Year 11 - Maths
Operations 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 multiply, divide, add and subtract with algebraic fractions.
Key Notes
- When multiplying/dividing, it can be easier to fully factorise every expression first.
- When dividing by an expression, it is equivalent to multiplying by the reciprocal of that expression.
- When adding/subtracting with algebraic fractions, a common denominator is required.
Vocabulary To Learn
- Reciprocal: The reciprocal is the multiplicative inverse of any non-zero number. Any non-zero number multiplied by its reciprocal is equal to 1
- Factorise: To factorise is to express a term as the product of its factors.
Common Mistakes To Avoid
- Trying to simplify a division calculation by identifying common factors before calculating.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
When multiplying/dividing, it can be easier to fully factorise every expression first. When dividing by an expression, it is equivalent to multiplying by the reciprocal of that expression.
2. Use this key word in a maths sentence and explain it clearly. 'Reciprocal'
The reciprocal is the multiplicative inverse of any non-zero number. Any non-zero number multiplied by its reciprocal is equal to 1. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Trying to simplify a division calculation by identifying common factors before calculating. Correction: Pupils need to understand why this works with multiplication questions to understand why this does not work with division. Encourage pupils to write their division as a multiplication of the reciprocal before identifying common factors.
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
- Problem solving with advanced algebraic fractions Study Guide
- Simplifying algebraic fractions Study Guide
- Solving equations with algebraic fractions Study Guide
Browse all guides in the Year 11 Maths guide library.