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HW # 56 - p # odd Warm up Mr. Lynch bought some oranges and pears. After giving away 10 oranges, he had twice as many pears as oranges left. If he had 24 pears in the end, what was the ratio of oranges to pears in the beginning? Week 16, Day Three

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Warm Up Response 24/2 = 12 He had 12 oranges in the end = 22 He had 22 oranges in the beginning Oranges:Pears 22:24 11:12 The ratio of oranges to pears in the beginning was 11:12

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Homework Check p # 1-35 odd and # 36 1)2/5 3) 10/7 5) 15/1 7) No 9) Yes 11) Yes 13) 25/12 15) 12/1 17) 2/5 19) yes 21) No 23) no; she needs 3 ½ c of pancake mix to make 14 servings 25) – 27) Yes 29) No 5/6 31) Yes 33) No 11/6 35) 39/18 36) ----

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Review for Mastery 5-1 Review for Mastery 5-2 Challenge 5-2

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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.

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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

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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? Write a rate. = Geoff can type 60 words in one minute. Multiply to find words per minute. 60 words 1 minute 30 words minute words 2 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. = 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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Additional Example 2A: 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 8,960 kg/m 3. 44,800 kg 5 m 3 Write the rate. Divide to find kilograms per 1 m 3. 44,800 kg ÷ 5 5 m 3 ÷ 5 8,960 kg 1 m 3

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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? Gold has a density of 19,300 kg/m kg 0.5 m 3 Write the rate. Multiply to find kilograms per 1 m kg m ,300 kg 1 m 3

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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? The precious metal has a density of 4,532 kg/m 3. 18,128 kg 4 m 3 Write the rate. Divide to find kilograms per 1 m 3. 18,128 kg ÷ 4 4 m 3 ÷ 4 4,532 kg 1 m 3

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Check It Out! Example 2B A piece of gemstone with a volume of 0.25 cubic meters weighs 3540 kilograms. What is the density of the gemstone? The gemstone has a density of 14,160 kg/m kg 0.25 m 3 Write the rate. Multiply to find kilograms per 1 m kg m ,160 kg 1 m 3

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Estimate each unit rate. Additional Example 3A: Estimating Unit Rates Choose a number close to 468 that is divisible by 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. Additional Example 3B: Estimating Unit Rates Choose a number close to 313 that is divisible by feet in 8 seconds 313 feet to 8 seconds is approximately 40 feet per second. 313 feet 8 seconds 320 feet 8 seconds 40 feet 1 second Divide to find feet per second.

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Estimate each unit rate. Check It Out! Example 3A Choose a number close to 583 that is divisible by 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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Estimate each unit rate. Check It Out! Example 3B Choose a number close to 271 that is divisible by yards in 3 hours 271 yards to 3 hours is approximately 90 yards per hour. 271 yards 3 hours 270 yards 3 hours 90 yards 1 hour Divide to find yards per hour.

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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 = $ =$0.39 price for package number of pens = $ $0.41 The 5-pack for $1.95 has the lower unit price.

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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? Additional Example 4B: Finding Unit Prices to Compare Costs $ = $0.15 = $ $0.14 The 20 oz jar for $2.78 has the lower unit price. price for jar number of ounces price for jar number of ounces Divide the price by the number of ounces.

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Golf balls can be purchased in a 3-pack for $4.95 or a 12-pack for $ Which pack has the lower unit price? Check It Out! Example 4A Divide the price by the number of balls. price for package number of balls $ =$1.65 price for package number of balls = $ $1.58 The 12-pack for $18.95 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? $ = $0.09 = $ $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 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 $ pens for $5.16 or a ten-pack for $ a dozen They cost the same.

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