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**Chapter 6: Ratio, Proportion and Percent**

Chapter 6 Lesson 1 Ratios and Rates Pgs What you will learn: Write ratios as fractions in simplest form Determine unit rates

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Vocabulary Ratio (264): a comparison of two numbers by division. Ratios can be written in the following three ways: 2 to : 4 Remember that a fraction bar represents division. When the First number being compared is less that the second, the ratio Is usually written as a fraction in simplest form. Rate (265): a ratio of two measurements having different kinds of units. Ex) 65 miles in 3 hours miles and hours are different kinds of units $16 for 2 pounds Dollars and pounds are

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**Unit Rate (265): when a rate is simplified so that it has a**

denominator of 1. Ex) $5 per pound, which means $5 per 1 pound Example Uno: Write Ratios as Fractions Express the ratio 9 goldfish out of 15 fish in simplest form 9 = Divide the numerator and denominator by the GCF, 3 The ratio of goldfish to fish is 3 to 5. This means that for every 5 fish, 3 of them are goldfish

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**When writing a ratio involving measurements, both quantities**

Should have the same unit of measure. Example Dos: Write Ratios as Fractions Express the ratio 3 feet to 16 inches as a fraction in simplest form. 3 feet = inches Here we convert feet to inches 16 inches inches Simplify: inches = 9 inches We divide the numerator 16 inches inches & denominator by the GCF of 4. “Inches” cancel with each other. Written in simplest form, the ratio is 9 to 4.

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**Example Tres: Find Unit Rate**

A package of 20 recordable CDs costs $18, and a package of 30 recordable CDs costs $28. Which package has the lower cost per CD? Recall the definition of Unit Rate (265): when a rate is simplified so that it has a denominator of 1. Ex) $5 per pound, which means $5 per 1 pound 18 dollars = Divide the numerator and 20 CDs 1 CD denominator of 18 by 20 so the 20 new denominator will = 1 Do the same with the second rate: 28 dollars = Divide the numerator & denomintor 30 CDs CD by 30 to get a denominator of 1.

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**Now compare the two unit rates:**

For the 20-pack, the unit rate is $.90 per CD. For the 28-pack, the unit rate is $.93 per CD. So the package that contains 20 CDs has the lower cost per CD. Concept Check: Is $50 in 3 days a rate or a unit rate? Explain. Since the ratio doesn’t have a denominator of 1, it is a rate.

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**To convert a rate such as miles per hour to a rate such as feet **

per second, you can use dimensional analysis (Lesson 5-3). remember that this is the process of carrying units throughout a computation. Example Cuatro: Convert Rates A grizzly bear can run 30 miles in 1 hour. How many feet is this per second? You need to convert 30 miles to ft 1 hr s There are 5280 ft in 1 mile and 3600 seconds in 1 hour. 30 mi = 30 mi 5280 ft 3600s Convert feet to miles and hours to seconds 1 hr hr mi hr = 30 mi ft 1 hr Remember, use the reciprocal when 1 hr mi s dividing fractions = 30 mi 5280 ft 1 hr 1 hr mi s Divide the common factors and units

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44 1 = 30 mi 5280 ft 1 hr 1 hr mi s Divide the common factors and units = 44 ft s So, 30 miles per hour is equivalent to 44 feet per second. When working on problems like this, work carefully and logically think through what you are doing!! 120 1

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Your Turn!! Express each ratio as a fraction in simplest form. 18 cups to 45 cups 9 pounds to 16 tons (2000 pounds/ton) 155 apples to 75 oranges Express each ratio as a unit rate, round to nearest tenth if needed $3 for 6 cans of tuna 68 meters in 15 seconds 236.7 miles in 4.5 days 18 = 6 = 2 9 = 9 ,000 155 = 31 $0.50/can 4.5 m/sec 52.6 mi/day

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**Take a practice sheet & see me during study hall if you**

have questions !!

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