Percentages (Edexcel GCSE Maths): Revision Notes
Percentages
What are percentages?
Percentage means "per cent" which translates to "out of 100". When you see a percentage, you're looking at how many parts out of 100 total parts something represents.
You can write any percentage as a fraction over 100. This makes percentages easy to understand and work with in calculations.
Think of percentages as a universal language for comparing parts of a whole. Whether you're looking at test scores, discounts, or statistics, percentages allow you to quickly understand proportions on the same scale.
Understanding percentages visually
Looking at grid squares helps you visualise what percentages actually mean. Each grid represents 100 squares, making it easy to see the proportion:
- 20% = = (one-fifth of the grid is shaded)
- 50% = = (half of the grid is shaded)
- 75% = = (three-quarters of the grid is shaded)
- 100% = = (the entire grid is shaded)
The visual representation shows that percentages are simply another way of expressing fractions and proportions.
Finding a percentage of an amount
When you need to calculate a percentage of a number, follow these two simple steps:
- Divide the percentage by 100
- Multiply by the amount
For example, to find 12% of 80:
Worked Example: Price Reduction
A car rental company reduces its prices by 15% in a sale. A car normally costs £120 per week to rent. What is the weekly rental cost in the sale?
Step 1: Find 15% of £120
Step 2: Subtract the reduction from the original price
The car costs £102 per week in the sale.
Alternative method: You can also find 1% first (£120 ÷ 100 = £1.20) then multiply by the percentage you need (£1.20 × 15 = £18).
Writing one quantity as a percentage of another
Sometimes you need to express one number as a percentage of another number. The method is:
- Divide the first quantity by the second quantity
- Multiply your answer by 100
Worked Example: Student Statistics
In a year group of 96 students, 60 own a bicycle. Express 60 as a percentage of 96.
Step 1: Divide 60 by 96
Step 2: Multiply by 100
Therefore, 62.5% of the students own a bicycle.
Common Mistake to Avoid: Don't forget which number goes on top! When finding "A as a percentage of B", always divide A by B first, then multiply by 100. Getting this the wrong way around is a frequent error in exams.
Exam tips
Essential Exam Strategies:
- Show your working clearly - you can get marks for method even if your final answer is wrong
- Use a calculator efficiently - practice the two-step method for finding percentages
- Check your answers make sense - if you're finding 50% of something, your answer should be roughly half the original amount
- Remember the units - if the question involves money, include the £ sign in your answer
Common percentage calculations to remember
Quick Reference Guide:
- 1% = divide by 100
- 10% = divide by 10
- 25% = divide by 4 (quarter)
- 50% = divide by 2 (half)
- 75% = find 25% then multiply by 3
These shortcuts can save valuable time in calculations and help you check if your answers are reasonable.
Key Points to Remember:
- Percentage means "out of 100" - it's just another way of writing fractions
- To find a percentage of an amount: divide the percentage by 100, then multiply by the amount
- To write one quantity as a percentage of another: divide the first by the second, then multiply by 100
- Visual grids help you understand what percentages actually represent
- Always show your working in exam questions - you can gain marks for correct methods even with calculation errors