Pre-Algebra

7-2 Ratios, Rates, and Unit Rates7-2 Ratios, Rates, and Unit Rates

Pre-Algebra

Warm UpWarm Up

Problem of the DayProblem of the Day

Lesson PresentationLesson Presentation

Pre-Algebra

7-2 Ratios, Rates, and Unit Rates

Warm UpDivide. Round answers to the nearest tenth.

1. 2.

3. 4.

23.3 3.5

23.8

Pre-Algebra

7-2 Ratios, Rates, and Unit Rates

23.9

420 18

73 21

380 16

430 18

Pre-Algebra

7-2 Ratios, Rates, and Unit Rates

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

Pre-Algebra

7-2 Ratios, Rates, and Unit Rates

Learn to work with rates and ratios.

Pre-Algebra

7-2 Ratios, Rates, and Unit Rates

Vocabulary

rateunit rateunit price

Pre-Algebra

7-2 Ratios, Rates, and Unit Rates

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.

Pre-Algebra

7-2 Ratios, Rates, and Unit Rates

Additional Example 1A: Ordering Ratios

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

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.

Pre-Algebra

7-2 Ratios, Rates, and Unit Rates

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

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

= = .

Pre-Algebra

7-2 Ratios, Rates, and Unit Rates

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

Try This: Example 1A

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.

Pre-Algebra

7-2 Ratios, Rates, and Unit Rates

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

Try This: Example 1B

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

= = .

Pre-Algebra

7-2 Ratios, Rates, and Unit Rates

Ratio: 903

Rate: 90 miles3 hours

Read as “90 miles per 3hours.”

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

A ratio is a comparison of two quantities.

Pre-Algebra

7-2 Ratios, Rates, and Unit Rates

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

Pre-Algebra

7-2 Ratios, Rates, and Unit Rates

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

640,000 acres52 weeks

Pre-Algebra

7-2 Ratios, Rates, and Unit Rates

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

750,000 acres52 weeks

Pre-Algebra

7-2 Ratios, Rates, and Unit Rates

Montana =

18,269 acres1 week

950,000 acres52 weeks

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.

Pre-Algebra

7-2 Ratios, Rates, and Unit Rates

Idaho =

26,923 acres1 week

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.

Pre-Algebra

7-2 Ratios, Rates, and Unit Rates

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

Pre-Algebra

7-2 Ratios, Rates, and Unit Rates

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

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

Pre-Algebra

7-2 Ratios, Rates, and Unit Rates

Jamie can buy a 15oz 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

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.

Pre-Algebra

7-2 Ratios, Rates, and Unit Rates

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

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.

Pre-Algebra

7-2 Ratios, Rates, and Unit Rates

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?

$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.

Pre-Algebra

7-2 Ratios, Rates, and Unit Rates

What’s the error?A clothing store charges $30 for 12 pairs of socks. A student says that the unit price is $0.40 per pair. What is the error? What is the correct unit price?

Pre-Algebra

7-2 Ratios, Rates, and Unit Rates

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?