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Year 11 - Maths

Checking and securing understanding of solving with simple algebraic fractions

Algebraic fractions

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 solve equations involving simple algebraic fractions.

Key Notes

  • The product of a number and its reciprocal is 1
  • The product of a term and its reciprocal is 1
  • Equivalence can be maintained by multiplying the connected statements by the same reciprocal.
  • This step can help you simplify an equation so you can solve it.

Vocabulary To Learn

  • Solution: A solution to an equality with one variable is a value which, when substituted, maintains the equality between the expressions.
  • Reciprocal: The reciprocal is the multiplicative inverse of any non-zero number. Any non-zero number multiplied by its reciprocal is equal to 1

Common Mistakes To Avoid

  • When solving equations with fractional coefficients, pupils may divide by the reciprocal rather than multiply. E.g. $$\\frac{1}{2}x = 8$$ pupils may just halve $$8$$

3 Quick Questions (With Answers)

1. Solve this in steps: explain the method from this lesson and why each step matters.

The product of a number and its reciprocal is 1. The product of a term and its reciprocal is 1.

2. Use this key word in a maths sentence and explain it clearly. 'Solution'

A solution to an equality with one variable is a value which, when substituted, maintains the equality between the expressions. Use this word when showing your method, then check your final answer is reasonable.

3. Spot and fix this common maths mistake.

Mistake: When solving equations with fractional coefficients, pupils may divide by the reciprocal rather than multiply. E.g. $$\\frac{1}{2}x = 8$$ pupils may just halve $$8$$. Correction: Start with integer coefficients, and get pupils used to the idea of multiplying by the reciprocal (not just dividing by the coefficient). This step should be written as part of the working. Answers can be checked by substitution.

More Lessons In This Unit

Browse all guides in the Year 11 Maths guide library.