OCR GCSE Maths: Calculating Percentages and Percentage Change

OCR GCSE Maths: Mastering Percentages and Percentage Change

This tutorial will guide you through the essential skills of calculating percentages and percentage change, equipping you to tackle real-life applications like discounts, simple interest, and original value problems.

Calculating a Percentage of a Quantity

1. Understanding Percentages:

A percentage represents a part out of a hundred. The symbol "%" signifies "out of one hundred".

2. Conversion to a Decimal:

To calculate a percentage of a quantity, first convert the percentage into a decimal. This is done by dividing the percentage by 100.

• Example: 25% = 25/100 = 0.25

3. Multiplication:

Multiply the decimal form of the percentage by the given quantity.

• Example: Find 25% of 80.
• 25% = 0.25
• 0.25 x 80 = 20

Therefore, 25% of 80 is 20.

Expressing One Quantity as a Percentage of Another

1. Division:

Divide the smaller quantity by the larger quantity.

2. Multiplication:

Multiply the result by 100 to express it as a percentage.

• Example: Express 15 as a percentage of 60.
• 15 / 60 = 0.25
• 0.25 x 100 = 25%

Therefore, 15 is 25% of 60.

Percentage Change

1. Finding the Difference:

Calculate the difference between the original value and the new value.

2. Division:

Divide the difference by the original value.

3. Multiplication:

Multiply the result by 100 to express it as a percentage.

• Example: A price increased from £50 to £60. Calculate the percentage increase.
• Difference: £60 - £50 = £10
• Division: £10 / £50 = 0.2
• Multiplication: 0.2 x 100 = 20%

Therefore, the price increased by 20%.

Percentage Change: Multiplication Method

1. Increase:

• Add the percentage increase to 100.
• Divide the resulting number by 100.
• Multiply the original value by the decimal result.

2. Decrease:

• Subtract the percentage decrease from 100.
• Divide the resulting number by 100.

• Multiply the original value by the decimal result.

• Example: A price of £120 is reduced by 15%. Calculate the new price.

• 100 - 15 = 85
• 85/100 = 0.85
• 0.85 x £120 = £102

Therefore, the new price is £102.

Real-Life Applications

1. Discounts:

• Calculate the discount amount using percentage of a quantity.
• Subtract the discount from the original price to find the sale price.

2. Simple Interest:

• Calculate the interest earned using percentage of a quantity.
• Add the interest to the principal amount to find the total amount.

3. Original Value Problems:

• If you know the new value and the percentage change, you can calculate the original value.

Practice makes perfect! Apply your understanding of percentages and percentage change to various real-life scenarios to solidify your skills.