Sure! When working with proportional relationships, we typically look at how two quantities increase or decrease in relation to each other, maintaining a constant ratio. Here are some practice exercises and examples to help you understand proportional relationships in tables:
Example of a Proportional Relationship
Consider a table that shows the relationship between hours worked and money earned:
| Hours Worked | Money Earned ($) | |--------------|------------------| | 1 | 10 | | 2 | 20 | | 3 | 30 | | 4 | 40 | | 5 | 50 |
Observation: The ratio of Money Earned to Hours Worked is constant (10:1). This indicates a proportional relationship.
Practice Exercise 1: Fill in the Blanks
Fill in the blanks in the following table to establish the proportional relationship:
| Hours Worked | Money Earned ($) | |--------------|------------------| | 1 | 5 | | 2 | ____ | | 3 | ____ | | 4 | ____ | | 5 | 25 |
(Solution: Each hour worked earns $5. So for 2 hours, it would be $10; for 3 hours, it would be $15; for 4 hours, it would be $20.)
Practice Exercise 2: Identify the Relationship
Determine whether the following pairs of quantities are proportional. If they are, state the constant of proportionality.
| \( x \) | \( y \) | |---------|---------| | 2 | 4 | | 3 | 6 | | 4 | 9 | | 5 | 10 |
Solution: To determine if they are proportional, check if the ratio \( \frac{y}{x} \) is constant:
- For \( x = 2, y = 4 \): \( \frac{4}{2} = 2 \)
- For \( x = 3, y = 6 \): \( \frac{6}{3} = 2 \)
- For \( x = 4, y = 9 \): \( \frac{9}{4} = 2.25 \) (not proportional)
- For \( x = 5, y = 10 \): \( \frac{10}{5} = 2 \)
(The first two pairs are proportional; the third pair is not; the last is.)
Practice Exercise 3: Create a Table
Create a table for a proportional relationship where the constant of proportionality is \( 3 \).
| \( x \) | \( y \) (where \( y = 3x \) | |---------|--------------------------| | 0 | | | 1 | | | 2 | | | 3 | | | 4 | |
Fill in the blanks: (Solution: 0, 3, 6, 9, 12)
Practice Exercise 4: Problem Solving
If a car travels 60 miles in 1 hour, how far will it travel in 5 hours? Fill in the table below:
| Time (hours) | Distance (miles) | |---------------|------------------| | 1 | 60 | | 2 | | | 3 | | | 4 | | | 5 | |
Solution: The car travels 60 miles each hour, so in 2 hours it travels 120 miles, in 3 hours it travels 180 miles, in 4 hours it travels 240 miles, and in 5 hours it travels 300 miles.
Summary
Identifying proportional relationships in tables involves recognizing consistent ratios or finding missing values that maintain the constant ratio between the quantities. If you have specific problems or tables you want to explore, feel free to share!
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