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

In foundation tier, the denominators when adding or subtracting algebraic fractions are always numbers, not letters.

(a) Express $\frac{5y}{8}-\frac{3y}{10}$ as a single fraction.

Answer:

Write the fractions over the lowest common denominator

The lowest common denominator of 8 and 10 is 40

You could also write them with a common denominator of 80, but this makes the numbers slightly harder to work with

$$\begin{gathered} \frac{5y\left(5\right)}{8\left(5\right)}-\frac{3y\left(4\right)}{10\left(4\right)} \\ \frac{25y}{40}-\frac{12y}{40} \end{gathered}$$

Write as a single fraction

$\frac{25y-12y}{40}$

Simplify

$\frac{13y}{40}$

Check if the answer can be simplified

In this case the answer does not simplify any further (as 13 is prime)

$\frac{13y}{40}$

(b) Express $\frac{2x+7}{4}-\frac{x-3}{6}$ as a single fraction.

Answer:

Write the fractions over the lowest common denominator

The lowest common denominator of 4 and 6 is 12

You could also write them with a common denominator of 24, but this makes the numbers slightly harder to work with

$\frac{\left(2x+7\right)\left(3\right)}{4\left(3\right)}-\frac{\left(x-3\right)\left(2\right)}{6\left(2\right)}$

Simplify, being careful to expand each term in the numerators

$\frac{6x+21}{12}-\frac{2x-6}{12}$

Write as one fraction

To help avoid mistakes when dealing with the subtraction, use brackets around the numerator of each fraction

$\frac{\left(6x+21\right)-\left(2x-6\right)}{12}$

Simplify the numerator, being careful with the subtraction

$\frac{6x+21-2x+6}{12}$

$\frac{4x+27}{12}$

Check if the answer can be simplified

4 and 12 share a factor of 4, but 27 does not have a factor of 4

So this cannot be further simplified

$\frac{4x+27}{12}$