Unit Rates (Grade 7)

For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2 &divides; 1/4 miles per hour, equivalently 2 miles per hour.

Common Core: 7.RP.1

Suggested Learning Targets

• I can compute unit rates of quantities associated with ratios of fractions (length, area, & other quantities).
• I can use proportional relationships to solve real-world problems.
• I can simplify a rate, unit rate, ratio by dividing.
• I can compute unit rate as a complex fraction.
• Compute unit rates associated with ratios of fractions

What is Unit Rate?
A unit rate is a rate where the denominator is 1. It tells you how much of something you get for one unit of something else.
Examples:
Speed: Miles per hour (mph) - How many miles are traveled for one hour.
Price: Dollars per pound - How many dollars it costs for one pound.
Earnings: Dollars per hour - How many dollars are earned for one hour of work.
Fuel Efficiency: Miles per gallon (mpg) - How many miles a vehicle can travel on one gallon of fuel.

The following diagram shows how unit rates can be used to solve problems. Scroll down the page for more examples and solutions on how to use unit rates.

 

• Rates & Proportions Worksheets

  Rates & Unit Rates
  Proportional Relationships in Tables
  Proportional Relationships in Graphs
  Proportional Relationships in Equations
  Proportional Relationships (Speed)
  Rate Word Problems
  

Rate vs. Unit Rate
Rate: Compares two different quantities (e.g., 150 miles/3 hours).
Unit Rate: Simplifies the rate to “per 1 unit” (e.g., 50 mph).

How to Find a Unit Rate:
To get the unit rate for “Quantity A per one unit of Quantity B”, you perform the division:
Unit Rate = Quantity A / Quantity B

Ratios & Unit Rates
Ratio is a comparison between two quantities by division
A rate is a ratio that compares quantities in different units
A unit rate is a rate with a denominator of 1.

Examples:

1. The table show prices for different packages of index cards. Which size has the lowest unit cost?
2. Convert 30gals/min cups/second. (Hint: 16 cups = 1 gallon)
3. A contractor has a job that requires 540 person-day. How many workers are needed to complete the job in 60 days?

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Unit Rate Word Problems

Examples:

1. Find the unit rate if Suzie reads 45 books in 15 days.
2. Tom swims a 1/2 mile every 1/4 hour. How far will he swim in one hour?
3. A 4.5 pound of apples costs $22.50. What is the unit price?
4. How much would you pay for a pint of milk if you bought 5 gallons of milk for $28?

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7.RP.1: Ratios and Unit Rates
Quick instruction on ratios and how to calculate unit rates.

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Finding Unit Rates by Simplifying Complex Fractions
This video demonstrates two methods of find a unit rate: algebraic and symbolic. This skill directly address CCSS.Math.Content.7.RP.A.1 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units.

Example:
William can run 1/2 of mile in 1/10 of an hour. How many miles can he run in one hour?

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Rate/Unit Rate word problems

Examples:

1. Express each ratio as a fraction in the simplest form.
2. Express each phrase as a rate and unit rate.
3. An amusement park had 350 people come in over the course of 7 hours. At this rate, how many would they expect to come over 15 hours? What was the rate per hour?
4. Sam can make 15 pizzas in 2.5 hours. At this rate, how many could he make in an 8 hour work day? What is Sam’s rate per hour?
5. Over 5 days, Kimberly sheared 300 sheep. How many would she be able to shear in 26 days? What was her rate per day?

Why are Unit Rates Useful?
Comparison: They allow for easy comparison of different rates. For example, you can compare the price per pound of apples at different stores.
Decision Making: They help in making informed decisions, such as choosing the best value when shopping or comparing job offers based on hourly pay.
Problem Solving: They are essential for solving many real-world problems involving ratios and proportions.

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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