GCSE MATHS • HIGHER TIER

Advanced Rearranging Made Simple

Manipulate complex formulae using inverse operations while keeping equations balanced.

Start Learning
Practice Questions
Download Worksheet

Clear method

Exam practice

Worked proofs

Advanced Rearranging in Four Moves

1

Identify

Decide which variable needs to become the subject.

2

Undo

Use inverse operations to remove terms in the correct order.

3

Isolate

Continue until the required variable is alone.

4

Check

Simplify and check the rearrangement carefully.

What You’ll Learn

Maintain Balance

Apply the same operation to both sides of an equation.

Use Inverse Operations

Undo addition, subtraction, multiplication, division, powers and roots.

Handle Fractions and Brackets

Choose efficient steps for more complex formulae.

Rearrange Powers and Roots

Use square roots or squaring when required.

Change the Subject

Make different variables the subject of real-world formulae.

Key Rules

Whatever operation is performed on one side of an equation must also be performed on the other side. This rule applies throughout every rearrangement question and ensures the equation remains balanced.

Worked Proof: Advanced Rearranging

Step-by-Step Method

  • 1. Decide which variable should become the subject.
  • 2. Remove brackets if necessary.
  • 3. Move addition and subtraction terms first.
  • 4. Move multiplication and division terms next.
  • 5. Deal with powers and roots last.
  • 6. Simplify the final answer.
  • 7. Check your rearrangement carefully.

More Worked Examples

1

Make x the subject of y = x + 8

Subtract 8 from both sides

y − 8 = x
Answer: x = y − 8

2

Make x the subject of y = 3x + 6

Subtract 6 first

y − 6 = 3x
Then divide by 3
x = (y − 6)/3

3

Make a the subject of b = 4a − 12

Add 12

b + 12 = 4a
Divide by 4
a = (b + 12)/4
Answer: a = (b + 12)/4

4

Make x the subject of y = √x

Square both sides

y² = x
Answer: x = y²
  • Common GCSE Mistakes
  • Balance: Perform every operation on both sides of the equation.
  • Order: Remove operations in a logical inverse order.
  • Signs: Take care when moving or undoing positive and negative terms.
  • Fractions: Handle denominators correctly before continuing the rearrangement.
  • Exam Tips
  • Identify the required subject before starting.
  • Write one algebraic change per line so your method is easy to follow.
  • Use inverse operations and keep both sides balanced.
  • Multiplying by a denominator can remove a fraction cleanly.
  • Deal with powers and roots after simpler operations where appropriate.
  • Check your result by substituting or reversing the rearrangement.

Skills Used in Advanced Rearranging

Inverse Operations

Changing the Subject

Algebraic Manipulation

Fractions

Brackets

Powers

Roots

Formulae

Substitution

Ready to Practise?

Printable Worksheet

Download and print practice questions with answers.

Open Resource

Interactive Quiz

Test your knowledge with instant feedback and hints.

Open Resource

Exam-Style Questions

Timed questions to build confidence for the real exam.

Open Resource

Watch the Advanced Rearranging Tutorial

Step-by-step walkthroughs of Advanced Rearranging with clear methods and exam tips.

Watch Video

Frequently Asked Questions

It is changing the subject of more complex equations involving several algebraic operations.

Whatever operation is performed on one side must also be performed on the other side.

The source method moves addition and subtraction first, then multiplication and division, and deals with powers and roots last.

It is often useful to multiply both sides by the denominator first.

Square both sides of the equation.

The source recommends checking carefully and, during revision, substituting back into the original formula.