Simplifying Algebraic Fractions (WJEC GCSE Maths & Numeracy (Double Award): Foundation): Revision Note

Simplifying algebraic fractions

What is an algebraic fraction?

• An algebraic fraction is a fraction with an algebraic expression on the top (numerator) and/or the bottom (denominator)

How do you simplify an algebraic fraction?

• If possible, factorise fully the top and bottom

  • E.g. $\frac{2x-4}{4x-10}=\frac{2\left(x-2\right)}{2\left(2x-5\right)}$

• Cancel common factors

  • This factor may be a single number or letter

    • E.g. $\frac{\cancel{2}\left(x-2\right)}{\cancel{2}\left(2x-5\right)}=\frac{\left(x-2\right)}{\left(2x-5\right)}$

    • The final answer is $\frac{x-2}{2x-5}$

• A common mistake is to cancel a factor that is not common to all terms in either the top or the bottom of a fraction

  • E.g. The fraction $\frac{6x}{x+1}$ cannot be simplified

    • $x$ is not common to all terms in the bottom of the fraction

    • i.e. you cannot factorise an $x$ out of the bottom

• You may need to use laws of indices to help simplify algebraic fractions

  • E.g. $\frac{6z^7}{2z^3}$ can be simplified using the fact that $\frac{z^7}{z^3}=z^{7-3}=z^4$ and $\frac{6}{2}=3$

    • $\frac{6z^7}{2z^3}=3z^4$