Divide. Round answers to the nearest tenth.

1. 2.

3. 4.

23.3 3.5

23.8 23.9

420 18

73 21

380 16

430 18

Warm Up

Pre-Algebra

7.2

Ratios, Rates, and Unit Rates

Learn to work with rates and ratios.

rateunit rateunit price

Vocabulary

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.

Aspect Ratio

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.

Example: Ordering Ratios

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

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

= = .

Additional Example: Ordering Ratios

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

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.

Try This

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

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

= = .

Try This

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.

Ratio and Rate

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

Unit Rate

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

Example: 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.

Alaska =

14,423 acres1 week

750,000 acres52 weeks

Example Continued

Montana =

18,269 acres1 week

950,000 acres52 weeks

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

Try This

Idaho =

26,923 acres1 week

1,400,000 acres52 weeks

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

Try This Continued

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

Unit Price

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

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.

Example: Finding Unit Prices to Compare Costs

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

$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.

Example: Finding Unit Prices to Compare Costs

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

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

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.

Try This

1. 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

They cost the same.

Lesson Quiz