Understanding how to find a unit rate is a crucial math skill used constantly in everyday life—from figuring out the best grocery deals to calculating travel speeds.
This page features a comprehensive lesson and Grade 7 practice questions on finding unit rates. Each question comes with a detailed, step-by-step solution to help students, teachers, and parents confidently master the concept.
A rate is a ratio that compares two different quantities with different units (like miles and hours, or dollars and pounds). A unit rate is a rate where the second quantity is exactly one unit.
Scenario: A car travels 110 kilometers in 2 hours. How many kilometers does the car travel in one hour?
Solution: To find the unit rate, we divide the total distance by the total time.
\[ \dfrac{110 \text{ kilometers}}{2 \text{ hours}} = 55 \text{ kilometers per hour (km/hour)} \]
The unit rate is 55 km/hour.
Find the unit rate in each of the following situations. Expand the solution blocks to check your work.
I traveled 300 kilometers in 5 hours. Find the unit rate in kilometers/hour.
The unit rate is the total distance divided by the total time. In this context, it is also called the speed.
\[ \dfrac{300 \text{ kilometers}}{5 \text{ hours}} = \left(\dfrac{300}{5}\right) \text{ km/hour} = \mathbf{60 \text{ km/hour}} \]
An international phone call costs $10 for 4 minutes. Find the unit rate in dollars/minute.
Divide the total cost by the total number of minutes.
\[ \dfrac{10 \text{ dollars}}{4 \text{ minutes}} = \left(\dfrac{10}{4}\right) \text{ dollars/minute} = \mathbf{2.50 \text{ dollars/minute}} \]
Joelle reads 18 pages in 9 minutes. Find the unit rate in pages/minute.
Divide the total number of pages by the total time.
\[ \dfrac{18 \text{ pages}}{9 \text{ minutes}} = \left(\dfrac{18}{9}\right) \text{ pages/minute} = \mathbf{2 \text{ pages/minute}} \]
A car consumes 12 gallons of fuel for a distance of 240 miles. Find the unit rate in miles/gallon (mpg).
Divide the total distance traveled by the total amount of fuel consumed.
\[ \dfrac{240 \text{ miles}}{12 \text{ gallons}} = \left(\dfrac{240}{12}\right) \text{ miles/gallon} = \mathbf{20 \text{ miles/gallon}} \]
A pump moves 45 liters of water every 5 minutes. What is the unit rate of the pump in liters/minute?
Divide the total volume of water by the total time.
\[ \dfrac{45 \text{ liters}}{5 \text{ minutes}} = \left(\dfrac{45}{5}\right) \text{ liters/minute} = \mathbf{9 \text{ liters/minute}} \]
Joe bought 4 kilograms of apples at the cost of $16. Find the unit rate (or price of 1 kilogram) in dollars/kilogram.
Divide the total cost by the total weight.
\[ \dfrac{16 \text{ dollars}}{4 \text{ kilograms}} = \left(\dfrac{16}{4}\right) \text{ dollars/kilogram} = \mathbf{4 \text{ dollars/kilogram}} \]
Which moves faster: Object A that moves 15 centimeters every 5 seconds, or Object B that moves 24 centimeters every 8 seconds?
Find the unit rate (speed) for each object to compare them equally:
Object A: \[ \dfrac{15 \text{ cm}}{5 \text{ s}} = 3 \text{ cm/second} \]
Object B: \[ \dfrac{24 \text{ cm}}{8 \text{ s}} = 3 \text{ cm/second} \]
Both objects move at the same speed.
Car A consumes 12 gallons of fuel for a distance of 240 miles. Car B consumes 25 gallons of fuel for a distance of 550 miles. Which of the two cars travels further per gallon (has better fuel efficiency)?
Find the unit rate (miles per gallon) for each car:
Car A: \[ \dfrac{240 \text{ miles}}{12 \text{ gallons}} = 20 \text{ miles/gallon} \]
Car B: \[ \dfrac{550 \text{ miles}}{25 \text{ gallons}} = 22 \text{ miles/gallon} \]
Since \( 22 > 20 \), Car B gets more miles out of each gallon.
Car B travels further per gallon.
Convert the unit rate of 60 kilometers/hour into kilometers/minute.
Since 1 hour is exactly 60 minutes, we can substitute "60 minutes" into the denominator.
\[ 60 \dfrac{\text{km}}{\text{hour}} = \dfrac{60 \text{ km}}{60 \text{ minutes}} = \left(\dfrac{60}{60}\right) \dfrac{\text{km}}{\text{minute}} = \mathbf{1 \text{ km/minute}} \]
Convert the unit rate of 72 kilometers/hour into meters/second.
We need to convert the distance from kilometers to meters, and the time from hours to seconds.
Now, find the new unit rate by dividing meters by seconds:
\[ \dfrac{72{,}000 \text{ meters}}{3600 \text{ seconds}} = \left(\dfrac{72{,}000}{3600}\right) \text{ m/second} = \mathbf{20 \text{ meters/second}} \]