Ratio
A ratio compares two or more quantities of the same kind, showing how many times one contains the other.
▶ Interact
Play with the controls to see the idea in action.
📘 Learn
A ratio compares two or more quantities of the same kind, showing how many times one contains the other.
- Write ratios in simplest form like 2 to 3
- Share a total by adding the ratio parts
- Ratios have no units when quantities match
🧠 Quick quiz
Three questions. Score 2 or more to complete the topic.
What is Ratio?
Within Mathematics, which covers numbers, algebra, geometry, trigonometry and statistics from first principles to exam level, this topic explains Ratio. 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 Ratio in your own words and give one example from everyday life. If you can do that, you have understood the core idea.
Understanding Ratio gives you a reliable method you will reuse in later maths units, in science lessons and in data work.
Ratio in detail
A ratio compares the sizes of two or more quantities and is written with a colon, such as 3 : 2. It tells you how much of one thing there is for each amount of another, without stating actual amounts. Ratios can be simplified by dividing every part by a common factor, just like fractions.
To share a quantity in a given ratio, add the parts to find the total number of shares, divide the amount by that total and multiply by each part. Ratios are used in mixing paint, scale drawings, recipes and map reading, and they underpin proportion and rates.
How the interactive helps you understand Ratio
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 Ratio.
Real-life uses and examples
- Spot Ratio in exam questions, where it often sits inside a short word problem.
- Check a homework answer about Ratio by estimating first, then working it out step by step.
- Use Ratio when comparing prices, discounts or recipe quantities in everyday life.
Common mistakes to avoid
- Forgetting units, signs or brackets when you apply Ratio.
- Memorising the steps for Ratio 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 Ratio
What is Ratio?
A ratio compares two or more quantities of the same kind, showing how many times one contains the other.
What are the most important points about Ratio?
The main points are: Write ratios in simplest form like 2 to 3; Share a total by adding the ratio parts; Ratios have no units when quantities match.
Why is Ratio useful?
Understanding Ratio gives you a reliable method you will reuse in later maths units, in science lessons and in data work.
How can I practise Ratio?
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 Ratio?
Related topics in Mathematics include Indices and Powers, Square Roots and Cube Roots, Rational and Irrational Numbers.