# How do you Multiply FractionsSupport Page

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.

## How do you Multiply Fractions

### How do you Multiply Fractions Support

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!

#### How to Multiply Fractions Examples

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: ${3 \over 5} \times {4 \over 7} \times {5 \over 9} = {4 \over 21}$

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### Learning Fractions Math Help Page

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