Real-World Examples of Multi-Step Ratio and Rate Problems Grade 7

📚 Quick Study Guide

• 比例 Ratio: A comparison of two quantities. Can be written as a fraction, using a colon, or with the word "to."
• ⏱️ Rate: A ratio that compares two quantities with different units. For example, miles per hour.
• 步 Multi-Step Problems: Problems that require more than one operation (addition, subtraction, multiplication, division) to solve.
• 📐 Proportions: An equation stating that two ratios are equal. If $\frac{a}{b} = \frac{c}{d}$, then $ad = bc$ (cross-multiplication).
• 💡 Unit Rate: A rate with a denominator of 1. To find a unit rate, divide the numerator by the denominator.
• ➕ Solving Multi-Step Ratio and Rate Problems:
  • Read the problem carefully to identify the knowns and unknowns.
  • Set up ratios or rates to compare the quantities.
  • Use proportions to solve for unknown quantities.
  • Check your answer to make sure it makes sense in the context of the problem.

Practice Quiz

1. A recipe calls for 2 cups of flour and 3 cups of sugar. If you want to make half the recipe, how many cups of flour do you need?
   1. 1 cup
   2. 1.5 cups
   3. 2 cups
   4. 3 cups
2. John can run 5 miles in 1 hour. How long will it take him to run 12.5 miles, assuming he maintains the same pace?
   1. 1.5 hours
   2. 2 hours
   3. 2.5 hours
   4. 3 hours
3. A store sells apples at a rate of 3 apples for $2. How much will 9 apples cost?
   1. $4
   2. $6
   3. $8
   4. $10
4. Sarah earns $12 per hour. If she works 20 hours a week and saves 25% of her earnings, how much does she save each week?
   1. $40
   2. $60
   3. $80
   4. $100
5. A map has a scale of 1 inch = 50 miles. If two cities are 3.5 inches apart on the map, what is the actual distance between them?
   1. 150 miles
   2. 175 miles
   3. 200 miles
   4. 225 miles
6. A train travels 120 miles in 2 hours. At the same rate, how far will it travel in 5 hours?
   1. 240 miles
   2. 300 miles
   3. 360 miles
   4. 420 miles
7. If 4 workers can complete a task in 6 days, how many days will it take 8 workers to complete the same task, assuming they work at the same rate?
   1. 2 days
   2. 3 days
   3. 4 days
   4. 5 days