final fraction if possible.

Multiplying fractions – Examples with answers

Each of the following examples has its respective solution. We use the steps to solve the multiplication of fractions seen above.

EXAMPLE 1

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

Step 1: We don’t have mixed fractions or whole numbers.

Step 2: Multiplying the numerators, we have:

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

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

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

Step 3: Multiplying the denominators, we have:

$$=\frac{2}{6}$$

Step 4: We divide by 2 to simplify:

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

EXAMPLE 2

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

Step 1: This multiplication doesn’t have whole numbers or mixed fractions.

Step 2: By multiplying the numerators, we have:

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

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

$$=\frac{15}{7\times 5}$$

Step 3: By multiplying the denominators, we have:

$$=\frac{15}{35}$$

Step 4: We divide by 5 to simplify:

$$=\frac{3}{7}$$

EXAMPLE 3

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

Step 1: Converting the mixed fraction to an improper fraction, we have:

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

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

Step 2: Multiplying the numerators, we have:

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

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

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

Step 3: Multiplying the denominators, we have:

$$=\frac{5}{12}$$

Step 4: The fraction is now simplified.

EXAMPLE 4

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

Step 1: We write the integer as follows:

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

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

Step 2: By multiplying the numerators, we have:

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

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

Step 3: By multiplying the denominators, we have:

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

Step 4: We divide by 2 to simplify:

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

EXAMPLE 5

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

Step 1: We don’t have mixed fractions or whole numbers.

Step 2: Multiplying the numerators, we have:

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

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

$$=\frac{8}{3\times 5 \times 2}$$

Step 3: Multiplying the denominators, we have:

$$=\frac{8}{30}$$

Step 4: We can simplify by dividing by 2:

$$=\frac{4}{15}$$

EXAMPLE 6

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

Step 1: Converting the mixed fractions to improper fractions, we have:

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

$$=\frac{11}{4}\times \frac{3}{2}\times \frac{4}{5}$$

Step 2: By multiplying the numerators, we have:

$$=\frac{11\times 3 \times 4}{4\times 2 \times 5}$$

$$=\frac{132}{4\times 2 \times 5}$$

Step 3: By multiplying the denominators, we have:

$$=\frac{132}{40}$$

Step 4: We divide by 4 to simplify and convert to a mixed fraction:

$$=\frac{33}{10}$$

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

Multiplying fractions – Practice problems

Solve the following multiplication of fractions problems to apply everything learned here.