Rates Examples in Math
Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Rates.
This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.
Concept Recap
A rate is a ratio that compares two quantities measured in different units, expressing how much of one quantity corresponds to a given amount of another. It is often written as 'per' one unit of the second quantity, such as miles per hour or dollars per pound.
60 miles per hour tells you how many miles you travel for each hour — it compares distance to time.
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: Rates answer 'how much of one quantity do you get for each single unit of another quantity?'
Common stuck point: Keeping track of which unit belongs in the numerator and which in the denominator — label both clearly.
Sense of Study hint: When you see a rate problem, write the word 'per' as a fraction bar and place the unit that follows 'per' in the denominator. First, identify the two quantities and their units. Then, divide the first quantity by the second to get the rate.
Worked Examples
Example 1
easySolution
- 1 Write the rate as a fraction: \frac{240 \text{ miles}}{4 \text{ hours}}.
- 2 Divide numerator and denominator by 4: \frac{240 \div 4}{4 \div 4} = \frac{60 \text{ miles}}{1 \text{ hour}}.
- 3 The unit rate is 60 miles per hour.
Answer
Example 2
mediumPractice Problems
Try these problems on your own first, then open the solution to compare your method.
Example 1
easyExample 2
hardBackground Knowledge
These ideas may be useful before you work through the harder examples.