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2.6 Ratios, Rates and Conversions:

Ratio: a comparison of two numbers using division. 2.6 Ratios, Rates and Conversions:. Rate: A ratio that compares quantities measured in different units. Unit Rate: A rate with 1 in the denominator. Conversion Factor: A ratio of two equivalent measures in different units.

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2.6 Ratios, Rates and Conversions:

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  1. Ratio: a comparison of two numbers using division. 2.6 Ratios, Rates and Conversions: Rate: A ratio that compares quantities measured in different units. Unit Rate: A rate with 1 in the denominator.

  2. Conversion Factor: A ratio of two equivalent measures in different units. Unit Analysis (Dimension Analysis): The process of including the units of quantities in a conversion to obtain the desired units.

  3. GOAL:

  4. REAL-WORLD: Justin runs for 25 minutes and does 8 laps around the track. What is the time he takes to do a lap?

  5. Solution: Justin runs 25 minutes Justin does 8 laps The unit rate is: by 8 Justin takes an average of 3.125 minutes per lap.

  6. We can use unit rates to compare quantities: Ex: There are three stores that sell the same shirt. Use the info to tell which stores is the most affordable? Store A: $25 for 2 shirts Store B: $45 for 4 shirts Store C: $30 for 3 shirts In order to compare the prices, we must find out the price of a single shirt.

  7. SOLUTION:To find the price per shirt we must find the ratio of price to one shirt. A: $25 for 2 shirts B: $45 for 4 shirts = = C: $30 for 3 shirts = Looking at the price per shirt, Store C is the most affordable.

  8. Converting Units: When we are given units different from the ones we want to work with, therefore we must use the conversion factor(a ratio of two equivalent measures in different units). Ex:What is 125 cm in meters? Here x represents thenumber of cm that makeup a meter, that is x = 100 125cm ∙ ∙ = = 1.25 m Hence: 125cm is equivalent to 1.25 m.

  9. NOTICE: By now you must have a knowledge of the conversions we use in everyday life, such as: ALSO: This is the on that will be given to you on the baselines, interims and EOCs.

  10. YOU TRY IT: Convert 5 kg to milligrams?

  11. YOU TRY IT: (Solution) Here we must start by relating kilograms to milligrams: • We must know that: 1 kg = 1000 grams and 1 gram = 100 milligrams Using this info we set up the conversion as: ∙ ∙ Then:

  12. YOU TRY IT: What is 9 yards in meters?

  13. Solution: Here we must start by relating yards to meters. • We must know that: 1 yrd = 3ftand 1 ft = 12 in • and 1 in = 2.54 cm • and 100 cm = 1 meter. Using this info we set up the conversion as: ∙ ∙ ∙ ∙ Then:

  14. YOU TRY IT: Copy and complete the statement. 2.5 days = ____ sec.

  15. Solution: Relate days to minutes: • 1 day = 24 hrsand 1 hr = 24 min • and 1 min = 60 sec. Using this info we set up the conversion as: ∙ ∙ ∙ Then:

  16. VIDEOS: Unit Conversion https://www.khanacademy.org/math/arithmetic/rates-and-ratios/unit_conversion/v/converting-yards-into-inches https://www.khanacademy.org/math/arithmetic/rates-and-ratios/unit_conversion/v/converting-gallons-to-quarts-pints-and-cups https://www.khanacademy.org/math/arithmetic/rates-and-ratios/unit_conversion/v/converting-pounds-to-ounces

  17. CLASS WORK: Pages: 121 – 123 Problems: As many as it takes to master the concept.

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