Presentation on theme: "Ratios, Rates, and Unit Rates"— Presentation transcript:
1Ratios, Rates, and Unit Rates 7-2Ratios, Rates, and Unit RatesWarm UpProblem of the DayLesson PresentationPre-Algebra
2Ratios, Rates, and Unit Rates Pre-Algebra7-2Ratios, Rates, and Unit RatesWarm UpDivide. Round answers to the nearest tenth.420 1873 2123.33.5380 16430 1823.923.8
3Problem of the DayThere 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
6Movie and television screens range in shape from almost perfect squares to wide rectangles. An aspect ratio describes a screen by comparing its width to its height.Common aspect ratios are 4:3, 37:20, 16:9, and 47:20.
7Additional Example 1A: Ordering Ratios A. Order the ratios 4:3, 23:10, 13:9, and 47:20 from the least to greatest.4 34 3Divide. =1.3 14:3 == 1.323 1023:10 == 2.313 913:9 == 1.447 2047:20 == 2.35The decimals in order are 1.3, 1.4, 2.3, and 2.35.The ratios in order from least to greatest are 4:3, 13:9, 23:10, and 47:20.
8Additional Example 1B: 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 ratio can be simplified:20 155(4) 5(3)4 3= = .The screen has the aspect ratio 4:3.
9Try This: Example 1AA. Order the ratios 2:3, 35:14, 5:3, and 49:20 from the least to greatest.2 32 3Divide. =0.6 12:3 == 0.635 1435:14 == 2.55 35:3 == 1.649 2049:20 == 2.45The decimals in order are 0.6, 1.6, 2.45, and 2.5.The ratios in order from least to greatest are 2:3, 5:3, 49:20, 35:14.
10Try This: Example 1BB. 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 ratio can be simplified:36 204(9) 4(5)9 5= = .The screen has the aspect ratio 9:5.
11A ratio is a comparison of two quantities. A rate is a comparison of two quantities that have different units.903Ratio:Read as“90 miles per 3hours.”90 miles3 hoursRate:
12Unit rates are rates in which the second quantity is 1. The ratio903can be simplified by dividing:903301=30 miles,1 hourunit rate:or 30 mi/h
13Additional 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.640,000 acres52 weeksNevada =12,308 acres1 week
14Additional Example 2 Continued Use the bar graph to find the number of acres, to the nearest acre, destroyed in Nevada and Alaska per week.750,000 acres52 weeksAlaska =14,423 acres1 week
15950,000 acres Montana = 52 weeks 18,269 acres 1 week Try This: Example 2Use the bar graph to find the number of acres, to the nearest acre, destroyed in Montana and Idaho per week.950,000 acres52 weeksMontana =18,269 acres1 week
16Try 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.1,400,000 acres52 weeksIdaho =26,923 acres1 week
17Unit price is a unit rate used to compare costs per item.
18Additional Example 3A: Finding Unit Prices to Compare Costs Pens can be purchased in a 5-pack for $1.95 or a 15-pack for $ Which is the better buy?Divide the price by the number of pens.price for packagenumber of pens$1.955=$0.39price for packagenumber of pens$6.2015=$0.41The better buy is the 5-pack for $1.95.
19Additional Example 3B: Finding Unit Prices to Compare Costs Jamie can buy a 15oz jar peanut butter for $2.19 or a 20 oz jar for $ Which is the better buy?Divide the price by the number of ounces.price for jarnumber of ounces$2.1915=$0.15price for jarnumber of ounces$2.7820=$0.14The better buy is the 20-oz jar for $2.78.
20Try This: Example 3AGolf balls can be purchased in a 3-pack for $4.95 or a 12-pack for $ Which is the better buy?Divide the price by the number of balls.price for packagenumber of balls$4.953=$1.65price for packagenumber of balls$18.9512=$1.58The better buy is the 12-pack for $18.95.
21Try This: Example 3BJohn can buy a 24 oz bottle of ketchup for $2.19 or a 36 oz bottle for $ Which is the better buy?Divide the price by the number of ounces.price for bottlenumber of ounces$2.1924=$0.09price for bottlesnumber of ounces$3.7936=$0.11The better buy is the 24-oz jar for $2.19.
22What’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?
23Lesson 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?