1. Ratios, Rates, and Unit Rates 4-1 Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes

2. Ratios, Rates, and Unit Rates 4-1 Warm Up 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

3. Ratios, Rates, and Unit Rates 4-1 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

4. Ratios, Rates, and Unit Rates 4-1 Learn to work with rates and ratios.

5. Ratios, Rates, and Unit Rates 4-1 Vocabulary rate unit rate unit price

6. Ratios, Rates, and Unit Rates 4-1 Ratio: 90 3 Rate: 90 miles 3 hours Read as “90 miles per 3 hours.” A rate is a comparison of two quantities that have different units.

7. Ratios, Rates, and Unit Rates 4-1 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

8. Ratios, Rates, and Unit Rates 4-1 Additional Example 1: Finding Unit Rates Geoff can type 30 words in half a minute. How many words can he type in 1 minute? Write a rate. = Geoff can type 60 words in one minute. Multiply to find words per minute. 60 words 1 minute 30 words minute 1212 30 words 2 minute 2 1212

9. Ratios, Rates, and Unit Rates 4-1 Check It Out: Example 1 Penelope can type 90 words in 2 minutes. How many words can she type in 1 minute? 90 words 2 minutes Write a rate. = Penelope can type 45 words in one minute. 90 words ÷ 2 2 minutes ÷ 2 Divide to find words per minute. 45 words 1 minute

10. Ratios, Rates, and Unit Rates 4-1 Additional Example 2A: Chemistry Application Five cubic meters of copper has a mass of 44,800 kilograms. What is the density of copper? Copper has a density of 8,960 kg/m 3. 44,800 kg 5 m 3 Write a rate. Divide to find kilograms per 1 m 3. 44,800 kg ÷ 5 5 m 3 ÷ 5 8,960 kg 1 m 3

11. Ratios, Rates, and Unit Rates 4-1 Additional Example 2B: Chemistry Application A piece of gold with a volume of 0.5 cubic meters weighs 9650 kilograms. What is the density of gold? Gold has a density of 19,300 kg/m 3. 9650 kg 0.5 m 3 Write a rate. Multiply to find kilograms per 1 m 3. 9650 kg 2 0.5 m 3 2 19,300 kg 1 m 3

12. Ratios, Rates, and Unit Rates 4-1 Check It Out: Example 2A Four cubic meters of precious metal has a mass of 18,128 kilograms. What is the density of the precious metal? Precious metal has a density of 4,532 kg/m 3. 18,128 kg 4 m 3 Write a rate. Divide to find kilograms per 1 m 3. 18,128 kg ÷ 4 4 m 3 ÷ 4 4,532 kg 1 m 3

13. Ratios, Rates, and Unit Rates 4-1 Check It Out: Example 2B A piece of gem stone with a volume of 0.25 cubic meters weighs 3540 kilograms. What is the density of the gem stone? The gem stone has a density of 14,160 kg/m 3. 3540 kg 0.25 m 3 Write a rate. Multiply to find kilograms per 1 m 3. 3540 kg 4 0.25 m 3 4 14,160 kg 1 m 3

14. Ratios, Rates, and Unit Rates 4-1 A driver is competing in a 500-mile auto race. Additional Example 3A: Application Find the ratio of distance to time. In the first 2 hours of the race, the driver travels 356 miles. What is the driver's average speed? The driver's average speed is 178 mi/h. = 356 mi 2 h = 178 mi/h Substitute 356 for d and 2 hours for t. dtdt r = Divide to find the unit rate.

15. Ratios, Rates, and Unit Rates 4-1 A driver is competing in a 500-mile auto race. Additional Example 3B: Application Use the formula d = rt. The driver estimates that he will finish the race in less than 3 hours. If the driver keeps traveling at the same average speed, is his estimate reasonable? Explain. 500 = 178t Substitute 500 for d and 178 for r. Determine how long the trip will take. _ ___ 178 178 Divide both sides by 178. Simplify. 2.8 ≈ t Yes; at an average speed of 178 mi/h, the race will take about 2.8 hours.

16. Ratios, Rates, and Unit Rates 4-1 Helpful Hint The formula r = is equivalent to d= rt, as shown below. r = r ▪ t = ▪ t rt = d dtdt dtdt dtdt

17. Ratios, Rates, and Unit Rates 4-1 A cyclist is competing in a 70-mile bike race. Check It Out: Example 3A Find the ratio of distance to time. In the first 2 hours of the race, the cyclist travels 14 miles. What is the cyclist's average speed? The cyclist's average speed is 7 mi/h. = 14 mi 2 h = 7 mi/h Substitute 14 for d and 2 hours for t. dtdt r = Divide to find the unit rate.

18. Ratios, Rates, and Unit Rates 4-1 Check It Out: Example 3B Use the formula d = rt. The cyclist estimates that he will finish the race in less than 8 hours. If the cyclist keeps traveling at the same average speed, is the estimate reasonable? Explain. 70 = 7t Substitute 70 for d and 7 for r. Determine how long the trip will take. _ ___ 7 7 Divide both sides by 7. Simplify. 10 = t No; at an average speed of 7 mi/h, the race will take about 10 hours. A cyclist is competing in a 70-mile bike race.

19. Ratios, Rates, and Unit Rates 4-1 Unit price is a unit rate used to compare price per item.

20. Ratios, Rates, and Unit Rates 4-1 Jamie can buy a 15-oz jar of peanut butter for $2.19 or a 20-oz jar for $2.78. Which is the better buy? Additional Example 4: Finding Unit Prices to Compare Costs  $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.

21. Ratios, Rates, and Unit Rates 4-1 Golf balls can be purchased in a 3-pack for $4.95 or a 12-pack for $18.95. Which is the better buy? Check It Out: Example 4 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.

22. Ratios, Rates, and Unit Rates 4-1 Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

23. Ratios, Rates, and Unit Rates 4-1 Lesson Quiz: Part I 1. Meka can make 6 bracelets per half hour. How many bracelets can she make in 1 hour? 2. A penny has a mass of 2.5 g and a volume of approximately 0.360 cm 3. What is the approximate density of a penny? 3. Melissa is driving to her grandmother's house. In the first 3 hours of the drive, she travels 159 miles. What is Melissa's average speed? ≈ 6.94 g/cm 3 53 mi/h 12

24. Ratios, Rates, and Unit Rates 4-1 Lesson Quiz: Part II Determine the better buy. 5. A half dozen carnations for $4.75 or a dozen for $9.24 a dozen

25. Ratios, Rates, and Unit Rates 4-1 1. John can walk 16 miles in 4 hours. How many miles can he walk in one hour? A. 16 miles B. 8 miles C. 4 miles D. 2 miles Lesson Quiz for Student Response Systems

26. Ratios, Rates, and Unit Rates 4-1 2. Estimate the unit rate. 272 sailors in 17 ships A. 12 sailors per ship B. 14 sailors per ship C. 16 sailors per ship D. 18 sailors per ship Lesson Quiz for Student Response Systems

27. Ratios, Rates, and Unit Rates 4-1 3. Which of the following would be a better buy than purchasing 4 mangoes for $16? A. 2 mangoes for $10 B. half a dozen mangoes for $25 C. 8 mangoes for $ 28 D. one dozen mangoes for $54 Lesson Quiz for Student Response Systems