1. Course 3 5-2 Ratios, Rates, and Unit Rates 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

2. Course 3 5-2 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

3. Course 3 5-2 Ratios, Rates, and Unit Rates Learn to work with rates and ratios. TB P. 220-223

4. Course 3 5-2 Ratios, Rates, and Unit Rates Vocabulary rate unit rate unit price

5. Course 3 5-2 Ratios, Rates, and Unit Rates 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.

6. Course 3 5-2 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 90 3 can be simplified by dividing: 90 3 = 30 1

7. Course 3 5-2 Ratios, Rates, and Unit Rates 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

8. Course 3 5-2 Ratios, Rates, and Unit Rates 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

9. Course 3 5-2 Ratios, Rates, and Unit Rates 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

10. Course 3 5-2 Ratios, Rates, and Unit Rates Estimate each unit rate. Additional Example 3A: Estimating Unit Rates Choose a number close to 468 that is divisible by 91. 468 students to 91 computers 468 students to 91 computers is approximately 5 students per computer.  468 students 91 computers 455 students 91 computers  5 students 1 computer Divide to find students per computer.

11. Course 3 5-2 Ratios, Rates, and Unit Rates Estimate each unit rate. Additional Example 3B: Estimating Unit Rates Choose a number close to 313 that is divisible by 8. 313 feet in 8 seconds 313 feet to 8 seconds is approximately 39 feet per second.  313 feet 8 seconds 312 feet 8 seconds  39 feet 1 second Divide to find feet per second.

12. Course 3 5-2 Ratios, Rates, and Unit Rates Unit price is a unit rate used to compare price per item.

13. Course 3 5-2 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 4A: Finding Unit Prices to Compare Costs 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.

14. Course 3 5-2 Ratios, Rates, and Unit Rates 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 4B: 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.

15. Course 3 5-2 Ratios, Rates, and Unit Rates Lesson Quiz Part 1 1. 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? 2. Meka can make 6 bracelets per half hour. How many bracelets can she make in 1 hour? Estimate the unit rate. 3. $2.22 for 6 stamps 4. 8 heartbeats in 6 seconds $0.37 per stamp ≈ 6.94 g/cm 3  1.3 beats/s 12

16. Course 3 5-2 Ratios, Rates, and Unit Rates Lesson Quiz: Part 2 Determine the better buy. 5. A half dozen carnations for $4.75 or a dozen for $9.24 6. 4 pens for $5.16 or a ten-pack for $12.90. a dozen They cost the same.