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Divide Algebraic Fractions

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

'Divide Algebraic Fractions' worksheet

Key stage:  KS 3

Year:  Year 9 Maths worksheets

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.





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:




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




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