5-2 Rates

Course 2

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Problem of the DayProblem of the Day

Lesson PresentationLesson Presentation

Learn to find units and compare unit rates, such as average speed and unit price.

Course 2

5-2 Rates

Vocabulary

rateunit rate

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Course 2

5-2 Rates

Course 2

5-2 Rates

A rate is a ratio that compares two quantities measured in different units.

A unit rate is a rate whose denominator is 1. To change a rate to a unit rate, divide both the numerator and denominator by the denominator.

We use the key word per or the division symbol / to indicate a unit rate.

For example: If a student earns $7.65 per hour, it is the same as $7.65/hour, and means $7.65 for every

hour of work.

On a bicycle you can travel 20 miles in 4 hours. What are the unit rates in this situation, (the distance you can travel in 1 hour and the

amount of time required to travel 1 mile)?

1 mile

1 hour

Find the unit rate.

A Ferris wheel revolves 35 times in 105 minutes. How many minutes does 1 revolution take?

105 minutes35 revolutions

Write a rate that compares minutes and revolutions.

Simplify.

Divide the numerator and denominator by 35.

Course 2

5-2 Rates

105 minutes ÷ 35 35 revolutions ÷ 35

3 minutes1 revolution

The Ferris wheel revolves 1 time in 3 minutes.

Find the unit rate.

A Ferris wheel revolves 35 times in 105 minutes. How many revolutions does it complete in 1 minute?

35 revolutions105 minutes

Write a rate that compares revolutions and minutes.

Simplify.

Divide the numerator and denominator by 105.

Course 2

5-2 Rates

35 revolutions ÷ 105 105 minutes ÷ 105

0.333.. revolutions1 minute

The Ferris wheel makes 1/3 of a revolution in 1 minute.

Find the unit rate.

To make 12 smoothies, Henry needs 30 cups of ice. How many cups of ice does he need for one smoothie?

30 cups of ice12 smoothies

Write a rate that compares cups of ice and smoothies.

Simplify.

Divide the numerator and denominator by 12.

Course 2

5-2 Rates

30 cups of ice ÷ 12 12 smoothies ÷ 12

2.5 cups of ice1 smoothie

Henry needs 2.5 cups of ice per smoothie.

Find the unit rate.

To make 12 smoothies, Henry needs 30 cups of ice. How many smoothies can he make with one cup of ice?

12 smoothies30 cups of ice

Write a rate that compares smoothies and cups of ice.

Simplify.

Divide the numerator and denominator by 30.

Course 2

5-2 Rates

12 smoothies÷ 30 30 cups of ice ÷ 30

0.4 smoothies1 cup of ice

Henry can make 0.4 smoothies with one cup of ice.

Find the unit rate.

A dog walks 60 steps in 2 minutes. How many steps does he walk in one minute?

60 steps2 minutes

Write a rate that compares steps and minutes.

Simplify.

Divide the numerator and denominator by 2.

Course 2

5-2 Rates

60 steps ÷ 2 2 minutes ÷ 2

30 steps1 minute

The dog walks 30 steps per minute.

Find the unit rate.

A dog walks 60 steps in 2 minutes. How many minutes does it take him to walk 1 step?

2 minutes60 steps

Write a rate that compares minutes and steps.

Simplify.

Divide the numerator and denominator by 2.

Course 2

5-2 Rates

2 minutes÷ 60 60 steps÷ 60

1/30 minute1 step

It takes the dog 1/30 of a minute (or two seconds) to walk a step.

36 inches in 3 feet

Rate 1

• How many inches in one foot?

Rate 2

• How many feet in one inch?

5 gallons of gas cost $6.50

Rate 1

• How much does 1 gallon cost?

Rate 2

• How much gas can I get for $1.00?

In 25 minutes Jenny can run 10 laps

Rate 1

• How long does it take Jenny to run ONE lap?

Rate 2

• How many laps can Jenny run in ONE minute?

The copier makes 120 copies in 5 minutes

Rate 1 Rate 2

The copier makes 120 copies in 5 minutes

Rate 1

• How many copies does it make in ONE minute?

Rate 2

• How long does it takes to make ONE copy?

A 12-ounce sports drink costs $0.99, and a 16-ounce sports drink costs $1.19. Which size is the best buy?

Size Price

12 ounces $0.99

16 ounces $1.19

Divide the price by the number of ounces (oz) to find the unit price of each size.

$0.9912 oz

≈ $0.08oz

Since $0.07 < $0.08, the 16 oz sports drink is the best buy.

Course 2

5-2 Rates

$1.1916 oz

≈ $0.07oz

A 1.5 gallon container of milk costs $4.02, and a 3.5 gallon container of milk costs $8.75. Which size is the best buy?

Size Price

1.5 gal $4.02

3.5 gal $8.75

Divide the price by the number of grams (g) to find the unit price of each size.

$4.021.5 gal

= $2.68gal

Since $2.50 < $2.68, the 3.5 gallon container is the best buy.

Course 2

5-2 Rates

$8.753.5 gal

= $2.50g

Let’s build a table!

The Fall Movie Double Issue of Entertainment Weekly said The Dark Knight Rises earned $354 million in three weeks. Total Recall earned $26 million in its first week. Ice Age: Continental drift earned $132 million in four weeks. Which movie has earned more on average per week? At this rate, how much will each movie earn in five weeks? Let’s set up a table of values to illustrate this information. What should our column headings be? That will tell us how many boxes our table needs.

Movie Rate(in millions)

Unit Rate(millions/one

week)

Earned in5 weeks

(in millions)

What about a title for the table?

Top Movie Revenues

Movie Rate(in millions)

Unit Rate(millions/one

week)

Earned in5 weeks

(in millions)

What goes in the columns?

Top Movie Revenues

Movie Rate(in millions)

Unit Rate(millions/one

week)

Earned in5 weeks

(in millions)

The Dark Knight $354/3 weeks $118/week $590

Total Recall $26/1 week $26/week $130

Ice Age $132/4 weeks $33/week $165

1. Which movie earned more on average per week?2. At this rate, what will each movie earn in 5 weeks?3. Which movie would you like to own a piece of?

Lesson Quiz

1. Ian earned $96 babysitting for 12 hours. How much did he earn each hour?

2. It takes Mia 49 minutes to complete 14 homework problems. On average, how long did it take to solve each problem?

3. Seth plans to drive 220 miles to his vacation. He would like to complete the drive in 4 hours. What should his average speed be in miles per hour?

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Course 2

5-2 Rates

$8

3.5 minutes

55

4. Abby can buy a 7-pound bag of cat food for $7.40, or she can purchase a 3-pound bag for $5.38. Which size is the best buy? 7 lb bag