Proportions
A proportion says two ratios are equal.
About this topic
A proportion states that two ratios are equal, such as 2/3 = 8/12. If three of the four numbers are known, you can find the missing one by cross-multiplying: a/b = c/d means a × d = b × c.
Proportional thinking solves scaling problems, such as how much a recipe for 4 people needs for 10, how far a car travels at a steady speed, or the real distance behind a map scale. Two quantities are in direct proportion when one doubles whenever the other doubles, and their ratio stays constant.
Suppose 3 notebooks cost 7.50 dollars and you want the price of 8. Set up 3/7.50 = 8/x, then cross-multiply: 3x = 60, so x = 20 dollars. Another way is to find the unit price first, 2.50 dollars each, and multiply by 8. If a photo 6 cm wide is 4 cm tall and you enlarge the width to 15 cm, the height becomes 10 cm.
Proportions are used in medicine for dosages, in cooking, in model building and in currency exchange. A common mistake is setting up the equation with mismatched order, such as putting dollars on top on one side and notebooks on top on the other. Label each quantity, keep the same units in the same positions, and check whether the answer is reasonable. Not all relationships are proportional: a taxi with a fixed start fee is not.
Key ideas
- a/b = c/d
- Cross multiply to solve
- Scale factors keep ratios constant
Quick check
Use cases: where Proportions helps
- Homework: review the key idea behind Proportions before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Proportions without notes.
- Visual learning: play with the interactive lab to see how Proportions changes when you adjust its inputs.
- Teaching a friend: explain Proportions 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 Proportions?
A proportion says two ratios are equal.
What will I learn in Proportions?
a/b = c/d. Cross multiply to solve. Scale factors keep ratios constant.
Is Proportions 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 Proportions 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 Proportions?
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.