130 likes | 284 Views
73 21. 420 18. 380 16. 430 18. Warm Up Divide. Round answers to the nearest tenth. 1. 2. 3. 4. 23.3. 3.5. 23.9. 23.8. A rate is a comparison of two quantities measured in different units. 90 3. Ratio:. Read as “ 90 miles per 3 hours. ”. 90 miles 3 hours. Rate:. 90 3.
E N D
73 21 420 18 380 16 430 18 Warm Up Divide. Round answers to the nearest tenth. 1.2. 3.4. 23.3 3.5 23.9 23.8
A rate is a comparison of two quantities measured in different units. 90 3 Ratio: Read as “90 miles per 3 hours.” 90 miles 3 hours Rate:
90 3 The ratio can be simplified by dividing: Unit rates are rates in which the second quantity is 1. 90 3 30 1 = 30 miles, 1 hour unit rate: or 30 mi/h
30 words minute 1 2 30 words • 2 minute • 2 1 2 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. Multiply to find words per minute. 60 words 1 minute = Geoff can type 60 words in one minute.
Additional Example 2A: Chemistry Application Five cubic meters of copper has a mass of 44,800 kilograms. What is the density of copper? 44,800 kg 5 m3 Write the rate. 44,800 kg ÷ 5 5 m3 ÷ 5 Divide to find kilograms per 1 m3. 8,960 kg 1 m3 Copper has a density of 8,960 kg/m3.
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? 9650 kg 0.5 m3 Write the rate. 9650 kg • 2 0.5 m3 • 2 Multiply to find kilograms per 1 m3. 19,300 kg 1 m3 Gold has a density of 19,300 kg/m3.
455 students 91 computers 468 students 91 computers 5 students 1 computer Additional Example 3A: Estimating Unit Rates Estimate each unit rate. 468 students to 91 computers Choose a number close to 468 that is divisible by 91. Divide to find students per computer. 468 students to 91 computers is approximately 5 students per computer.
320 feet 8 seconds 313 feet 8 seconds 40 feet 1 second Additional Example 3B: Estimating Unit Rates Estimate each unit rate. 313 feet in 8 seconds Choose a number close to 313 that is divisible by 8. Divide to find feet per second. 313 feet to 8 seconds is approximately 40 feet per second.
Additional Example 4A: 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 pack has the lower unit price? 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 5-pack for $1.95 has the lower unit price.
price for jar number of ounces price for jar number of ounces Additional Example 4B: Finding Unit Prices to Compare Costs Jamie can buy a 15 oz jar of peanut butter for $2.19 or a 20 oz jar for $2.78. Which jar has the lower unit price? Divide the price by the number of ounces. $2.19 15 = $0.15 $2.78 20 = $0.14 The 20 oz jar for $2.78 has the lower unit price.
Lesson Review: Part I 1. Meka can make 6 bracelets per half hour. How many bracelets can she make per hour? 2. A penny has a mass of 2.5 g and a volume of approximately 0.360 cm3. What is the approximate density of a penny? Estimate each unit rate. 3. $2.22 for 6 stamps 4. 8 heartbeats in 6 seconds 12 ≈ 6.94 g/cm3 $0.37 per stamp 1.3 beats/s
Lesson Review: Part II Find each unit price. Then tell which has the lower unit price. 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.