Math with Mr. J: Unit Rate Word Problems

Overview

• Focus on solving unit rate word problems.
• Three example problems covered.

Key Concepts

• Unit Rate: A rate in which the second quantity in the comparison is one unit.
• Fractional Ratio: An expression representing the relationship between two quantities.
• Order Matters: The order of quantities in a ratio must reflect the question being asked.

Example Problems

Problem 1: Gas Price Calculation

• Situation: 4 gallons of gas cost $12.80.
• Question: Price of gas per gallon?
• Step-by-Step Solution:
  1. Set up the fractional ratio: $12.80/4 gallons.
  2. Find the unit rate:
     • Divide both numerator and denominator by 4.
     • $12.80 ÷ 4 = $3.20.
  3. Answer: $3.20 per gallon.
• Note: Order in the question (price per gallon) determines variable order in ratio.

Problem 2: Car Travel Distance

• Situation: A car traveled 480 miles in 8 hours.
• Question: Miles traveled per hour?
• Step-by-Step Solution:
  1. Set up the fractional ratio: 480 miles/8 hours.
  2. Find the unit rate:
     • Divide both numerator and denominator by 8.
     • 480 ÷ 8 = 60.
  3. Answer: 60 miles per hour.

Problem 3: Cookie Baking

• Situation: A baker bakes 180 cookies in 3 batches.
• Question: Cookies baked per batch?
• Step-by-Step Solution:
  1. Set up the fractional ratio: 180 cookies/3 batches.
  2. Find the unit rate:
     • Divide both numerator and denominator by 3.
     • 180 ÷ 3 = 60.
  3. Answer: 60 cookies per batch.

Tips and Common Mistakes

• Order of operation in ratios: Always align with the question's requirement.
• Equivalent Fractions: Ensure both numerator and denominator are divided by the same number to maintain the ratio's equivalency.

Conclusion

• Successfully solved three unit rate problems.
• Reinforced understanding of setting up proper fractional ratios and converting to unit rates.

End of Lecture Notes