GCSE MATHS • HIGHER TIER
Changing the Subject of a Formula Made Simple
Learn how to rearrange formulas so a different variable becomes the subject, using inverse operations, fractions, powers and roots.
Clear method
Exam practice
Worked proofs
Changing the Subject in Four Moves
1
Identify
Identify the variable you want to make the subject.
2
Undo
Remove additions and subtractions first.
3
Isolate
Remove multiplication, division, powers or roots as needed.
4
Check
Make sure the required variable is alone on one side.
What You’ll Learn
Understand the Subject
Recognise which variable is currently isolated in a formula.
Use Inverse Operations
Undo operations in the correct order while keeping both sides balanced.
Rearrange Fractions
Clear denominators before isolating the required variable.
Rearrange Powers
Use roots to undo powers where necessary.
Check Rearrangements
Confirm that the required variable is isolated correctly.
Key Rules
What Does 'Changing the Subject' Mean?
The subject of a formula is the variable that is isolated on one side of the equation. For example, in the formula y = 3x + 5, the subject is y. Changing the subject means rearranging the formula so that another variable, such as x, becomes the subject.
The Golden Rule of Rearranging
When changing the subject of a formula, whatever operation is performed on one side of the equation must also be performed on the other side. This keeps the equation balanced.
Worked Proof: Changing the Subject of a Formula
Step-by-Step Method
- 1. Identify the variable you want to make the subject.
- 2. Remove additions and subtractions first.
- 3. Remove multiplications and divisions next.
- 4. Remove powers and roots last.
- 5. Check that the required variable is isolated.
More Worked Examples
1
Question: Make x the subject of y = x + 7.
Subtract 7 from both sides.
y - 7 = x
Answer: x = y - 7.
Answer: x = y - 7.
2
Question: Make x the subject of y = 3x.
Divide both sides by 3.
y/3 = x
Answer: x = y/3.
Answer: x = y/3.
3
Question: Make x the subject of y = 2x + 5.
Subtract 5.
y - 5 = 2x
Divide by 2.
x = (y - 5)/2
Divide by 2.
x = (y - 5)/2
4
Question: Make t the subject of d = vt.
Divide by v.
t = d/v
Answer: t = d/v.
Answer: t = d/v.
- Common GCSE Mistakes
- One side only: Apply every operation to both sides.
- Wrong inverse: Use the operation that undoes the original one.
- Fractions: Clear denominators carefully before rearranging.
- Powers: Use the correct root to undo a power.
- Powers: Use the correct root to undo a power.
- Exam Tips
- Identify the target first: Know which variable must become the subject.
- Undo in stages: Remove additions before multiplication or division.
- Show every step: Keep the rearrangement easy to follow.
- Watch brackets and fractions: Keep grouped terms together.
- Check the final form: The subject should be isolated.
Skills Used in Changing the Subject of a Formula
Substitution into Formulae
Algebra
Equations
Expanding Bracketsv
Factorising
Formulae
Graphs
Geometry
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Printable Worksheet
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Exam-Style Questions
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Watch the Changing the Subject of a Formula Tutorial
Step-by-step walkthroughs of Changing the Subject of a Formula with clear methods and exam tips.
Frequently Asked Questions
The subject is the variable that is isolated on one side of the formula.
It means rearranging the formula so that a different variable is isolated.
Usually remove additions and subtractions before multiplication and division.
Multiply by the denominator first to remove the fraction.
Isolate the squared variable first, then take the square root.
Make sure the required variable is alone and, where useful, substitute values to verify equivalence.
