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Comparison of Unit Rates

Use <, > or = to compare unit rates.

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Comparison of Unit Rates

Let’s Think About It

License: CC BY-NC 3.0

Mark adopted a dog today and is at the pet store looking for dog food. He researched the different brands before coming to the store and now he just needs to decide between two brands. Doggie Delights costs $46 for a 20 pound bag. Nature’s Choice costs $55 for a 25 pound bag. Mark wants to compare the cost of dog food per pound to find the better deal. Which bag should Mark buy?

In this concept, you will learn to write and compare unit rates.

Guidance

Equivalent rates can be used to compare different sets of quantities that have the same value. A rate that compares a quantity to one is called a unit rate. The unit rate has a denominator equal to one when written as a fraction. Unit rates can be used to find larger equivalent rates.

Let’s use a unit rate to solve a problem.

Mrs. Harris’ class went apple picking. Each student picked 8 apples. At this rate, how many apples were picked by 7 students?

The problem gives the unit rate of 8 apples per student. Solve by finding the equivalent rate where the number of students is 7.

First, write the unit rate as a fraction.

8 apples1 student

Next, multiply the numerator and denominator by 7 to find the equivalent rate for 7 students.

8 apples×71 student×7=56 apples7 students

There were 56 apples picked by 7 students.

Now let’s solve to find the unit rate.

Laquita picked 12 peaches in 6 minutes. How many peaches did Laquita pick per minute?

The problem gives the larger rate of 12 peaches per 6 minutes. Simplify the rate so the denominator is equal to 1 to find the unit rate.

First, write the rate as a fraction.

12 peaches6 minutes

Next, simplify the denominator to equal 1. Divide the numerator and denominator by 6.

12 peaches÷66 minutes÷6=2 peaches1 minute

Laquita picked 2 peaches per minute.

Guided Practice

Find the unit rate for the following problem.

Harold cuts 7 lawns in 4 hours. How many lawns does Harold cut per hour?

First, write the rate as a fraction.

7 lawns6 hours

Next, simplify the denominator to equal 1. Divide the numerator and denominator by 4.

7 lawns÷44 hours÷4=1.75 lawns1 hour

Harold cuts 1.75 lawns per hour.

Example

Find the unit rate for the following problems.

Example 1

24 buttons on 4 shirts

First, write the rate as a fraction.

24 buttons4 shirts

Next, divide the numerator and denominator by 4.

24 buttons÷44 shirts÷4=6 buttons1 shirt
 

The unit rate is 6 buttons per shirt.

Example 2

4 ice cream cones for 2 people

First, write the rate as a fraction.

4 ice cream cones2 people

Next, divide the numerator and denominator by 2.

4 ice cream cones÷22 people÷2=2 ice cream cones1 person
 

The unit rate is 2 ice cream cones per person.

Example 3

45 gallons in 3 miles

First, write the rate as a fraction.

45 miles3 gallons

Next, divide the numerator and denominator by 3.

45 miles÷33 gallons÷3=15 miles1 gallon

The unit rate is 15 miles per gallon.

Follow Up

License: CC BY-NC 3.0

Remember Mark at the pet store?

Mark is trying to make a choice. Doggie Delights costs $46 for a 20 pound bag and Nature’s Choice costs $55 for a 25 pound bag. To find the better deal, Mark must compare the price per pound.

First, find the unit price for each brand.

Doggie DelightsNature’s Choice==$4620 pound=46÷2020÷20=2.301$5525 pound=55÷2525÷25=2.201

Next, compare the price per pound. Doggie Delights is $2.30 per pound. Nature’s Choice is $2.20 per pound.

$2.30>$2.20

Nature’s Choice is cheaper than Doggie Delights.

Mark decides to buy Nature’s Choice.

Explore More

Find the unit rate.

  1. Fourteen apples in two barrels
  2. Thirty-two crayons in two boxes
  3. Eighteen bottles in three carriers
  4. Twenty students on four teams
  5. Twenty-five students on five teams
  6. Fifty students in two classes
  7. Ninety students on three buses
  8. Thirteen students ate twenty-six cupcakes
  9. Twelve campers in two tents
  10. Forty- eight hikers on two trails
  11. 16 hikers on 4 trails
  12. 72 bikes on 6 racks
  13. 15 backpacks for 5 children
  14. 28 slices of pizza for 7 teenagers
  15. $24.00 for 2 people

Answers for Explore More Problems

To view the Explore More answers, open this PDF file and look for section 8.5. 

Vocabulary

Rate

Rate

A rate is a special kind of ratio that compares two quantities.
Unit Rate

Unit Rate

A unit rate is a ratio that compares a quantity to one. The word “per” is a key word with unit rates.

Image Attributions

  1. [1]^ License: CC BY-NC 3.0
  2. [2]^ License: CC BY-NC 3.0

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