7 -2 Ratios Rates and Unit Rates Warm

7 -2 Ratios, Rates, and Unit Rates Warm Up Problem of the Day Lesson Presentation Pre-Algebra

7 -2 Ratios, Rates, and Unit Rates Warm Up Divide. Round answers to the nearest tenth. 1. 420 23. 3 18 2. 73 3. 5 21 3. 380 23. 8 16 4. 430 23. 9 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 rate unit price Pre-Algebra

7 -2 Ratios, Rates, and Unit Rates Movie 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. Pre-Algebra

7 -2 Ratios, Rates, and Unit Rates Additional Example 1 A: Ordering Ratios A. Order the ratios 4: 3, 23: 10, 13: 9, and 47: 20 from the least to greatest. Divide. 4 = 1. 3 4: 3 = 4 = 1. 3 3 3 1 23: 10 = 23 = 2. 3 10 13: 9 = 13 = 1. 4 9 47: 20 = 47 = 2. 35 20 The 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. Pre-Algebra

7 -2 Ratios, Rates, and Unit Rates Additional Example 1 B: 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 20 can be simplified: 20 = 5(4) = 4. 15 15 5(3) 3 The screen has the aspect ratio 4: 3. Pre-Algebra

7 -2 Ratios, Rates, and Unit Rates Try This: Example 1 A A. Order the ratios 2: 3, 35: 14, 5: 3, and 49: 20 from the least to greatest. Divide. 2 = 0. 6 2: 3 = 2 = 0. 6 3 3 1 35: 14 = 35 = 2. 5 14 5: 3 = 5 = 1. 6 3 49: 20 = 49 = 2. 45 20 The 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. Pre-Algebra

7 -2 Ratios, Rates, and Unit Rates Try This: Example 1 B B. A movie theater has a screen width 36 ft. and height 20 ft. What is the aspect ratio of this screen? The ratio of the width to the height is 36: 20. The ratio 36 can be simplified: 36 = 4(9) = 9. 20 20 4(5) 5 The screen has the aspect ratio 9: 5. Pre-Algebra

7 -2 Ratios, Rates, and Unit Rates A ratio is a comparison of two quantities. A rate is a comparison of two quantities that have different units. Ratio: 90 3 Rate: 90 miles 3 hours Pre-Algebra Read as “ 90 miles per 3 hours. ”

7 -2 Ratios, Rates, and Unit Rates Unit rates are rates in which the second quantity is 1. The ratio 90 can be simplified by dividing: 3 90 = 30 3 1 unit rate: 30 miles, or 30 mi/h 1 hour 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 = 640, 000 acres 52 weeks 12, 308 acres 1 week 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 = 750, 000 acres 52 weeks 14, 423 acres 1 week Pre-Algebra

7 -2 Ratios, Rates, and Unit Rates 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. Montana = 950, 000 acres 52 weeks 18, 269 acres 1 week Pre-Algebra

7 -2 Ratios, Rates, and Unit Rates 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. Idaho = 1, 400, 000 acres 52 weeks 26, 923 acres 1 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 Additional Example 3 A: Finding Unit Prices to Compare Costs Pens can be purchased in a 5 -pack for $1. 95 or a 15 -pack for $6. 20. Which is the better buy? price for package = $1. 95 $0. 39 Divide the price by the number of pens 5 of pens. price for package = $6. 20 $0. 41 number of pens 15 The better buy is the 5 -pack for $1. 95. Pre-Algebra

7 -2 Ratios, Rates, and Unit Rates Additional Example 3 B: Finding Unit Prices to Compare Costs 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? price for jar = $2. 19 $0. 15 number of ounces 15 Divide the price by the number of ounces. price for jar = $2. 78 $0. 14 number of ounces 20 The better buy is the 20 -oz jar for $2. 78. Pre-Algebra

7 -2 Ratios, Rates, and Unit Rates Try This: Example 3 A Golf balls can be purchased in a 3 -pack for $4. 95 or a 12 -pack for $18. 95. Which is the better buy? price for package = $4. 95 $1. 65 Divide the price by the number of balls 3 of balls. price for package = $18. 95 $1. 58 number of balls 12 The better buy is the 12 -pack for $18. 95. Pre-Algebra

7 -2 Ratios, Rates, and Unit Rates Try This: Example 3 B 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? price for bottle = $2. 19 $0. 09 number of ounces 24 Divide the price by the number of ounces. price for bottles = $3. 79 $0. 11 number of ounces 36 The better buy is the 24 -oz jar for $2. 19. 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 Quiz 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? Pre-Algebra