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
Revision 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

Teaching in a Bubble

Practical tips and advice for preparing to teach in year group bubbles.

Problem Solving – Perimeter and Area

Students are challenged to apply the rules of arithmetic to a series of real-life, functional problems.

Behaviour Management in a Mathematics Lesson

As we approach the start of the next term I thought I would share some tips on behaviour management in a mathematics lesson. These are things that I have picked up over the years and have worked well for me. I am sure there are opposing viewpoints and you may find some of these tips […]