1. Course 3 5-2 Ratios, Rates, and Unit Rates 5-2 Ratios, Rates, and Unit Rates Course 3 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

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

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

4. 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.

5. 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

6. 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

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

8. Course 3 5-2 Ratios, Rates, and Unit Rates YOUR TURN: 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_________________. 44,800 kg 5 m 3 Write a rate.

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

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 Estimate each unit rate. YOUR TURN! Choose a number close to 583 that is divisible by 85. 583 soccer players to 85 soccer balls. 583 soccer players to 85 soccer balls is approximately ____ players per soccer ball.  583 players 85 soccer balls 595 players 85 soccer balls Divide to find players per soccer ball.

13. Course 3 5-2 Ratios, Rates, and Unit Rates Estimate each unit rate. YOUR TURN! Choose a number close to 271 that is divisible by 3. 271 yards in 3 hours 271 yards to 3 hours is approximately _____ yards per hour.  271 yards 3 hours 276 yards 3 hours Divide to find yards per hour.

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

15. 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.

16. 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? YOUR TURN!  $2.19 15 = = $2.78 20  The better buy is the _____________________. price for jar number of ounces price for jar number of ounces Divide the price by the number of ounces.

17. Course 3 5-2 Ratios, Rates, and Unit Rates Golf balls can be purchased in a 3-pack for $4.95 or a 12-pack for $18.95. Which is the better buy? YOUR TURN! Divide the price by the number of balls. price for package number of balls  $4.95 3 = price for package number of balls = $18.95 12  The better buy is the ______________________.

18. Course 3 5-2 Ratios, Rates, and Unit Rates YOUR TURN, AGAIN! 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.

19. 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

20. 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.