Percentage change 1 Revision Notes for Edexcel GCSE Maths

Percentage change 1

When you need to increase or decrease an amount by a percentage, there are two main methods you can use. Both methods will give you the same answer, so choose the one that works best for you.

Method 1: Direct calculation

This method involves working out the actual amount of change first, then applying it to the original value. This approach is particularly useful when you want to see the exact amount of change before applying it.

For a decrease:

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

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Worked Example: Decreasing an Amount

Decrease £280 by 26%

Step 1: Work out 26% of £280 $(26 ÷ 100) × £280 = £72.80$

Step 2: Subtract the decrease $£280 − £72.80 = £207.20$

Method 2: Using multipliers

This method uses a single calculation by converting the percentage change into a multiplier. This approach is often faster and more efficient, especially for multiple calculations.

For an increase:

Add the percentage increase to 100%
Convert this to a decimal by dividing by 100
Multiply the original amount by this decimal

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Worked Example: Increasing with Multipliers

Increase 400g by 30%

Step 1: Add percentage to 100% $100\% + 30\% = 130\%$

Step 2: Convert to decimal $130 ÷ 100 = 1.3$

Step 3: Apply the multiplier $400g × 1.3 = 520g$

For a decrease:

Subtract the percentage decrease from 100%
Convert this to a decimal
Multiply the original amount by this decimal

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The multiplier method is particularly useful when you need to apply the same percentage change to multiple values, as you only need to calculate the multiplier once.

Worked example

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Worked Example: Annual Price Increase

A football club increases season ticket prices by 5.2% each year. In 2011, a top-price season ticket cost £650. What will the price be in 2012?

Using Method 2 (Multipliers):

Step 1: Calculate the multiplier $100\% + 5.2\% = 105.2\%$ $105.2 ÷ 100 = 1.052$

Step 2: Apply the multiplier $£650 × 1.052 = £683.80$

Answer: The price in 2012 will be £683.80

Important rules for money calculations

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Critical Money Calculation Rules:

When working with money, you must give your answer to 2 decimal places. Always check your answer makes sense - a small percentage increase should result in a small increase to the original amount.

Remember: £1.2 should be written as £1.20 in your final answer.

Calculating percentage increase or decrease

Sometimes you need to work backwards to find what percentage change has occurred. This is particularly useful for analysing real-world changes in prices, quantities, or measurements.

Steps:

Work out the amount of increase or decrease
Write this as a percentage of the original amount

Formula: $\text{Percentage Change} = \frac{\text{Amount of change}}{\text{Original amount}} × 100$

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Worked Example: Finding Percentage Decrease

An item was originally £60, now costs £39. What is the percentage decrease?

Step 1: Work out the amount of decrease $£60 − £39 = £21$

Step 2: Calculate as a percentage of original amount $\frac{£21}{£60} × 100 = 35\%$

Answer: This is a 35% decrease

Exam tips

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Exam Success Strategies:

Calculator questions: Use your calculator efficiently rather than trying mental methods
Check your work: Use common sense to verify your answers are reasonable
Percentage vs amount: Make sure you understand whether the question asks for a percentage or an amount
Show your working: Always show clear steps in your calculations - this can earn you partial marks even if your final answer is incorrect

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Key Points to Remember:

Two methods available: Direct calculation or multipliers - choose what works for you
Money answers: Always give money answers to 2 decimal places
Multipliers for increases: Add percentage to 100%, then divide by 100
Multipliers for decreases: Subtract percentage from 100%, then divide by 100
Finding percentage change: $\frac{\text{Change}}{\text{Original}} × 100$
Check answers: Use common sense to verify your results are reasonable

Percentage change 1 (Edexcel GCSE Maths): Revision Notes