Grade 7 Proportional Reasoning Test Prep: Multi-Step Questions

📚 Quick Study Guide

• 比例 Proportional Reasoning: Deals with relationships between ratios. If two ratios are equal, they form a proportion.
• 📐 Setting up Proportions: Write ratios as fractions. Ensure corresponding values are in the same position (numerator or denominator). For example, $\frac{a}{b} = \frac{c}{d}$.
• ➕ Multi-Step Problems: Often involve multiple proportional relationships or require you to find an intermediate value before solving for the final answer. Read carefully and break down the problem.
• 🧭 Cross-Multiplication: A useful technique to solve proportions: If $\frac{a}{b} = \frac{c}{d}$, then $ad = bc$.
• 💡 Unit Rate: Finding the value for a single unit. Useful for comparing prices or quantities. Divide the total cost by the number of units.
• 📝 Scale Factor: The ratio between two sets of measurements. Used in maps and models.
• 🧮 Percent Increase/Decrease: $\frac{\text{Amount of Increase or Decrease}}{\text{Original Amount}} \times 100$

🧪 Practice Quiz

1. A recipe calls for 2 cups of flour for every 3 eggs. If you want to use 9 eggs, how many cups of flour do you need?
   1. 1 cup
   2. 3 cups
   3. 6 cups
   4. 13.5 cups
2. A map has a scale of 1 inch = 50 miles. Two cities are 3.5 inches apart on the map. What is the actual distance between the cities?
   1. 17.5 miles
   2. 53.5 miles
   3. 175 miles
   4. 350 miles
3. John can type 60 words in 2 minutes. How many words can he type in 5 minutes?
   1. 120 words
   2. 150 words
   3. 24 words
   4. 300 words
4. A store sells 3 apples for $2.25. How much would 7 apples cost?
   1. $5.25
   2. $7.50
   3. $5.75
   4. $16.75
5. A car travels 120 miles in 3 hours. At this rate, how far will it travel in 7 hours?
   1. 280 miles
   2. 40 miles
   3. 360 miles
   4. 840 miles
6. If 4 workers can complete a job in 6 days, how long will it take 3 workers to complete the same job, assuming they work at the same rate?
   1. 4.5 days
   2. 8 days
   3. 9 days
   4. 12 days
7. A photograph is 4 inches wide and 6 inches long. It is enlarged so that the width is 10 inches. How long is the enlarged photograph?
   1. 8 inches
   2. 12 inches
   3. 15 inches
   4. 24 inches