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Ratios, Rates, and Unit Rates
5-2 Ratios, Rates, and Unit Rates Course 3 Warm Up Problem of the Day Lesson Presentation
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Warm Up Divide. Round answers to the nearest tenth. 420 18 73 21 23.3 3.5 380 16 430 18 23.9 23.8
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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
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Learn to work with rates and ratios.
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Vocabulary rate unit rate unit price
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A rate is a comparison of two quantities that have different units.
90 3 Ratio: Read as “90 miles per 3 hours.” 90 miles 3 hours Rate:
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Unit rates are rates in which the second quantity is 1.
The ratio 90 3 can be simplified by dividing: 90 3 30 1 = 30 miles, 1 hour unit rate: or 30 mi/h
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Additional Example 1: Finding Unit Rates
Geoff can type 30 words in half a minute. How many words can he type in 1 minute? 30 words minute 1 2 Write a rate. 30 words • minute • 2 1 2 60 words 1 minute Multiply to find words per minute. = Geoff can type 60 words in one minute.
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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. 90 words ÷ minutes ÷ 2 45 words 1 minute Divide to find words per minute. = Penelope can type 45 words in one minute.
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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 a 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.
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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 a 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.
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Precious metal has a density of 4,532 kg/m3.
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? 18,128 kg 4 m3 Write a rate. 18,128 kg ÷ 4 4 m3 ÷ 4 Divide to find kilograms per 1 m3. 4,532 kg 1 m3 Precious metal has a density of 4,532 kg/m3.
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The gem stone has a density of 14,160 kg/m3.
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? 3540 kg 0.25 m3 Write a rate. 3540 kg • 4 0.25 m3 • 4 Multiply to find kilograms per 1 m3. 14,160 kg 1 m3 The gem stone has a density of 14,160 kg/m3.
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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. 468 students 91 computers 455 students Divide to find students per computer. 5 students 1 computer 468 students to 91 computers is approximately 5 students per computer.
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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. 313 feet 8 seconds 312 feet 39 feet 1 second Divide to find feet per second. 313 feet to 8 seconds is approximately 39 feet per second.
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Check It Out: Example 3A Estimate each unit rate. 583 soccer players to 85 soccer balls. Choose a number close to 583 that is divisible by 85. 583 players 85 soccer balls 595 players Divide to find players per soccer ball. 7 players 1 soccer ball 583 soccer players to 85 soccer balls is approximately 7 players per soccer ball.
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Check It Out: Example 3B Estimate each unit rate. 271 yards in 3 hours Choose a number close to 271 that is divisible by 3. 271 yards 3 hours 276 yards 92 yards 1 hour Divide to find yards per hour. 271 yards to 3 hours is approximately 92 yards per hour.
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Unit price is a unit rate used to compare price per item.
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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 $ 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.
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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 $ Which is the better buy? Divide the price by the number of ounces. price for jar number of ounces $2.19 15 = $0.15 price for jar number of ounces $2.78 20 = $0.14 The better buy is the 20-oz jar for $2.78.
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Check It Out: Example 4A Golf balls can be purchased in a 3-pack for $4.95 or a 12-pack for $ 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.
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Check It Out: Example 4B John can buy a 24 oz bottle of ketchup for $2.19 or a 36 oz bottle for $ Which is the better buy? Divide the price by the number of ounces. price for bottle number of ounces $2.19 24 = $0.09 price for bottles number of ounces $3.79 36 = $0.11 The better buy is the 24-oz jar for $2.19.
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Lesson Quiz Part 1 1. A penny has a mass of 2.5 g and a volume of approximately cm3. 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 ≈ 6.94 g/cm3 12 $0.37 per stamp 1.3 beats/s
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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.
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