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Algebraic fraction: GCSE Maths Definition

Dan Finlay

Written by: Dan Finlay

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1 minutes

Contents

  1. 1. What is an algebraic fraction?
  2. 2. Algebraic fractions revision resources to ace your exams

What is an algebraic fraction?

In GCSE maths, an algebraic fraction is a fraction where the numerator and/or denominator contain an algebraic expression. Here are some examples of algebraic fractions:

  • fraction numerator 2 over denominator x plus 1 end fraction

  • fraction numerator 2 x plus 3 over denominator x plus 1 end fraction

  • fraction numerator x squared minus 1 over denominator x minus 1 end fraction

Algebraic fractions follow the usual rules of numerical fractions.

To simplify algebraic fractions, cancel out common factors from the numerator and the denominator.

fraction numerator open parentheses x plus 1 close parentheses open parentheses x minus 3 close parentheses over denominator open parentheses x plus 1 close parentheses open parentheses 2 x minus 5 close parentheses end fraction equals fraction numerator x minus 3 over denominator 2 x minus 5 end fraction

To add or subtract algebraic fractions, find equivalent fractions so that both fractions have a common denominator.

2 over x plus fraction numerator x minus 2 over denominator x plus 1 end fraction equals fraction numerator 2 open parentheses x plus 1 close parentheses over denominator x open parentheses x plus 1 close parentheses end fraction plus fraction numerator x open parentheses x minus 2 close parentheses over denominator x open parentheses x plus 1 close parentheses end fraction equals fraction numerator 2 open parentheses x plus 1 close parentheses plus x open parentheses x minus 2 close parentheses over denominator x open parentheses x plus 1 close parentheses end fraction

To multiply algebraic fractions, multiply the numerators together and multiply the denominators together.

fraction numerator x over denominator x plus 1 end fraction cross times fraction numerator x minus 1 over denominator 4 end fraction equals fraction numerator x open parentheses x minus 1 close parentheses over denominator 4 open parentheses x plus 1 close parentheses end fraction

To divide algebraic fractions, multiply the first fraction by the reciprocal of the second fraction.

fraction numerator x over denominator x plus 1 end fraction divided by fraction numerator x minus 1 over denominator 4 end fraction equals fraction numerator x over denominator x plus 1 end fraction cross times fraction numerator 4 over denominator x minus 1 end fraction equals fraction numerator 4 x over denominator open parentheses x plus 1 close parentheses open parentheses x minus 1 close parentheses end fraction



Algebraic fractions revision resources to ace your exams

You can find out more about algebraic fractions, and working with them, by reading our revision notes. To test your knowledge, try our exam questions for algebraic fractions.

For quick-fire GCSE maths revision, use our collection of interactive flashcards for GCSE maths. We also have past papers for your exam practice.

Explore GCSE maths revision resources

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Dan Finlay

Author: Dan Finlay

Expertise: Maths Lead

Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.

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