Ratios
A ratio compares two quantities by division.
About this topic
A ratio compares two or more quantities of the same kind, written as 3:2 or 3 to 2. It tells you how much of one thing there is for each amount of another, such as 3 cups of flour for every 2 cups of sugar. Ratios can be scaled up or down by multiplying or dividing every part by the same number.
Simplifying a ratio works just like simplifying a fraction. The ratio 12:8 becomes 3:2 when both parts are divided by 4. To share an amount in a ratio, add the parts, find the value of one part, then multiply. If 40 dollars is split 3:2, there are 5 parts, each worth 8 dollars, so the shares are 24 and 16. Ratios are used in recipes, maps, mixtures and gears.
A paint mix of 2 parts blue to 3 parts white makes 5 parts in total. For 10 litres of paint you need 4 litres of blue and 6 of white. Map scales such as 1:50,000 mean one centimetre on paper is 50,000 centimetres, or half a kilometre, on the ground. Even screen sizes use ratios, like 16:9.
A part-to-part ratio is not the same as a part-to-whole fraction. In a class with boys to girls of 3:2, boys are 3/5 of the class, not 3/2. Also remember the order matters: 3:2 is different from 2:3. Keeping units the same on both sides is essential.
Key ideas
- Written a:b or a to b
- Simplify by dividing by common factors
- Order matters
Quick check
Use cases: where Ratios helps
- Homework: review the key idea behind Ratios before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Ratios without notes.
- Visual learning: play with the interactive lab to see how Ratios changes when you adjust its inputs.
- Teaching a friend: explain Ratios in your own words, then compare your version with the key ideas.
Number and algebra skills are used in science, engineering, budgeting and computing.
Frequently asked questions
What is Ratios?
A ratio compares two quantities by division.
What will I learn in Ratios?
Written a:b or a to b. Simplify by dividing by common factors. Order matters.
Is Ratios part of Mathematics?
Yes. It is one of 200 Mathematics topics on LearnViz HighSchoolEdu, with 3 key ideas, a live animation and a quick check.
Does the Ratios lab work on a phone or tablet?
Yes. The animation resizes to fit your screen and supports touch, so you can drag, tap and slide with your finger.
How should I study Ratios?
Read the summary and key ideas first, play with the interactive lab to see the idea in motion, then answer the quick check. If you get a question wrong, go back to the key idea it tests.
Do I need an account, and is my progress saved?
No account is needed. Marking a topic as learned is saved in your own browser, so it stays on that device and is not sent to a server.