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Dividing Algebraic Fractions

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

'Dividing Algebraic Fractions' worksheet

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.




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 reducible 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


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