ratios and proportional relationships grade 7 quiz

📚 Quick Study Guide

• 🔢 A ratio compares two quantities. It can be written as $a:b$, $\frac{a}{b}$, or $a$ to $b$.
• ⚖️ A proportion is an equation stating that two ratios are equal. For example, $\frac{a}{b} = \frac{c}{d}$.
• 📈 Proportional relationships are relationships where the ratio between two quantities is constant. This constant is called the constant of proportionality, often denoted by $k$. So, $y = kx$.
• 🗺️ To check if a relationship is proportional, see if the ratio $y/x$ is the same for all pairs of $x$ and $y$ values.
• 💡 Cross-multiplication is a useful technique to solve proportions. If $\frac{a}{b} = \frac{c}{d}$, then $ad = bc$.
• 💰 Unit rate is a ratio where the denominator is 1. It helps to compare different rates.
• 📊 Proportional relationships can be represented graphically as a straight line passing through the origin (0,0).

🤔 Practice Quiz

1. Which of the following ratios is equivalent to $\frac{2}{5}$?
   1. $\frac{3}{6}$
   2. $\frac{4}{10}$
   3. $\frac{5}{2}$
   4. $\frac{2}{7}$
2. If 3 apples cost $2.25, what is the cost of 7 apples, assuming a proportional relationship?
   1. $4.50
   2. $5.25
   3. $6.00
   4. $7.75
3. Which equation represents a proportional relationship?
   1. $y = x + 2$
   2. $y = 3x$
   3. $y = x^2$
   4. $y = 2x + 1$
4. 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. 150 miles
   2. 175 miles
   3. 200 miles
   4. 225 miles
5. If $\frac{4}{x} = \frac{12}{9}$, what is the value of $x$?
   1. 2
   2. 3
   3. 4
   4. 5
6. Sarah can type 120 words in 3 minutes. How many words can she type in 5 minutes at the same rate?
   1. 180 words
   2. 200 words
   3. 220 words
   4. 240 words
7. Which table represents a proportional relationship between x and y?

   1. x	y
      1	2
      2	4
      3	6

   2. x	y
      1	2
      2	3
      3	4

   3. x	y
      1	3
      2	5
      3	7

   4. x	y
      1	4
      2	6
      3	8