Question
Unit Rates & Proportions Unit Test
Answers
GPT-4o mini
Certainly! Below are some sample questions that could be included in a unit test on unit rates and proportions. These cover various topics, including calculation of unit rates, solving proportions, and real-world applications.
### Unit Rates & Proportions Unit Test
#### Part 1: Unit Rates
1. **Calculating Unit Rates**
A car travels 300 miles on 10 gallons of gas. What is the unit rate in miles per gallon?
a) 20 miles per gallon
b) 30 miles per gallon
c) 25 miles per gallon
d) 15 miles per gallon
2. **Finding Unit Rate**
A store sells 4 apples for $2. How much does it cost for one apple?
a) $0.50
b) $0.25
c) $0.75
d) $1.00
3. **Comparative Unit Rates**
A bike can travel at a speed of 15 miles per hour while a car can travel at a speed of 60 miles per hour. How many times faster is the car than the bike?
a) 3 times
b) 4 times
c) 5 times
d) 6 times
#### Part 2: Proportions
4. **Setting Up Proportions**
If 5 pounds of bananas cost $3.00, how much will 8 pounds cost? Set up and solve the proportion.
5. **Cross-Multiplication**
Solve the following proportion for \( x \):
\[
\frac{3}{5} = \frac{x}{15}
\]
6. **Word Problem Involving Proportions**
If you can buy 6 notebooks for $4.50, how much would you pay for 10 notebooks? Set up and solve the proportion.
#### Part 3: Mixed Problems
7. **Real-Life Application**
A recipe requires 2 cups of flour for every 3 cups of sugar. If you use 10 cups of flour, how much sugar do you need?
8. **Unit Rate Comparison**
A machine can produce 60 widgets in 120 minutes. Another machine produces 100 widgets in 180 minutes. Which machine has the better unit rate in widgets per minute?
9. **Using a Graph**
The graph below represents the relationship between the number of hours worked and the amount earned. If it shows a straight line through the origin, what does the slope of that line represent?
a) The total amount earned
b) The hourly wage
c) The total hours worked
d) The fixed costs
### Part 4: Challenge Problem
10. **Complex Proportions**
A marathon is 26.2 miles long. If John runs at a speed of 8 miles per hour and Sarah runs at 6 miles per hour, how long would it take each of them to complete the marathon? Compare the times and determine how much longer it takes Sarah to finish than John.
---
### Answer Key
1. b) 30 miles per gallon
2. a) $0.50
3. b) 4 times
4. \( \frac{5}{3} = \frac{8}{x} \) → \( x = \frac{24}{5} = 4.80 \)
5. \( 3 \cdot 15 = 5 \cdot x \) → \( x = 9 \)
6. \( \frac{6}{4.50} = \frac{10}{x} \) → \( x = 7.50 \)
7. Using a proportion, \( \frac{2}{3} = \frac{10}{x} \) → \( x = 15 \) cups of sugar.
8. Machine 1: 0.5 widgets per minute; Machine 2: 0.555 widgets per minute. Machine 2 is better.
9. b) The hourly wage
10. Time for John: 3.25 hours. Time for Sarah: 4.37 hours. Sarah takes about 1.12 hours longer than John.
These questions should help students practice their knowledge of unit rates and proportions. Adjust the difficulty or add more context as needed!
### Unit Rates & Proportions Unit Test
#### Part 1: Unit Rates
1. **Calculating Unit Rates**
A car travels 300 miles on 10 gallons of gas. What is the unit rate in miles per gallon?
a) 20 miles per gallon
b) 30 miles per gallon
c) 25 miles per gallon
d) 15 miles per gallon
2. **Finding Unit Rate**
A store sells 4 apples for $2. How much does it cost for one apple?
a) $0.50
b) $0.25
c) $0.75
d) $1.00
3. **Comparative Unit Rates**
A bike can travel at a speed of 15 miles per hour while a car can travel at a speed of 60 miles per hour. How many times faster is the car than the bike?
a) 3 times
b) 4 times
c) 5 times
d) 6 times
#### Part 2: Proportions
4. **Setting Up Proportions**
If 5 pounds of bananas cost $3.00, how much will 8 pounds cost? Set up and solve the proportion.
5. **Cross-Multiplication**
Solve the following proportion for \( x \):
\[
\frac{3}{5} = \frac{x}{15}
\]
6. **Word Problem Involving Proportions**
If you can buy 6 notebooks for $4.50, how much would you pay for 10 notebooks? Set up and solve the proportion.
#### Part 3: Mixed Problems
7. **Real-Life Application**
A recipe requires 2 cups of flour for every 3 cups of sugar. If you use 10 cups of flour, how much sugar do you need?
8. **Unit Rate Comparison**
A machine can produce 60 widgets in 120 minutes. Another machine produces 100 widgets in 180 minutes. Which machine has the better unit rate in widgets per minute?
9. **Using a Graph**
The graph below represents the relationship between the number of hours worked and the amount earned. If it shows a straight line through the origin, what does the slope of that line represent?
a) The total amount earned
b) The hourly wage
c) The total hours worked
d) The fixed costs
### Part 4: Challenge Problem
10. **Complex Proportions**
A marathon is 26.2 miles long. If John runs at a speed of 8 miles per hour and Sarah runs at 6 miles per hour, how long would it take each of them to complete the marathon? Compare the times and determine how much longer it takes Sarah to finish than John.
---
### Answer Key
1. b) 30 miles per gallon
2. a) $0.50
3. b) 4 times
4. \( \frac{5}{3} = \frac{8}{x} \) → \( x = \frac{24}{5} = 4.80 \)
5. \( 3 \cdot 15 = 5 \cdot x \) → \( x = 9 \)
6. \( \frac{6}{4.50} = \frac{10}{x} \) → \( x = 7.50 \)
7. Using a proportion, \( \frac{2}{3} = \frac{10}{x} \) → \( x = 15 \) cups of sugar.
8. Machine 1: 0.5 widgets per minute; Machine 2: 0.555 widgets per minute. Machine 2 is better.
9. b) The hourly wage
10. Time for John: 3.25 hours. Time for Sarah: 4.37 hours. Sarah takes about 1.12 hours longer than John.
These questions should help students practice their knowledge of unit rates and proportions. Adjust the difficulty or add more context as needed!