7-2 Ratios, Rates, and Unit Rates Course 3 Warm Up Warm Up Problem of the Day Problem of the Day...

7-2 Ratios, Rates, and Unit Rates

Course 3

Warm UpWarm Up

Problem of the DayProblem of the Day

Lesson PresentationLesson Presentation

Warm UpDivide. Round answers to the nearest tenth.

1. 2.

3. 4.

23.3 3.5

23.8

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23.9

420 18

73 21

380 16

430 18

Problem of the Day

There are 3 bags of flour for every 2 bags of sugar in a freight truck. A bag of flour weighs 60 pounds, and a bag of sugar weighs 80 pounds. Which part of the truck’s cargo is heavier, the flour or the sugar?flour

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Learn to work with rates and ratios.

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Vocabulary

rateunit rateunit price

Insert Lesson Title Here

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Course 3


An aspect ratio describes a screen by comparing its width to its height.

Movie and television screens range in shape from almost perfect squares to wide rectangles.

Common aspect ratios are 4:3, 37:20, 16:9, and 47:20.

Additional Example 1A: Ordering Ratios

A. Order the ratios 4:3, 23:10, 13:9, and 47:20 from the least to greatest.


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4:3 =

23:10 =

13:9 =

47:20 =

4 3

4 3

Divide. = 1.3 1

= 1.3

23 10

13 947 20

= 1.4

= 2.3

= 2.35

The ratios in order from least to greatest are 4:3, 13:9, 23:10, and 47:20.

The decimals in order are 1.3, 1.4, 2.3, and 2.35.

B. A television has screen width 20 in. and height 15 in. What is the aspect ratio of this screen?


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Additional Example 1B: Ordering Ratios

The ratio of the width to the height is 20:15.

The screen has the aspect ratio 4:3.

The ratio can be simplified: 20 15

5(4) 5(3)

4 3

20 15

= = .

A. Order the ratios 2:3, 35:14, 5:3, and 49:20 from the least to greatest.


Try This: Example 1A

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2:3 =

35:14 =

5:3 =

49:20 =

2 3

2 3

Divide. = 0.6 1

= 0.6

35 14

5

3 49 20

= 1.6

= 2.5

= 2.45

The ratios in order from least to greatest are 2:3, 5:3, 49:20, 35:14.

The decimals in order are 0.6, 1.6, 2.45, and 2.5.

B. A movie theater has a screen width 36 ft. and height 20 ft. What is the aspect ratio of this screen?


Try This: Example 1B

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The ratio of the width to the height is 36:20.

The screen has the aspect ratio 9:5.

The ratio can be simplified: 36 20

4(9) 4(5)

9 5

36 20

= = .

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Ratio: 903

Rate: 90 miles3 hours

Read as “90 miles per 3

hours.”

A rate is a comparison of two quantities that have different units.

A ratio is a comparison of two quantities.

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Unit rates are rates in which the second quantity is 1.

unit rate: 30 miles,1 hour

or 30 mi/h

The ratio 903

can be simplified by dividing:

903

= 301


Additional Example 2: Using a Bar Graph to Determine Rates

Use the bar graph to find the number of acres, to the nearest acre, destroyed in Nevada and Alaska per week.

Nevada =

12,308 acres1 week

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640,000 acres52 weeks


Additional Example 2 Continued

Use the bar graph to find the number of acres, to the nearest acre, destroyed in Nevada and Alaska per week.

Alaska =

14,423 acres1 week

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Montana =

18,269 acres1 week

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Try This: Example 2

Use the bar graph to find the number of acres, to the nearest acre, destroyed in Montana and Idaho per week.


Idaho =

26,923 acres1 week

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1,400,000 acres52 weeks

Try This: Example 2 Continued

Use the bar graph to find the number of acres, to the nearest acre, destroyed in Montana and Idaho per week.

Unit price is a unit rate used to compare costs per item.

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Pens can be purchased in a 5-pack for $1.95 or a 15-pack for $6.20. Which is the better buy?

Additional Example 3A: Finding Unit Prices to Compare Costs

Divide the price by the number of pens.

price for packagenumber of pens

$1.955

= $0.39

price for packagenumber of pens

= $6.2015

$0.41

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The better buy is the 5-pack for $1.95.

Jamie can buy a 15-oz jar peanut butter for $2.19 or a 20-oz jar for $2.78. Which is the better buy?

Additional Example 3B: Finding Unit Prices to Compare Costs

$2.1915

= $0.15

= $2.7820

$0.14

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The better buy is the 20-oz jar for $2.78.

price for jarnumber of ounces

price for jarnumber of ounces

Divide the price by the number of ounces.

Golf balls can be purchased in a 3-pack for $4.95 or a 12-pack for $18.95. Which is the better buy?

Try This: Example 3A

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Divide the price by the number of balls.

price for packagenumber of balls

$4.953

= $1.65

price for packagenumber of balls

= $18.9512

$1.58

The better buy is the 12-pack for $18.95.

Try This: Example 3B

John can buy a 24 oz bottle of ketchup for $2.19 or a 36 oz bottle for $3.79. Which is the better buy?

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$2.1924

= $0.09

= $3.7936

$0.11

The better buy is the 24-oz jar for $2.19.

price for bottlenumber of ounces

price for bottlesnumber of ounces

Divide the price by the number of ounces.

Lesson Quiz1. At a family golf outing, a father drove the ball

285 ft. His daughter drove the ball 95 ft. Express the ratio of the father’s distance to his daughter’s in simplest terms.

2. Find the unit price of 6 stamps for $2.22.

3. Find the unit rate of 8 heartbeats in 6 seconds.

4. What is the better buy, a half dozen carnations

for $4.75 or a dozen for $9.24?

5. Which is the better buy, four pens for $5.16 or

a ten-pack for $12.90?

$0.37 per stamp

3:1


1.3 beats/s

a dozen

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They cost the same.

7-2 Ratios, Rates, and Unit Rates Course 3 Warm Up Warm Up Problem of the Day Problem of the Day...

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