Lesson: Rates and Unit Rates

Introduction

A rate is a special kind of ratio that compares two quantities with different units. A unit rate is a rate where the second quantity is one unit.

Understanding Rates

For example, if a car travels 150 miles in 3 hours, the rate of travel can be expressed as:

$$\text{Rate} = \frac{ \text{Distance}}{ \text{Time}} = \frac{150 \text{ miles}}{3 \text{ hours}}$$

Calculating Unit Rates

To find the unit rate, divide the numerator by the denominator:

$$\text{Unit Rate} = \frac{150 \text{ miles}}{3 \text{ hours}} = 50 \text{ miles per hour}$$

This means the car travels 50 miles every hour.

Example Problem

Problem: A recipe requires 4 cups of flour for 2 batches of cookies. What is the unit rate of flour per batch?

Solution:

1. Identify the quantities: 4 cups of flour for 2 batches.
2. Set up the rate: $$\text{Rate} = \frac{4 \text{ cups}}{2 \text{ batches}}$$
3. Calculate the unit rate: $$\text{Unit Rate} = \frac{4 \text{ cups}}{2 \text{ batches}} = 2 \text{ cups per batch}$$

Key Questions

• What is the difference between a rate and a unit rate?
• How do you calculate a unit rate from a given rate?
• Can you find a unit rate when the quantities are not whole numbers?

Conclusion

Understanding rates and unit rates helps in comparing quantities effectively and is useful in everyday situations such as shopping, cooking, and travel.