Working with Algebraic Fractions

Students learn how to simplify and perform addition, subtraction, multiplication and division with algebraic fractions.  As learning progresses they combine these skills to solve equations with algebraic fractions using the quadratic formula.  This unit takes place in Term 2 of Year 11 and follows on from solving quadratic equations.


Working with Algebraic Fractions Lessons


Prerequisite Knowledge
  • Solve linear equations in one unknown algebraically(including those with the unknown on both sides of the equation)
  • Apply the four operations, including formal written methods, simple fractions (proper and improper)
  • Calculate exactly with fractions
  • Simplify and manipulate algebraic expressions by factorising quadratic expressions of the form ax2 + bx + c

Success Criteria
  • Simplify and manipulate algebraic fractions by:
    • collecting like terms
    • multiplying a single term over a bracket
    • taking out common factors
    • expanding products of two or more binomials
    • simplifying expressions involving sums, products and powers, including the laws of indices
  • Know the difference between an equation and an identity; argue mathematically to show algebraic expressions are equivalent, and use algebra to support and construct arguments and proofs
    solve quadratic equations (including those that require rearrangement) algebraically by factorising, by completing the square and by using the quadratic formula


Key Concepts
  • Students need to apply the same numerical techniques with algebraic fractions as they have done with numerical ones.
  • Like numerical fractions algebraic fractions need to have a common denominator when performing addition or subtraction.
  • Simplifying algebraic fractions involves factorising the expression into either one or more brackets.
  • Multiply the fractions through by a common denominator to cancel out the division when solving fractions.

Common Misconceptions
  • Students who understand the need for common denominators when adding or subtracting fractions are often let down by their poor algebraic skills. Particularly when multiplying out by a negative.
  • When attempting to simplify fractions students tend to cancel down incorrectly thus losing marks for final accuracy.
  • Students can forget to use the difference of two squares when finding common denominators.
  • Students struggle with factorising quadratics when the coefficient of x2 is greater than one.
  • It is common for students to try and solve for the unknown when they have only been asked to simplify.

Leave a Reply

Your email address will not be published. Required fields are marked *

You may use these HTML tags and attributes:

<a href="" title=""> <abbr title=""> <acronym title=""> <b> <blockquote cite=""> <cite> <code> <del datetime=""> <em> <i> <q cite=""> <s> <strike> <strong>

This site uses Akismet to reduce spam. Learn how your comment data is processed.

Mr Mathematics Blog

Mathematics OFSTED Inspection – The Deep Dive

Earlier this week, my school took part in a trial OFSTED inspection as part of getting ready for the new inspection framework in September 2019. This involved three Lead Inspectors visiting our school over the course of two days. The first day involved a ‘deep dive’ by each of the Lead Inspectors into Mathematics, English […]

How to Solve Quadratics by Factorising

The method of how to solve quadratics by factorising is now part of the foundational knowledge students aiming for higher exam grades are expected to have.   Here is an example of such a question. Solve x2 + 7x – 18 = 0 In my experience of teaching and marking exam papers students often struggle with […]

How Write 3 Part Ratios

When learning how to write 3-part ratios students need to understand how ratios can be made equivalent. The start of the lesson reminds students by asking which of six ratios is the odd one out.  This is presented to the class as they come into the lesson.    Writing Equivalent Ratios  A few students immediately go […]