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Unit Rates and Ratios Mr. Swaner

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Rates/ratios Can be written three different ways a to b a:b

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**Because ratios are fractions, they must always be reduced to simplest form**

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Example On average, a baseball team scores 3 runs to every 7 hits. Write a ratio for the situation

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Example On average, a baseball team scores 3 runs to every 7 hits. Write a ratio for the situation 3 to 7 3:7

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Using the ratio We can use the ratio to find the runs or the hits for a scenario. The team scored 6 runs, how many hits did they have?

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**Unit Rates This is the value per unit. You use these all the time:**

At the grocery store For cars At your job Speed

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Unit Rates The denominator must be 1

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Example What is the unit rate: $15 for a 5oz package of cashews. (how much per oz)

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You A car can go 270 miles on 9 gallons of gas. What is the unit rate?

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**The Hamburglar Strikes Again!**

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You Jim can type 500 words in 10 minutes. What is the unit rate?

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You A plane can fly 480 miles per hour. What is the rate in minutes?

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Trial Number Passed Time Ratio Rate Unit Rate 1 2 3 4

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Class # of boys # of girls Ratio of boys to girls 1 2 3 5 6 Are the ratios of boys to girls in the two classes equivalent? What could these ratios tell us? If there is a larger ratio of boys to girls in one class than in the grade as a whole, what does that mean must be true about the boy/girl ratio in other classes?

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**Value-Mart is advertising a Back-to-School sale on pencils**

Value-Mart is advertising a Back-to-School sale on pencils. A pack of 30 sells for $7.97 whereas a 12-pack of the same brand cost for $ Which is the better buy? How do you know?

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Pack of 30 Pack of 12 Ratio: Rate: Unit Rate: Unit of Measure:

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Pack of 30 Pack of 12 Ratio: $7.97 for every 30 pencils $15.94 for every 60 pencils $4.77 for every 12 pencils $23.85 for every 60 pencils Rate: 7.97/30, or approx dollars per pencil 4.77/12, or approx dollars per pencil Unit Rate: 0.27 0.40 Unit of Measure: dollars per pencil

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**How is finding an associated rate or unit rate helpful when making comparisons between quantities?**

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Video

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Exit Ticket 1. At the conclusion of the video, your classmate takes out his calculator and says, “Wow that was amazing! That means the dog went about 5 meters in 1 second!” Is your classmate correct and how do you know? 2. After seeing this video, another dog owner trained his dog, Lightning, to try to break Tillman’s skateboarding record. Lightning’s fastest recorded time was on a 75-meter stretch where it took him 15.5 seconds. Based on this data, did Lightning break Tillman’s record for fastest dog? Explain how you know.

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Topic A: Proportional Relationships

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