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SOL 7.4, 8.3a Use measures expressed as rates (e.g., speed, density) and measures expressed as products (e.g., person- days) to solve problems; check the units of the solutions; and use dimensional analysis to check the reasonableness of the answer. Objective: Finding Unit Rates Finding Unit Prices to Compare Costs

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Rate Movie

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Ratio: 90 3 Rate: 90 miles 3 hours Read as “90 miles per 3 hours.” A rate is a comparison of two quantities measured in different units. Notes

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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 Notes

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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. = Penelope can type 45 words in one minute. 90 words ÷ 2 2 minutes ÷ 2 Divide to find words per minute. 45 words 1 minute

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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.

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Estimate each unit rate. Check It Out! Example 3A 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 7 players per soccer ball. 583 players 85 soccer balls 595 players 85 soccer balls 7 players 1 soccer ball Divide to find players per soccer ball.

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Pactice Estimate each unit rate –121 students in 3 buses –31.50 for 4 hours

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Unit price is a unit rate used to compare price per item.

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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? 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 5-pack for $1.95 has the lower unit price.

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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 $3.79. Which bottle has the lower unit price? $2.19 24 = $0.09 = $3.79 36 $0.11 The 24 oz jar for $2.19 has the lower unit price. price for bottle number of ounces price for bottle number of ounces Divide the price by the number of ounces.

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Lesson Quiz: 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 cm 3. What is the approximate density of a penny? Estimate each 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

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Lesson Quiz: 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.

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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.

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.

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