Year 11 - Maths
Solving equations with algebraic fractions
Algebraic fractions
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This pupil-friendly study guide includes a unit summary, clear notes, common mistakes, and quick questions with answers.
Unit Summary
In this unit, pupils apply skills in manupulating and solving various equations and formulae to algebraic fractions in order to change the subject and manipulate them.
Lesson Summary
You will learn to manipulate and solve equations involving algebraic fractions.
Key Notes
- Before performing any operation, equivalent fractions should be considered.
- Algebraic fractions follow the same rules as fractions.
- It is important to maintain equivalence between two algebraic statements.
- Multiplying both connected statements by the reciprocal can simplify.
Vocabulary To Learn
- Factorise: To factorise is to express a term as the product of its factors.
- Quadratic formula: The quadratic formula is a formula for finding the solutions to any quadratic equation of the form $$ax^2 + bx + c = 0$$
Common Mistakes To Avoid
- Assuming that 'cross multiplying' is always the best way to solve equations with fractions on both sides.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
Before performing any operation, equivalent fractions should be considered. Algebraic fractions follow the same rules as fractions.
2. Use this key word in a maths sentence and explain it clearly. 'Factorise'
To factorise is to express a term as the product of its factors. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Assuming that 'cross multiplying' is always the best way to solve equations with fractions on both sides. Correction: Examples are included in the lesson where this results in unnecessary quadratic equations. Factorising and looking for common factors allows pupils to spot efficient methods. This also links with fraction skills of finding a common denominator.
More Lessons In This Unit
- Changing the subject where the variable appears in multiple terms Study Guide
- Changing the subject with multiple algebraic fractions Study Guide
- Checking and securing understanding of changing the subject with simple algebraic fractions Study Guide
- Checking and securing understanding of solving with simple algebraic fractions Study Guide
- Operations with algebraic fractions Study Guide
- Problem solving with advanced algebraic fractions Study Guide
- Simplifying algebraic fractions Study Guide
Browse all guides in the Year 11 Maths guide library.