Percentage Change & Reverse Percentages — GCSE Mathematics Revision
Revise Percentage Change & Reverse Percentages for GCSE Mathematics. Step-by-step explanation, worked examples, common mistakes and exam-style practice aligned to AQA, Edexcel, OCR, WJEC, Eduqas, CCEA, Cambridge International (CIE), SQA, IB, AP.
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Go to Ratio of AmountsWhat is Percentage Change & Reverse Percentages?
Percentage change = (change ÷ original) × 100. A percentage increase of 20% means multiplying by 1.20. A percentage decrease of 15% means multiplying by 0.85. Reverse percentages work backwards: if a price after a 20% increase is £60, the original was £60 ÷ 1.20 = £50. The key insight is that the amount after the change represents a specific percentage of the original.
Step-by-step explanationWorked example
A jacket costs £84 after a 30% reduction. Find the original price. £84 represents 70% (100% - 30%). Original = £84 ÷ 0.70 = £120.
Mini lesson for Percentage Change & Reverse Percentages
1. Understand the core idea
Percentage change = (change ÷ original) × 100. A percentage increase of 20% means multiplying by 1.
Can you explain Percentage Change & Reverse Percentages without copying the notes?
2. Turn it into marks
A jacket costs £84 after a 30% reduction. Find the original price.
Underline the method, evidence, or command-word move that would earn credit in GCSE Number.
3. Fix the likely mark leak
Watch for this mistake: Dividing by the new amount instead of the original when calculating percentage change.
Write one correction rule before doing another practice question.
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Percentage Change & Reverse Percentages practice questions
These are original StudyVector questions for revision practice. They are not official exam-board questions.
Question 1
In one GCSE sentence, explain what Percentage Change & Reverse Percentages is testing.
Answer: Percentage change = (change ÷ original) × 100. A percentage increase of 20% means multiplying by 1.
Mark focus: Precise definition and topic focus.
Question 2
A student sees a Percentage Change & Reverse Percentages question but is not sure how to start. What should the first method line establish?
Answer: It should identify the rule, equation, diagram feature, or transformation before any calculation. That protects method marks and makes later checking easier.
Mark focus: Method selection and command-word control.
Question 3
A student makes this mistake: "Dividing by the new amount instead of the original when calculating percentage change." What should their next repair task be?
Answer: Do one Percentage Change & Reverse Percentages question and review the mistake type.
Mark focus: Error correction and next-step practice.
Percentage Change & Reverse Percentages flashcards
Core idea
What is the main idea in Percentage Change & Reverse Percentages?
Percentage change = (change ÷ original) × 100. A percentage increase of 20% means multiplying by 1.
Common mistake
What mistake should you avoid in Percentage Change & Reverse Percentages?
Dividing by the new amount instead of the original when calculating percentage change.
Practice
What is one useful practice task for Percentage Change & Reverse Percentages?
Answer one Percentage Change & Reverse Percentages question and review the mistake type.
Exam board
How should you use board notes for Percentage Change & Reverse Percentages?
Use your own GCSE specification for exact paper wording and depth.
Common mistakes
- 1Dividing by the new amount instead of the original when calculating percentage change.
- 2In reverse percentages, taking the percentage of the new amount instead of dividing by the multiplier.
- 3Confusing percentage increase with percentage of — a 20% increase on £50 is £60, not £10.
- 4Not using the multiplier method for repeated percentage changes (compound changes).
Percentage Change & Reverse Percentages exam questions
Exam-style questions for Percentage Change & Reverse Percentages with mark-scheme style solutions and timing practice. Aligned to AQA, Edexcel, OCR, WJEC, Eduqas, CCEA, Cambridge International (CIE), SQA, IB, AP specifications.
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Step-by-step method
Step-by-step explanation
4 steps · Worked method for Percentage Change & Reverse Percentages
Core concept
Percentage change = (change ÷ original) × 100. A percentage increase of 20% means multiplying by 1.20. A percentage decrease of 15% means multiplying by 0.85. Reverse percentages work backwards: if a …
Frequently asked questions
How do I find the percentage change between two values?
Percentage change = ((new - original) / original) × 100. A positive result means an increase, negative means a decrease.
What is a reverse percentage?
When you know the final amount after a percentage change and need to find the original. Divide the final amount by the multiplier (e.g. divide by 1.2 for a 20% increase, or by 0.85 for a 15% decrease).