Math with Mr. J: Basics of Rates and Unit Rates

Introduction

• Topic: Basics of rates and unit rates
• Objective: Understand what rates and unit rates are and how to find unit rates

Key Concepts

Rates

• Definition: Compare and show the relationship between quantities with different units
• Nature: Ratios that compare quantities with different units
  • Example: 36 miles in 4 days (miles and days are different units)
• Representation: Can be written as a fraction
  • Order Matters: Maintain the order of units (e.g., miles/day)

Unit Rates

• Definition: A rate with a denominator of one
• Purpose: Show the quantity per one unit
• Calculation: Adjust the denominator to one
• Example: 9 miles per one day (simplified from 36 miles in 4 days)

Examples

Example 1: Miles and Days

• Given: 36 miles in 4 days
• Rate as a Fraction: (\frac{36 \text{ miles}}{4 \text{ days}})
• Unit Rate Calculation:
  • Divide both numerator and denominator by 4
  • (\frac{36}{4} = 9) miles per day
  • Unit Rate: 9 miles per day

Example 2: Dollars and Hours

• Given: 96 dollars in 8 hours
• Rate as a Fraction: (\frac{96 \text{ dollars}}{8 \text{ hours}})
• Unit Rate Calculation:
  • Divide both numerator and denominator by 8
  • (\frac{96}{8} = 12) dollars per hour
  • Unit Rate: 12 dollars per hour

Conclusion

• Summary:
  • Rates compare different units
  • Unit rates focus on per one unit
  • Method: Adjust denominator to 1 for unit rates

Closing Remarks

• Intent: Helped explain rates and unit rates
• Sign-off: Thanks for watching, until next time!