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# Unit Rates

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Solving rates in Alge

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• ### Unit Rates

1. 1. Unit Rates
2. 2. 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>
3. 3. Examples Rate: 150 heartbeats 2 minutes Unit Rate (Divide to get it): 150 ÷ 2 = 75 heartbeats per minute.
4. 4. 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
5. 5. 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>
6. 6. 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.
7. 7. 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>
8. 8. 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.
9. 9. Rate of Work Problems
10. 10. Marge can clean the house in 3 hrs. Lisa can clean it in 5 hrs. How long will it take them to clean the house if they both work together?
11. 11. Use Unit Rates Marge can clean the house in 3 hrs., so she does 1 / 3 of the house per hour.
12. 12. Use Unit Rates Lisa can clean the house in 5 hrs., so she does 1 / 5 of the house per hour.
13. 13. Let T be the time in hours. 1 3 T + 1 5 T = 1
14. 14. 1 / 3 T + 1 / 5 T = 1 15( 1 / 3 T + 1 / 5 T) = 15(1) 5T + 3T = 15 8T = 15 T = 15 / 8 1 7 / 8 hrs.
15. 15. Bart can wash the car in 20 min. Homer can wash it in 30 min. How long will it take them to wash the car if they both work together?
16. 16. Use Unit Rates Bart can wash the car in 20 min., so he does 1 / 20 of the car per min.
17. 17. Use Unit Rates Homer can wash the car in 30 min., so he does 1 / 30 of the car per min.
18. 18. Let M be the time in minutes. 1 20 M + 1 30 M = 1
19. 19. 1 / 20 M + 1 / 30 M = 1 60( 1 / 20 M + 1 / 30 M) = 60(1) 3M + 2M = 60 5M = 60 M = 12 min.
20. 20. Springfield School
21. 21. 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?
22. 22. 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.
23. 23. 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.
24. 24. 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.