1. 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

2. Pre-Algebra 7.2 Ratios, Rates, and Unit Rates

3. Learn to work with rates and ratios.

4. rate unit rate unit price Vocabulary

5. 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

6. 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 = 4343 4343 Divide. = 1.3 1 = 1.3 23 10 13 9 47 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

7. 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) 4343 20 15 = =. Additional Example: Ordering Ratios

8. 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 = 2323 2323 Divide. = 0.6 1 = 0.6 35 14 5353 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

9. 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) 9595 36 20 = =. Try This

10. Ratio: 90 3 Rate: 90 miles 3 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

11. Unit rates are rates in which the second quantity is 1. unit rate: 30 miles, 1 hour or 30 mi/h The ratio 90 3 can be simplified by dividing: 90 3 = 30 1 Unit Rate

12. Use the bar graph to find the number of acres, to the nearest acre, destroyed in Nevada and Alaska per week. Nevada =  12,308 acres 1 week 640,000 acres 52 weeks Example: Using a Bar Graph to Determine Rates

13. Use the bar graph to find the number of acres, to the nearest acre, destroyed in Nevada and Alaska per week. Alaska =  14,423 acres 1 week 750,000 acres 52 weeks Example Continued

14. Montana =  18,269 acres 1 week 950,000 acres 52 weeks Use the bar graph to find the number of acres, to the nearest acre, destroyed in Montana and Idaho per week. Try This

15. Idaho =  26,923 acres 1 week 1,400,000 acres 52 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

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

17. 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 package number of pens  $1.95 5 =$0.39 price for package number of pens = $6.20 15  $0.41 The better buy is the 5-pack for $1.95. Example: Finding Unit Prices to Compare Costs

18. Jamie can buy a 15oz jar peanut butter for $2.19 or a 20 oz jar for $2.78. Which is the better buy?  $2.19 15 = $0.15 = $2.78 20  $0.14 The better buy is the 20-oz jar for $2.78. price for jar number of ounces price for jar number of ounces Divide the price by the number of ounces. Example: Finding Unit Prices to Compare Costs

19. 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 package number of balls  $4.95 3 =$1.65 price for package number of balls = $18.95 12  $1.58 The better buy is the 12-pack for $18.95. Try This

20. 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?  $2.19 24 = $0.09 = $3.79 36  $0.11 The better buy is the 24-oz jar for $2.19. price for bottle number of ounces price for bottles number of ounces Divide the price by the number of ounces. Try This

21. 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