Percentages
A percentage is a fraction out of one hundred, used to compare proportions on a common scale.
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Play with the controls to see the idea in action.
📘 Learn
A percentage is a fraction out of one hundred, used to compare proportions on a common scale.
- Percent means per hundred
- 25 percent equals 1/4 or 0.25
- Find a percentage by dividing by 100 then multiplying
🧠 Quick quiz
Three questions. Score 2 or more to complete the topic.
What is Percentages?
Within Mathematics, which covers numbers, algebra, geometry, trigonometry and statistics from first principles to exam level, this topic explains Percentages. Maths builds step by step, so each topic here gives you a rule, a picture and a quick check you can use on homework and in exams.
Check that you can explain Percentages in your own words and give one example from everyday life. If you can do that, you have understood the core idea.
Understanding Percentages gives you a reliable method you will reuse in later maths units, in science lessons and in data work.
Percentages in detail
A percentage is a fraction out of 100, written with the % sign, so 35% means 35/100 or 0.35. To find a percentage of an amount, convert to a decimal or fraction and multiply: 35% of 80 is 0.35 × 80 = 28. To express one number as a percentage of another, divide and multiply by 100.
Percentages make different quantities easy to compare because they share a common base of 100. They are used for test scores, discounts, tax, statistics in the news and nutritional labels, and they link directly to fractions, decimals and ratios.
How the interactive helps you understand Percentages
Watch the pie chart in the interactive. Use any sliders or buttons it offers to change the values and see how the pie chart responds.
Before you change anything, predict the result. Then change one value at a time and check whether your prediction was right. This is a quick way to build a correct mental model of Percentages.
Real-life uses and examples
- Use Percentages when comparing prices, discounts or recipe quantities in everyday life.
- Explain Percentages to a friend with a simple picture, such as a row of tiles or a bag of sweets.
- Spot Percentages in exam questions, where it often sits inside a short word problem.
Common mistakes to avoid
- Forgetting units, signs or brackets when you apply Percentages.
- Memorising the steps for Percentages without checking why they work.
- Learning the definition without testing it. Use the quiz and the interactive to check that you can apply the idea.
Frequently asked questions about Percentages
What is Percentages?
A percentage is a fraction out of one hundred, used to compare proportions on a common scale.
What are the most important points about Percentages?
The main points are: Percent means per hundred; 25 percent equals 1/4 or 0.25; Find a percentage by dividing by 100 then multiplying.
Why is Percentages useful?
Understanding Percentages gives you a reliable method you will reuse in later maths units, in science lessons and in data work.
How can I practise Percentages?
Open the interactive at the top of this page and change the controls one at a time. Predict the result before each change, then take the three-question quiz. A score of two or more marks the topic as complete on this device.
Which topics are related to Percentages?
Related topics in Mathematics include Ratio, Indices and Powers, Square Roots and Cube Roots.