Bot GPT 4-o mini It seems like you're looking for help with a unit test on unit rates and proportions, possibly from a math curriculum. While I cannot provide specific test answers, I can certainly help you understand the concepts and provide examples or practice questions related to unit rates and proportions.
Key Concepts:
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Unit Rates:
- A unit rate is a ratio that compares a quantity to one unit of another quantity.
- For example, if you drive 150 miles in 3 hours, the unit rate is 150 miles / 3 hours = 50 miles/hour.
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Proportions:
- A proportion states that two ratios are equal. For example, if we have a ratio of 3:4 and want to relate it to the ratio of 6:8, we can say that \( \frac{3}{4} = \frac{6}{8} \).
- To solve a proportion, you can use cross-multiplication.
Sample Problems:
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Finding Unit Rates:
- If a car travels 240 miles on 8 gallons of gas, what is the unit rate of miles per gallon?
- Solution: \[ \text{Unit Rate} = \frac{240 \text{ miles}}{8 \text{ gallons}} = 30 \text{ miles per gallon} \]
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Using Proportions:
- If 5 oranges cost $2.00, how much do 8 oranges cost?
- Setup the proportion: \[ \frac{5 \text{ oranges}}{2.00 \text{ dollars}} = \frac{8 \text{ oranges}}{x \text{ dollars}} \]
- Cross-multiply to solve for \( x \): \[ 5x = 16 \quad \Rightarrow \quad x = \frac{16}{5} = 3.20 \]
Practice Questions:
- If a store sells 3 shirts for $24, what is the unit rate for one shirt?
- A recipe calls for 4 cups of flour to make 12 cookies. How many cups of flour are needed for 30 cookies?
- If a person runs 12 miles in 2 hours, what is their pace in miles per hour?
- If 15 pencils cost $3.75, how much would 25 pencils cost?
Feel free to solve these practice questions, and let me know if you need help with any specific part of the study material!
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