Chapter 6: Ratio, Proportion and Percent

1. Chapter 6: Ratio, Proportion and Percent Chapter 6 Lesson 1 Ratios and Rates Pgs. 264-268 What you will learn: Write ratios as fractions in simplest form Determine unit rates

2. Vocabulary Ratio (264): a comparison of two numbers by division. Ratios can be written in the following three ways: 2 to 4 2:4 2 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 insimplest 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 different kinds of units

3. 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 = 3 Divide the numerator and denominator 15 5 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

4. 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 feetto 16 inches as a fraction in simplest form. 3 feet = 36 inches Here we convert feet to inches 16 inches 16 inches Simplify: 36 inches = 9 inches We divide the numerator 16 inches 4 inches & denominator by the GCF of 4. “Inches” cancel with each other. Written in simplest form, the ratio is 9 to 4.

5. 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 = 0.9 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 = .93 Divide the numerator & denomintor 30 CDs 1 CD by 30 to get a denominator of 1.

6. 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.

7. 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 1 s There are 5280 ft in 1 mile and 3600 seconds in 1 hour. 30 mi = 30 mi 5280 ft 3600sConvert feet to miles and hours to seconds 1 hr 1 hr 1 mi 1 hr = 30 mi  5280 ft  1 hr Remember, use the reciprocal when 1 hr 1 mi 3600 s dividing fractions = 30 mi  5280 ft  1 hr 1 hr 1 mi 3600 s Divide the common factors and units

8. 44 1 = 30 mi  5280 ft  1 hr 1 hr 1 mi 3600 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

9. 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 45 15 5 9 = 9 16 32,000 155 = 31 75 15 $0.50/can 4.5 m/sec 52.6 mi/day

10. Take a practice sheet & seeme during study hall if you have questions !!