GCSE Maths • Foundation & Higher
GCSE Rearranging Formulae Revision Guide
Change the subject confidently using balanced inverse operations.
Foundation
Exam practice
Inverse Operations
What You'll Learn
Identify the Subject
Recognise which variable is currently isolated and which variable must become the new subject.
Use Inverse Operations
Undo addition, subtraction, multiplication, division, powers and roots while keeping equality.
Rearrange Fractions
Clear denominators safely and isolate variables in numerator or denominator positions.
Handle Brackets
Choose whether to keep a useful factorised form or expand before collecting terms.
Deal with Powers and Roots
Apply appropriate roots or powers and state contextual sign restrictions.
Collect the New Subject
Factorise when the required variable occurs in more than one term.
Key Rules and Formulas
Rearranging Formulae Lessons
Advanced Rearranging
Rearrange multi-step formulae involving fractions, brackets, powers, roots and repeated variables.
Basic Rearranging
Use balanced inverse operations to isolate a variable in straightforward equations and formulae.
CORE SUBTOPICS
One-Step Rearranging
Undo one addition, subtraction, multiplication or division.
Multi-Step Rearranging
Reverse the order of operations around the new subject.
Algebraic Fractions
Clear denominators before isolating the subject.
Brackets and Factorising
Preserve helpful brackets or collect and factorise repeated subject terms.
Powers and Roots
Use inverse powers and interpret plus-or-minus solutions correctly.
Checking Equivalence
Reverse the manipulation or substitute admissible values into both forms.
Worked Example
Required Variable Appearing Twice
QUESTION
Make x the subject of y = ax + bx + c.
- Given information: The x-terms share a common factor. The final division requires a+b ≠ 0.
- Method: Move the term without x, factorise x, then divide by its complete coefficient.
- Subtract c from both sides: y - c = ax + bx.
- Factorise the right side: y - c = x(a + b).
- Divide both sides by a + b: x = (y - c)/(a + b).
- State the condition: a + b ≠ 0.
- Check by substituting: ax + bx + c = x(a+b)+c = y-c+c = y.
- Final answer: x = (y - c)/(a + b), where a + b ≠ 0.
- Independent answer check: Substitution returns the original left side y.
- One common mistake: Do not divide by a and b separately; factorise x first.
- Common GCSE Mistakes
- Changing Only One Side
- Using the Wrong Inverse
- Losing Brackets
- Dividing by a Variable Without a Condition
- Ignoring Both Square-Root Solutions
- Stopping Before the Subject Is Isolated
- Exam Tips
- Circle the variable that must become the subject.
- Write each balanced operation on a separate line.
- Undo operations in reverse order.
- Clear a denominator by multiplying every term on both sides.
- Factorise if the new subject appears in more than one term.
- Check by reversing the steps or substituting valid values.
Ready to Practice?
Printable Worksheet
Practise one-step, multi-step, fractional and factorising rearrangements.
Interactive Quiz
Test your knowledge with instant feedback and hints.
Exam-Style Questions
Timed questions to build confidence for the real exam.
Watch the Rearranging Formulae Tutorial
Clear, step-by-step explanation of expanding brackets, simplifying complex expressions, and solving for x. Perfect for visual learners who need a breakdown of the rules in action.
- 12 minute comprehensive guide
- High-definition whiteboard walk-through
Continue Your GCSE Maths Revision
Continue Your GCSE Maths Revision
Frequently Asked Questions
It is the variable isolated on one side of the equals sign.
To expand a single bracket, multiply the term outside the bracket by each term inside the bracket. For example, 3(x + 4) becomes 3 × x + 3 × 4, which simplifies to 3x + 12.
Multiply both sides by the denominator, simplify, then continue isolating the required variable.
Expand when it helps collect repeated subject terms; otherwise keeping a bracket may make the inverse operations clearer.
Algebraically an even power may produce two roots. Context can restrict the value, such as a radius being non-negative.
Reverse the algebra or substitute admissible values into the original and rearranged forms and compare the results.
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