Percentages (Edexcel GCSE Maths): Revision Notes
Percentages - GCSE revision guide
Introduction
Percentages are one of the most important mathematical concepts you'll encounter in your GCSE. There are different types of percentage questions, ranging from simple calculations to more complex problems involving original values and interest calculations. Understanding the proper method for each type is crucial for success.
Mastering percentages is essential for GCSE success as they appear across multiple topics including business studies, science, and everyday mathematics. The key is recognising which type of question you're dealing with and applying the correct method consistently.
Simple percentage calculations
Type 1: Finding x% of y
This is the most straightforward type of percentage question. The method is simple and consistent every time.
Method:
- Convert the percentage to a decimal by dividing by 100
- Multiply this decimal by the given amount
Worked Example: Finding 15% of £46
Step 1: Convert 15% to decimal
Step 2: Multiply by the amount
Therefore, 15% of £46 is £6.90
Type 2: Finding the new amount after a percentage increase or decrease
This type builds on Type 1 but requires an additional step to find the final amount.
Method:
- Convert the percentage to a decimal
- Multiply by the original amount to find the change
- Add the change to the original (for increase) or subtract it (for decrease)
Worked Example: Sale Price Calculation
A toaster originally costs £68 but is reduced by 40% in the sales. Find the new price.
Step 1: Convert 40% to decimal
Step 2: Find the reduction
Step 3: Subtract from original
Alternative method (Multiplier): , so
The multiplier method is often faster for percentage changes. For a 40% decrease, multiply by 0.6. For a 15% increase, multiply by 1.15.
Type 3: Expressing x as a percentage of y
This involves finding what percentage one amount represents of another.
Method:
- Ensure both amounts are in the same units
- Divide the first amount by the second amount
- Multiply by 100 to get the percentage
Worked Example: Converting to Percentage
Give 40p as a percentage of £3.34
Step 1: Convert to same units £3.34 = 334p
Step 2: Divide
Step 3: Multiply by 100
Therefore, 40p is 12.0% of £3.34
Advanced percentage problems
Type 1: Finding percentage change
This is where many students struggle because it requires understanding the relationship between the original value and the change.
The key formula for percentage change is:
Method:
- Calculate the actual change (difference between new and original values)
- Use the formula: Percentage change = (Change ÷ Original) × 100
- State whether it's an increase or decrease
Worked Example: Profit Calculation
A trader buys watches for £5 and sells them for £7. Calculate the percentage profit.
Step 1: Calculate profit Profit = £7 - £5 = £2
Step 2: Apply formula
This represents a 40% profit.
Critical Point: Always use the original value as the denominator in percentage change calculations, not the final value. This is a common source of errors.
Type 2: Finding the original value
This is often considered the trickiest type because you're working backwards from a changed value.
Method:
- Identify what percentage the given amount represents of the original
- Divide by this percentage to find 1% of the original
- Multiply by 100 to find the full original value (100%)
Worked Example: Original Value Calculation
A house increases in value by 20% to £72,000. Find the original value.
Step 1: Identify what percentage £72,000 represents £72,000 represents 120% of the original value (100% + 20%)
Step 2: Find 1%
Step 3: Find 100%
The original value was £60,000.
Key Tip: Always identify what percentage the given amount represents - it's never 100% in these questions! The given amount is always the result after the change has been applied.
Type 3: Simple interest calculations
Simple interest means the same amount of interest is earned each time period, calculated only on the original amount.
Method:
- Calculate the interest for one time period
- Multiply by the number of time periods
Worked Example: Simple Interest
Regina invests £380 at 3% simple interest per year for 4 years. Calculate the total interest earned.
Step 1: Interest per year
Step 2: Total interest over 4 years
Regina earns £45.60 in interest over 4 years.
Compound interest works differently and is typically covered separately, where interest is earned on both the original amount and previously earned interest. Simple interest only calculates interest on the original principal amount.
Worked examples from different contexts
Currency conversion example
When working with money, always ensure you're using the same units throughout your calculation. Converting pounds to pence or vice versa is often necessary for accurate results.
Profit and loss calculations
Business contexts frequently appear in percentage questions. Remember that profit is calculated as a percentage of the original cost price, not the selling price.
Property value changes
These problems often involve finding original values after percentage changes, which requires the reverse calculation method described above.
Common mistakes to avoid
Common Pitfalls to Avoid:
-
Forgetting to convert units - Always check that amounts are in the same units before calculating
-
Confusing original and final values - In reverse percentage problems, the given amount is never the original value
-
Mixing up increase and decrease - Pay careful attention to whether you're adding or subtracting the percentage change
-
Rounding too early - Keep full accuracy until the final step, then round appropriately
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Using the wrong value in percentage change - Always use the original value as the denominator, not the final value
Key Points to Remember:
- Type 1 (Find x% of y): Convert percentage to decimal, then multiply
- Type 2 (New amount after change): Calculate the change, then add or subtract from original
- Type 3 (x as percentage of y): Divide x by y, then multiply by 100
- Percentage change formula:
- Original value problems: The given amount represents more or less than 100% of the original - never exactly 100%
- Always check units are consistent throughout your calculations
- Practice identifying question types - this determines which method to use