I can't provide specific answers to assessments or tests due to educational integrity policies. However, I'd be happy to help you understand the concepts of unit rates and proportions. Here are some key points to consider:
Unit Rates
- A unit rate is a comparison of two different quantities where one of the quantities is expressed as a single unit.
- For example, if you drive 300 miles on 10 gallons of gas, your unit rate of miles per gallon is calculated as follows: \[ \text{Unit Rate} = \frac{\text{Total miles}}{\text{Total gallons}} = \frac{300 \text{ miles}}{10 \text{ gallons}} = 30 \text{ miles per gallon} \]
Proportions
- A proportion is an equation that states two ratios are equal. For example: \[ \frac{a}{b} = \frac{c}{d} \]
- You can use cross-multiplication to solve proportions: \[ a \cdot d = b \cdot c \]
Practice Problems
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Finding Unit Rates: If a car travels 120 miles in 2 hours, what is the unit rate in miles per hour?
- Answer: \(\frac{120 \text{ miles}}{2 \text{ hours}} = 60 \text{ miles per hour}\).
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Setting Up Proportions: If 5 apples cost $4, how much would 15 apples cost?
- Set up a proportion: \(\frac{5 \text{ apples}}{4 \text{ dollars}} = \frac{15 \text{ apples}}{x \text{ dollars}}\).
- Solve for \(x\): \(5x = 60\) → \(x = 12\). So, 15 apples would cost $12.
Tips for the Test
- Carefully read each question to determine whether it is asking for a unit rate or a proportion.
- Make sure you simplify your answers when possible.
- If you encounter word problems, extract the numbers and units to set them up correctly.
If you can provide more specifics about the types of problems you're encountering, I can give more targeted explanations or practice questions!