Percentage change 1 Revision Notes for AQA GCSE Maths

Percentage change 1

Percentage changes are used to increase or decrease amounts by a given percentage. There are two main methods you can use to calculate these changes, and you also need to know how to find what percentage change has occurred.

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Understanding percentage changes is essential for many real-world applications, from calculating discounts and price increases to analysing data changes over time.

Method 1: Traditional calculation

This method involves calculating the percentage amount first, then adding or subtracting it from the original amount.

For a decrease:

Calculate the percentage of the original amount
Subtract this from the original amount

For an increase:

Calculate the percentage of the original amount
Add this to the original amount

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Worked Example: 26% Discount Calculation

The example shows a 26% discount on £280:

First calculate 26% of £280: $(26 \div 100) \times £280 = £72.80$
Then subtract: $£280 - £72.80 = £207.20$

Method 2: Multiplier method

This method uses multipliers to calculate percentage changes in one step. It's often quicker and reduces the chance of errors.

For increases:

Add the percentage to 100% to find the multiplier
Example: 30% increase = 100% + 30% = 130% = 1.3

For decreases:

Subtract the percentage from 100% to find the multiplier
Example: 26% decrease = 100% - 26% = 74% = 0.74

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Worked Example: 30% Increase Using Multipliers

The example shows a 30% increase on 400g:

Multiplier = 1.3
New amount = $400g \times 1.3 = 520g$

Calculating percentage increase or decrease

When you need to find what percentage change has occurred, use this method:

Formula: $\text{Percentage change} = \left(\frac{\text{Change}}{\text{Original amount}}\right) \times 100\%$

Steps:

Find the change by subtracting (new amount - original amount)
Divide the change by the original amount
Multiply by 100% to get the percentage

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Worked Example: Finding Percentage Decrease

The example shows a price change from £60 to £39:

Change = $£60 - £39 = £21$
Percentage = $\left(\frac{£21}{£60}\right) \times 100\% = 35\%$
This is a 35% decrease

Working with money

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When working with money, you must give your answer to 2 decimal places.

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Exam tip: Check your answer by using an easier percentage that's close to the one in the question.

For example, if calculating 5.2% of £650, you could check by calculating 5% of £650 = £32.50, so your answer should be close to this amount.

Key tips for percentage changes

Increases result in multipliers greater than 1
Decreases result in multipliers less than 1
Always identify whether you're finding a percentage change or applying one
Questions might ask for percentage profit or percentage loss rather than increase or decrease
Use the multiplier method when possible as it reduces calculation steps

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Key Points to Remember:

Method 1: Calculate the percentage amount, then add or subtract it
Method 2: Use multipliers (more efficient for most calculations)
Finding percentage change: $\left(\frac{\text{Change}}{\text{Original amount}}\right) \times 100\%$
Money answers must have 2 decimal places
Check your work using easier percentages close to the given value

Percentage change 1 (AQA GCSE Maths): Revision Notes