Question

Unit 4 Lesson 16 Unit Rates & Proportions Unit Test

Answer 1

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:

1. **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.

2. **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:

1. **Finding Unit Rates**:
- If a car travels 240 miles on 8 gallons of gas, what is the unit rate of miles per gallon?
- **Solution**:
\[
\text{Unit Rate} = \frac{240 \text{ miles}}{8 \text{ gallons}} = 30 \text{ miles per gallon}
\]

2. **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:

1. If a store sells 3 shirts for $24, what is the unit rate for one shirt?
2. A recipe calls for 4 cups of flour to make 12 cookies. How many cups of flour are needed for 30 cookies?
3. If a person runs 12 miles in 2 hours, what is their pace in miles per hour?
4. 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!