EDEXCEL GCSE HIGHER MATHS - What are Percentages and Percentage Changes

Edexcel GCSE Higher Maths - Percentages and Percentage Changes

What are Percentages?

A percentage is a way of expressing a part of a whole as a fraction out of 100. The symbol for percentage is %.

Example: 50% means 50 out of 100, which is equivalent to the fraction 50/100 or the decimal 0.5.

Calculating Percentages

1. Using a calculator:

• Divide the part by the whole and multiply by 100.

For example, to find what percentage 15 is of 60:

(15 / 60) * 100 = 25%

2. Without a calculator:

• Find the equivalent fraction out of 100.

For example, to find what percentage 3 is of 20: * Simplify the fraction 3/20 to 15/100. * Therefore, 3 is 15% of 20.

Finding a Percentage of a Number

1. Using a calculator:

• Multiply the number by the percentage and divide by 100.

For example, to find 20% of 150:

(20 * 150) / 100 = 30

2. Without a calculator:

• Convert the percentage to a decimal or fraction.

For example, to find 30% of 80: * Convert 30% to the decimal 0.3. * Multiply 0.3 by 80, which equals 24.

Percentage Change

Percentage change is a way of expressing how much a quantity has increased or decreased compared to its original value.

Formula:

Percentage change = (New value - Original value) / Original value * 100%

Example: If the original price of a product was £50 and it is now £60, the percentage increase is:

(60 - 50) / 50 * 100% = 20%

Types of Percentage Change:

• Percentage increase: When the new value is greater than the original value.
• Percentage decrease: When the new value is less than the original value.

Reverse Percentage Calculations

Sometimes, you may need to find the original value when you know the new value and the percentage change.

Example: If a price is increased by 20% to £60, what was the original price?

• Let the original price be x.
• Increased price = x + 0.2x = 1.2x
• 1.2x = £60
• x = £60 / 1.2 = £50

Therefore, the original price was £50.

Key Points to Remember

• Percentages are a way of representing fractions out of 100.
• You can calculate percentages using a calculator or without one.
• Percentage change is a way of expressing how much a quantity has changed compared to its original value.
• Reverse percentage calculations involve working backwards to find the original value.

Practice regularly to improve your understanding and confidence in dealing with percentages and percentage changes.