16. Higher Order Thinking This Venn diagram shows the relationship of ratios to rates to unit rates. Describe a real-world situation involving a ratio relationship. Then write the ratio as 2 different equivalent rates and as a unit rate.

### Real-World Situation Involving a Ratio Relationship **Scenario:** Imagine you’re planning a road trip and want to understand how fuel-efficient your car is. You note that your car consumes 12 gallons of gasoline to travel 300 miles. ### Writing the Ratio as Two Different Equivalent Rates 1. **Rate 1: Miles per Gallon (mi/gallon)** - **Calculation:** \[ \text{Miles per Gallon} = \frac{300 \text{ miles}}{12 \text{ gallons}} = 25 \text{ mi/gallon} \] - **Interpretation:** The car travels 25 miles for every gallon of gasoline consumed. 2. **Rate 2: Gallons per Mile (gallons/mile)** - **Calculation:** \[ \text{Gallons per Mile} = \frac{12 \text{ gallons}}{300 \text{ miles}} = 0.04 \text{ gallons/mile} \] - **Interpretation:** The car uses 0.04 gallons of gasoline for every mile driven. ### Writing the Ratio as a Unit Rate A **unit rate** is a rate with a denominator of one. It allows for easy comparison and understanding of the relationship. - **Unit Rate (Miles per One Gallon):** Since the original rate is already in miles per gallon, it serves as the unit rate: \[ 25 \text{ miles per gallon} \] Alternatively, if we prefer to express how much gas is used per mile as a unit rate: - **Unit Rate (Gallons per One Mile):** \[ 0.04 \text{ gallons per mile} \] ### Summary - **Real-World Situation:** Tracking fuel consumption on a road trip. - **Equivalent Rates:** - 25 miles per gallon - 0.04 gallons per mile - **Unit Rate:** - 25 miles per one gallon *or* - 0.04 gallons per one mile These different expressions of the ratio allow you to understand and communicate fuel efficiency from various perspectives, whether you're focusing on how far you can travel per gallon or how much gasoline you use per mile.