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Welcome to our How do you Multiply Fractions support page.

This page will support you in learning how to multiply two fractions together, and show you some worked examples.

We have a calculator to help you to multiply fractions.

You can use the calculator for multiplying improper fractions or mixed numbers too.

All the working out is shown step-by-step so you can see how it is worked out.

Before your child tackles multiplying fractions, they should be confident with converting mixed fractions to improper fractions and reducing fractions to simplest form.

Using these sheets will help your child to:

- multiply one fraction by another;
- apply their understanding of simplest form;
- convert an improper fraction to a mixed number.

For those of you who like to see some algebra, here is the simple formula for multiplying two fractions:

Formula for multiplying two fractions

\[{a \over b} \times {c \over d} = {ac \over bd} \]

Frazer says "To multiply a fraction by another fraction, follow these simple steps."

Before you start:

- Convert any mixed numbers into improper fractions;
- Put any integers over a denominator of 1.

Step 1

Re-write the fraction equation into a single fraction.

Step 2 (optional)

Cancel any common factors of both the numerator and the denominator.

This make the next couple of steps easier!

Step 3 (this may not be needed after Step 2)

Work out the products in the numerator and denominator. This will give you the answer.

Step 4 (optional)

Simplify the answer if needed.

You should have now found your fraction of a number!

Example 1) Calculate \[{3 \over 5} \times {4 \over 9} \]

Step 1)

\[{3 \over 4} \times {4 \over 9} = {3 \times 4 \over 4 \times 9}\]

Step 2) Cancel out common factors

\[{3 \times \cancel 4 \over \cancel 4 \times 9} = {3 \over 9} \]

Steps 3 & 4)

Simplify the answer by dividing numerator and denominator by 3: \[{3 \over 9} \; = \; {1 \over 3}\]

Final answer: \[{3 \over 4} \times {4 \over 9} \; = \; {1 \over 3}\]

Example 2) Calculate \[{2 \over 5} \times {5 \over 8} \]

Step 1)

\[{2 \over 5} \times {5 \over 8} = {2 \times 5 \over 5 \times 8} \]

Step 2) Cancel out common factors

\[{2 \times \cancel 5 \over \cancel 5 \times 8} = {2 \over 8} \]

Steps 3 & 4)

Simplify the answer by dividing numerator and denominator by 2: \[{2 \over 8} \; = \; {1 \over 4}\]

Final answer: \[{2 \over 5} \times {5 \over 8} \; = \; {1 \over 4}\]

Example 3) Calculate \[{7 \over 4} \times {9 \over 5} \]

Step 1)

\[{7 \over 4} \times {9 \over 5} = {7 \times 9 \over 4 \times 5} \]

Step 2)

There are no common factors so we can leave out this part.

Step 3)

\[{7 \times 9 \over 4 \times 5} = {63 \over 20}\]

Step 4)

This answer is already in simplest form, but we can convert it to a mixed number: \[{63 \over 20} \; = \; 3 {3 \over 20} \]

Final answer: \[{7 \over 4} \times {9 \over 5} \; = \; {63 \over 20} \; or \; 3 {3 \over 20}\]

Example 4) Calculate \[{11 \over 7} \times 8 \]

First we need to put the integer over a denominator of 1. \[8 = {8 \over 1} \]

Step 1)

\[{11 \over 7} \times {8 \over 1} = {11 \times 8 \over 7 \times 1} \]

Step 2)

There are no common factors to cancel.

Step 3)

\[{11 \times 8 \over 7 \times 1} = {88 \over 7}\]

Step 4)

This fraction is already in its simplest form, but we can convert it into a mixed number: \[{88 \over 7} \; = \; 12 {4 \over 7} \]

Final answer: \[{11 \over 7} \times 8 \; = \; {88 \over 7} \; or \; 12 {4 \over 7} \]

Example 5) Work out \[{3 \over 5} \times {4 \over 7} \times {5 \over 9}\]

Step 1)

\[{3 \over 5} \times {4 \over 7} \times {5 \over 9} = {3 \times 4 \times 5 \over 5 \times 7 \times 9}\]

Step 2)

Cancel common factors.

\[{3 \times 4 \times \cancel 5 \over \cancel 5 \times 7 \times 9} = {3 \times 4 \over 7 \times 9} \]

Step 3)

\[{3 \times 4 \over 7 \times 9} = {12 \over 63}\]

Step 4)

Simplify the answer by dividing numerator and denominator by 3: \[{12 \over 63} = {4 \over 21}\]

Final answer: \[{3 \over 5} \times {4 \over 7} \times {5 \over 9} = {4 \over 21}\]

Take a look at some more of our resources similar to these.

Multiplying mixed fractions is very similar to multiplying fractions.

If you would like to see some worked examples and support for multiplying mixed fractions, use the link below.

We also have a series of worksheets to help you practice multiplying fractions or multiplying mixed fractions.

The sheets are all carefully graded and the easiest sheets are supported.

This is also sometimes called reducing fractions to their simplest form.

This involves dividing both the numerator and denominator by a common factor to reduce the fraction to the equivalent fraction with the smallest possible numerator and denominator.

This support page shows how to convert improper fractions to mixed numbers, and how to convert mixed numbers to improper fractions.

You will also find printable support sheets, and several practice math worksheets for this learning fractions skill.

Here you will find the Math Salamanders free online Math help pages about Fractions.

There is a wide range of help pages including help with:

- fraction definitions;
- equivalent fractions;
- converting improper fractions;
- how to add and subtract fractions;
- how to convert fractions to decimals and percentages;
- how to simplify fractions.

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