Percentage change 2 (Edexcel GCSE Maths): Revision Notes
Percentage change 2
Understanding percentage change
When dealing with percentage changes, you need to master calculations without a calculator. There are two main types of percentage change:
- Percentage increase - the value goes up (e.g. adding VAT, pay rises, interest)
- Percentage decrease - the value goes down (e.g. sales discounts, depreciation)
The Key Rule to Remember:
- For increases: add the percentage to the original amount
- For decreases: subtract the percentage from the original amount
Calculating percentages without a calculator
You can work out percentages efficiently by using multiples of 1% and 10%. This method breaks down complex percentages into simpler calculations.
Step-by-step method
- Find 10% by dividing the original number by 10
- Find 1% by dividing the original number by 100
- Find 0.5% by halving the 1% value
- Combine these to reach your target percentage
Worked Example: Finding 12.5% of £600
To find 12.5% of £600:
- 10% of £600 = £60 (600 ÷ 10)
- 1% of £600 = £6 (600 ÷ 100)
- 0.5% of £600 = £3 (6 ÷ 2)
- 12.5% = 10% + 1% + 1% + 0.5% = £60 + £6 + £6 + £3 = £75
Worked example - comparing prices
When comparing products with different percentage changes, you must calculate the final price for each item and then compare.
Worked Example: Television Price Comparison
Television A: £440 + 20% VAT
Television B: £550 with 25% discount
For Television A:
- 10% of £440 = £44
- 20% = £44 × 2 = £88
- Final price = £440 + £88 = £528
For Television B:
- 1% of £550 = £5.50
- 0.5% of £550 = £2.75
- 25% = £5.50 + £5.50 + £5.50 + £5.50 + £2.75 = £22.75
- Final price = £550 - £22.75 = £527.25
Conclusion: Television A is cheaper by 75p.
Types of percentage changes
Percentage increases
Common examples include:
- Interest on savings or loans
- Pay rises for employees
- VAT added to purchases
Percentage decreases
Common examples include:
- Sales discounts in shops
- Depreciation of assets over time
- Reductions in prices
Understanding the context of percentage changes helps you identify whether you're dealing with an increase or decrease, which determines whether you add or subtract the calculated percentage.
Essential Exam Tips:
- Show your working clearly - marks are awarded for method even if the final answer is wrong
- Give reasons for your conclusions when comparing options
- Use correct units throughout your calculations
- Write your conclusion in words - don't just circle the cheaper option
- Be prepared - percentage change questions appear frequently in GCSE exams
Key Points to Remember:
- Add for increases, subtract for decreases - this fundamental rule applies to all percentage change calculations
- Use multiples of 1% and 10% to calculate percentages without a calculator efficiently
- Always show your working step-by-step in exam questions for maximum marks
- Compare final amounts when deciding which option is better value
- Write conclusions in words rather than just giving numerical answers