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- 1. Unit Rates
- 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. Examples Rate: 150 heartbeats 2 minutes Unit Rate (Divide to get it): 150 ÷ 2 = 75 heartbeats per minute.
- 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. 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. 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. 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. 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. Rate of Work Problems
- 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. Use Unit Rates Marge can clean the house in 3 hrs., so she does 1 / 3 of the house per hour.
- 12. Use Unit Rates Lisa can clean the house in 5 hrs., so she does 1 / 5 of the house per hour.
- 13. Let T be the time in hours. 1 3 T + 1 5 T = 1
- 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. 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. Use Unit Rates Bart can wash the car in 20 min., so he does 1 / 20 of the car per min.
- 17. Use Unit Rates Homer can wash the car in 30 min., so he does 1 / 30 of the car per min.
- 18. Let M be the time in minutes. 1 20 M + 1 30 M = 1
- 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. Springfield School
- 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. 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. 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. 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.
- 25. Grading Papers
- 26. 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?
- 27. Use Unit Rates Minutes work better than hours. Mrs. Krabappel grades 1 / 90 of a set per min.
- 28. Use Unit Rates Miss Hoover grades 1 / 80 of a set per min.
- 29. 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.
- 30. Approximately how long would it take them to grade 3 sets if they both work together?
- 31. 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.
- 32. Math Is Fun

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