Ratios and RatesSection 5.1 & 5.2

Objectives:• Solve problems involving average

speed, distance, and time. (AF 4.2)

• Choose an appropriate unit measure and use ratios to convert within and between measurement systems. (MG 1.0)

• Compare measures within and between measurement items (MG 1.1)

Words to know ~• Ratio – a comparison of a number “a” and a

nonzero number “b” using division.

ExampleExample – – 12 games to 7 games ; 12 games to 7 games ;

12 to 7; 12:712 to 7; 12:7

• Rate – a type of ratio that compares two

• quantities that have different kinds of units of measure.

ExampleExample – – 100 miles in 2 hours100 miles in 2 hours

• - 6 pencils for $1.40- 6 pencils for $1.40

Writing a Ratio • Voting – Barack Obama won 333 electoral

votes while John McCain won 156. What’s the ratio of Obama’s votes to McCain’s votes?

• Ratio – Obama votes =

McCain votes

Ratio can be written also as 111:52 , or “111 to 52”

Rewriting with the same units

• A map shows the distance between the classroom and the bathroom as 16 inches. In reality, the distance is 4 yards.

MUST CONVERT TO THE SAME UNIT OF MEASURE!!!

Finding a RateFinding a Rate• You and your family drove 400 miles in 8

hours.

• What was the average rate of speed?

Reduce the numbers.

Summary:

Ratio is ….

Rate is ….

Finding a Unit Rate

• A 6 pack of soda costs $1.60. A 12 pack of soda costs $ 3.00. Which is the better buy?

Finding a Unit Finding a Unit RateRate

Golf balls can be purchased in a 3-pack for $4.95 or a 12-pack for $18.95. Which pack has the lower unit price?

price for packagenumber of balls

$4.953

= $1.65

price for packagenumber of balls

= $18.9512

$1.58

The 12-pack for $18.95 has the lower unit price.

Finding a Unit Finding a Unit RateRate

John can buy a 24 oz bottle of ketchup for $2.19 or a 36 oz bottle for $3.79. Which bottle has the lower unit price?

$2.1924

$0.09

$3.7936

$0.11

The 24 oz jar for $2.19 has the lower unit price.

price for bottlenumber of ounces

price for bottlenumber of ounces

=

=

PracticeIdentify if the problems are rates or ratios.

Practice• Write each fraction in simplest terms.

SummarySummary• Remember that a ratio is a comparison of two numbers.

Example = number of A’s compared to the number of B’s

• Remember that a rate is a type of ratio that compares two quantities that have different kinds of units of measure.• Example = 2 pairs of pants for $25. (comparing the number of

pants to the dollar amount.)

Lesson QuizLesson QuizWrite each ratio in simplest form.Write each ratio in simplest form.

1. 22 tigers to 44 lions

2. 5 feet to 14 inches

12

307

3. Meka can make 6 bracelets per half hour. How many bracelets can she make per hour?

12Estimate each unit rate.

4. $2.22 for 6 stamps

5. 8 heartbeats in 6 seconds

$0.37 per stamp

1.3 beats/s

Find each unit price. Then tell which has the lower unit price.

6. A half dozen carnations for $4.75 or a dozen for $9.24

7. 4 pens for $5.16 or a ten-pack for $12.90.

a dozen

They cost the same.

Activity• Using the grocery store flyers (with a partner), create 3

rates and 3 ratios.

• Exchange them with another team.

• Solve the other team’s rates and ratios.