  # Dividing Algebraic Fractions

In this worksheet, students 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.

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

 a3 ÷ 7a2 10 5

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

 a3 x 5 10 7a2

We look for any top term which has a common factor with any bottom term.

If we find such a reduceable pair of terms, we divide them by their common factor.

 = a3 ÷ a2 x 5 10 7a2 ÷ a2

 = a x 5 10 7

 = a x 5 ÷ 5 10 ÷ 5 7

 = a x 1 2 7

 = a 14

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