# Dividing Algebraic Fractions(KS3, Year 8)

## The Lesson

Algebraic fractions can be divided. Imagine you wanted to divide ab by cd.

## How to Divide Algebraic Fractions

To divide algebraic fractions, use the rule:

## Question

Divide the algebraic fractions below.

# 1

Compare the fractions you are dividing 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)(3) = x × 3 = 3x (2)(y) = 2 × y = 2y

We have divided x2 by y3:

## Lesson Slides

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

## Understanding The Rule

Dividing fractions requires:
• replacing the divisor (the fraction you are dividing by) with its reciprocal...
• ... and replacing the division with a multiplication:

Then the fractions can be multiplied:
• 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 means 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.
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