## The Lesson

Algebraic fractions can be multiplied. Imagine you wanted to multiply ab and cd.

## How to Multiply Algebraic Fractions

To multiply algebraic fractions, use the rule:

## Question

Multiply the algebraic fractions below.

# 1

Compare the fractions you are multiplying with the rule shown above.

By comparing, we see that a = x, b = 2, c = y, d = 3.

# 2

Use the rule, with a = x, b = 2, c = y, d = 3:

# 3

Calculate the terms in the rule. Where we have written two numbers or letters in brackets together, multiply them together:
(x)(y) = x × y = xy (2)(3) = 2 × 3 = 6

We have multiplied x2 and y3 together:

## Lesson Slides

The slider below shows a real example of how to multiply algebraic fractions. Open the slider in a new tab

## Understanding The Rule

Multiplying fractions requires:
• multiplying the numerators together to form the numerator of the product...

• ... and multiplying the denominators together to form the denominator of the product:

This gives the rule:

The letters written next to each other denotes that they are multiplying each other. The rule works when the a, b, c and d are numbers, letters, terms or expressions. Make sure you can:

## Cancelling Terms

When the numerator of one fraction equals the denominator of the other fraction, they cancel each other out:

This is how to simplify algebraic fractions.