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Warm Up Log on to Math Forward

LESSON - Ratio

Begin Warm Up You have ten minutes to complete Warm Up.

Course 2

5-2 Rates

Do we really need math?

Course 2

5-2 Rates

http://www.youtube.com/watch?v=oruy1AucQsA

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.

Find the rate.

Additional Example 1A: Finding Unit Rates

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.

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105 minutes ÷ 35 35 revolutions ÷ 35

3 minutes1 revolution

The Ferris wheel revolves 1 time in 3 minutes.

Find the rate.

Additional Example 1B: Finding Unit Rates

Teancum walks 6 yards and passes 24 security lights set along the sidewalk. How many security lights does she pass in 1 yard?

24 lights6 yards

Write a rate that compares security lights and yards.

Simplify.

Divide the numerator and denominator by 6.

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5-2 Rates

24 lights ÷ 6 6 yards ÷ 6

4 lights1 yard

Teancum passes 4 security lights in 1 yard.

Quick Poll – Find the Rate

Check It Out: Example 1A

Mrs. Lizama walks 696 steps in 12 minutes. How many steps Mrs. Lizama take in 1 minute?

696 steps12 minutes

Write a rate that compares steps and minutes.

Simplify.

Divide the numerator and denominator by 12.

Course 2

5-2 Rates

696 steps ÷ 12 12 minutes ÷ 12

58 steps1 minute

Mrs. Lizama walks 58 steps per minute.

Quick Poll

Check It Out: Example 1B

To make 12 smoothies, Tyrone 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

Tyrone needs 2.5 cups of ice per smoothie.

Course 2

5-2 Rates

An average rate of speed is the ratio of distance traveled to time. The ratio is a rate because the units in the numerator and denominator are different.

Danielle is cycling 68 miles as a fundraising commitment. She wants to complete her ride in 4 hours. What should be her average speed in miles per hour?

Additional Example 2: Finding Average Speed

68 miles4 hours

Write the rate as a fraction.

68 miles ÷ 4 4 hours ÷ 4

= 17 miles1 hour

Divide the numerator and denominator by the denominator

Danielle’s average speed should be 17 miles per hour.

Course 2

5-2 Rates

Mr. Cooper is a pilot and needs to fly 1191 miles to the next city. He wants to complete his flight in 3 hours. What should be his average speed in miles per hour?

Check It Out: Example 2

1191 miles3 hours

Write the rate as a fraction.

1191 miles ÷ 3 3 hours ÷ 3

= 397 miles1 hour

Divide the numerator and denominator by the denominator

Mr. Cooper’s average speed should be 397 miles per hour.

Course 2

5-2 Rates

A unit price is the price of one unit of an item. The unit used depends on how the item is sold. The table shows some examples.

Course 2

5-2 Rates

Type of Item Example of Units

Liquid Ounces, quarts, gallons, liters

Solid Ounces, pounds, grams, kilograms

Any item Bottle, container, carton

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

Quick Poll : Consumer Math Application

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?

Check It Out: Example 3

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

Math Forward ActivityStatistics show that the average teenager sends or receives approximately 1,500 texts per month. An average of 4.1 billion daily text messages were sent or received in the US in 2009. Pedro Matias, the 2010 Guinness World Record holder for text strokes per minute, can text 264 characters in 1 minute 59 seconds. How many characters can he type per second?

Lesson Quiz: Part I

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’s family plans to drive 220 miles to their vacation spot. They would like to complete the drive in 4 hours. What should their average speed be in miles per hour?

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Course 2

5-2 Rates

$8

3.5 minutes

55

Course 2

5-2 Rates

QUICK POLL (yes or no)

Do you own a cell phone?

Does your phone plan allow texting?

Would you consider yourself good at using SMS Language (texting)?

QUICK POLL (open response)

What is your favorite school appropriate one word text?

What is your favorite school appropriate phrase to text?

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.

I Love Math

Mrs. Muhammad gives too much homework.

Lesson Quiz: Part II

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4. Abby can buy a 7-pound bag of dry 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

Course 2

5-2 Rates