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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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