grade 7 proportions quiz

📚 Quick Study Guide

• 📏 Ratio: A comparison of two quantities. Can be written as $a:b$, $\frac{a}{b}$, or $a$ to $b$.
• ⚖️ Proportion: An equation stating that two ratios are equal. For example, $\frac{a}{b} = \frac{c}{d}$.
• ✖️ Cross-Multiplication: A useful technique to solve proportions. If $\frac{a}{b} = \frac{c}{d}$, then $ad = bc$.
• 🧩 Direct Proportion: As one quantity increases, the other quantity increases proportionally. If $y$ is directly proportional to $x$, then $y = kx$, where $k$ is the constant of proportionality.
• ➗ Inverse Proportion: As one quantity increases, the other quantity decreases proportionally. If $y$ is inversely proportional to $x$, then $y = \frac{k}{x}$, where $k$ is the constant of proportionality.
• 💡 Unit Rate: A rate expressed as a quantity of 1. For example, if you travel 120 miles in 2 hours, the unit rate is 60 miles per hour.

Practice Quiz

1. What is the value of $x$ in the proportion $\frac{3}{5} = \frac{x}{15}$?
1. A) 5
2. B) 9
3. C) 12
4. D) 25
2. If 4 apples cost $2, how much will 10 apples cost?
1. A) $3
2. B) $4
3. C) $5
4. D) $6
3. Solve for $y$: $\frac{8}{y} = \frac{2}{3}$
1. A) 4
2. B) 6
3. C) 12
4. D) 24
4. A recipe calls for 2 cups of flour for every 3 cups of sugar. If you want to make a larger batch using 6 cups of sugar, how many cups of flour do you need?
1. A) 3
2. B) 4
3. C) 5
4. D) 6
5. If 3 workers can complete a job in 8 days, how long will it take 6 workers to complete the same job, assuming they work at the same rate?
1. A) 2 days
2. B) 4 days
3. C) 12 days
4. D) 16 days
6. Which of the following represents a direct proportion?
1. A) $y = \frac{5}{x}$
2. B) $y = 5x$
3. C) $y = x + 5$
4. D) $y = x^2$
7. A map has a scale of 1 inch = 20 miles. If two cities are 4.5 inches apart on the map, what is the actual distance between them?
1. A) 45 miles
2. B) 65 miles
3. C) 90 miles
4. D) 110 miles