Proportions Examples in Math
Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Proportions.
This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.
Concept Recap
An equation stating that two ratios are equal, used to find an unknown when three of the four values are known.
If 2 candies cost 1, then 4 candies cost 2—same proportion.
Read the full concept explanation →How to Use These Examples
- Read the first worked example with the solution open so the structure is clear.
- Try the practice problems before revealing each solution.
- Use the related concepts and background knowledge badges if you feel stuck.
What to Focus On
Core idea: Proportions let you find unknown values that maintain a ratio.
Common stuck point: Setting up the proportion so matching units are in the same position (both in numerator or both in denominator).
Sense of Study hint: Write the units next to each number in both fractions and make sure the same unit is on top in both ratios.
Worked Examples
Example 1
easySolution
- 1 Cross-multiply: 15x = 6 \times 10 = 60.
- 2 Divide both sides by 15: x = \frac{60}{15} = 4.
- 3 Check: \frac{4}{6} = \frac{2}{3} and \frac{10}{15} = \frac{2}{3} \checkmark
Answer
Example 2
mediumExample 3
mediumPractice Problems
Try these problems on your own first, then open the solution to compare your method.
Example 1
easyExample 2
hardRelated Concepts
Background Knowledge
These ideas may be useful before you work through the harder examples.