Simplifying Algebraic Fractions Worksheet

Simplifying algebraic fractions at a glance

Algebraic fractions are fractions where the numerator, denominator, or both are algebraic expressions. Algebraic fractions can be simplified by finding common factors between the numerator and denominator and cancelling them. These common factors could be integers or algebraic expressions.  Algebraic fractions are in their simplest form when there are no more common factors between the numerator and denominator. 

Often we will need to factorise the numerator and/or denominator in order to identify common factors. Algebraic fractions can consist of linear expressions, quadratic expressions or other expressions involving larger indices.

As well as simplifying single algebraic fractions, we can simplify expressions involving adding/subtracting/multiplying/dividing algebraic fractions. The same rules apply here as with numeric fractions. For example, to add or subtract algebraic fractions, we first need to write the fractions with a common denominator. We can then add/subtract the numerators giving a single fraction. 

Being able to work confidently with algebraic fractions is a skill that will come in useful for A Level maths.

Looking forward, students can then progress to additional simplifying expressions worksheets and other algebra worksheets, for example a sequences worksheet, simultaneous equations worksheet or straight line graphs worksheet.

For more teaching and learning support on Algebra our GCSE maths lessons provide step by step support for all GCSE maths concepts.