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Transcript of "Unit Rates"
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Unit Rates
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Vocabulary <ul><li>A rate is a ratio that compares two quantities measured in different units. </li></ul><ul><li>The unit rate is the rate for one unit of a given quantity. Unit rates have a denominator of 1. </li></ul>
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Examples Rate: 150 heartbeats 2 minutes Unit Rate (Divide to get it): 150 ÷ 2 = 75 heartbeats per minute.
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Find the Unit Rate Amy can read 88 pages in 4 hours. What is the unit rate? (How many pages can she read per hour?) 88 pages 4 hours 22 pages / hour
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Using Unit Rates <ul><li>You can find the missing terms of equal ratios. </li></ul><ul><li>Use the unit rate, and set it equal to another ratio. </li></ul><ul><li>Solve for what is missing by dividing or multiplying. </li></ul>
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Example Joe’s car goes 25 miles per gallon of gasoline. How far can it go on 8 gallons of gasoline? 25 miles 1 gallon Unit Rate = 8 gallons x 8 x 8 25 x 8 = 200. Joe’s car can go 200 miles on 8 gallons of gas.
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Comparing Unit Prices <ul><li>Use division to find the unit prices of the two products in question. </li></ul><ul><li>The unit rate that is smaller (costs less) is the better value. </li></ul>
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Example Juice is sold in two different sizes. A 48-fluid ounce bottle costs $2.07. A 32-fluid ounce bottle costs $1.64. Which is the better buy? $2.07 48 fl.oz. $0.04 per fl.oz. $1.64 32 fl.oz. $0.05 per fl.oz. The 48 fl.oz. bottle is the better value.
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Mr. Skinner can enroll 15 students per hr. Mr. Chalmer can enroll 20 students per hr. How long will it take them to enroll 140 students working together?
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Use Unit Rates Minutes work better than hours. Mr. Skinner enrolls 15 students per 60 min., so he enrolls 15 / 60 or 1 / 4 students per min.
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Use Unit Rates Minutes work better than hours. Mr. Chalmer enrolls 20 students per 60 min., so he enrolls 20 / 60 or 1 / 3 students per min.
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1 / 4 M + 1 / 3 M = 140 12( 1 / 4 M + 1 / 3 M) = 12(140) 3M + 4M = 1680 7M = 1680 M = 240 min. = 4 hrs.
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Mrs. Krabappel can grade a set of papers in 1 1 / 2 hrs. Miss Hoover can grade them in 80 min. How long will it take them to grade one set if they both work together?
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Use Unit Rates Minutes work better than hours. Mrs. Krabappel grades 1 / 90 of a set per min.
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Use Unit Rates Miss Hoover grades 1 / 80 of a set per min.
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1 / 90 M + 1 / 80 M = 1 720( 1 / 90 M + 1 / 80 M) = 720(1) 8M + 9M = 720 17M = 720 M = 42 6 / 17 min.
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Approximately how long would it take them to grade 3 sets if they both work together?
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1 / 90 M + 1 / 80 M = 3 720( 1 / 90 M + 1 / 80 M) = 720(3) 8M + 9M = 2160 17M = 2160 M = 127 1 / 17 min. A little more than 2 hrs.
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