# Divide Algebraic Fractions

In this worksheet, students will divide algebraic fractions giving their answers as a single fraction.

Key stage:  KS 3

Curriculum topic:   Algebra

Curriculum subtopic:   Use and Interpret Algebraic Notation

Difficulty level:

#### Worksheet Overview

When we divide algebraic fractions, we use the same method as when we divide numerical fractions.

Remember the KFC rule: Keep the first fraction, flip the second fraction and change the sign.

First, we invert the second fraction and then turn the ÷ sign into a x sign.

Then we try to reduce or cancel down any top term with a bottom term that has a common factor.

Example

Simplify:

 a3 ÷ 7a2 10 5

Invert the second fraction and change the ÷ sign to a x sign.

 a3 x 5 10 7a2

Now multiply the numerators to get 5a3

And multiply the denominators to get 70a2

This gives us:

 5a3 70a2

Now we simplify this by dividing the numbers by a common factor.

5 is a common factor of 5 and 70, so divide them both by 5. This gives us 1 as the numerator and 14 as the denominator.

Remember the rule for dividing by powers? a3 ÷ a2 = a3-2 = a

We end up with

 a 14

Let's try some questions.

### What is EdPlace?

We're your National Curriculum aligned online education content provider helping each child succeed in English, maths and science from year 1 to GCSE. With an EdPlace account you’ll be able to track and measure progress, helping each child achieve their best. We build confidence and attainment by personalising each child’s learning at a level that suits them.

Get started