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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
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
They cost the same.