Master

Unit Rates

Master unit rates with interactive lessons and practice problems! Designed for students like you!

Learn

Get the basics

Practice

Apply your skills

Master

Achieve excellence

Unit Rates

Study Guide

Key Definition

A unit rate is a rate that illustrates how many units of one quantity correspond to a single unit of another quantity. For example, if a car travels $78$ miles on $4$ gallons of gasoline, the unit rate is $\frac{78}{4} = 19.5$ miles per gallon.

Important Notes

Unit rates are used to compare quantities with different units.
Common examples include $\$$ per item, miles per hour, and price per pound.
To find a unit rate, divide the given quantity by the number of units.
Unit rates can simplify understanding of ratios in real-world contexts.
Always express unit rates in terms of 'per' one unit.

Mathematical Notation

$\frac{a}{b}$ represents a fraction or division

$\div$ represents division

Remember to use proper notation when solving problems

Why It Works

Unit rates help in understanding the efficiency or cost-effectiveness of various options. By converting a ratio to a unit rate, you can easily compare different scenarios using $\frac{a}{b}$ expressions.

Remember

Always divide the total quantity by the number of units to find the unit rate, using formulas like $\frac{78}{4} = 19.5$.

Quick Reference

Miles per Gallon:$\frac{\text{miles}}{\text{gallons}}$

Understanding Unit Rates

Choose your learning level

Watch & Learn

Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

A unit rate is found by dividing two quantities, such as $\frac{24}{8} = 3$ pages per minute.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

What is the unit rate if an SUV travels $104$ miles on $8$ gallons of gasoline?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

If a teenager earns $\$240$ for babysitting $15$ hours, what is the hourly rate?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

A copy machine makes $90$ copies in $30$ seconds. What is the unit rate in copies per second?

Challenge Quiz

Single Choice Quiz

Beginner

If a vehicle uses $20$ gallons of gasoline to travel $540$ miles, what is the unit rate in miles per gallon?

Recap

Watch & Learn

Review key concepts and takeaways