Presentation on theme: "Chapter 6: Ratio, Proportion and Percent"— Presentation transcript:
1 Chapter 6: Ratio, Proportion and Percent Chapter 6 Lesson 1Ratios and RatesPgsWhat you will learn:Write ratios as fractions in simplest formDetermine unit rates
2 VocabularyRatio (264): a comparison of two numbers by division. Ratioscan be written in the following three ways:2 to :4Remember that a fraction bar represents division. When theFirst number being compared is less that the second, the ratioIs usually written as a fraction in simplest form.Rate (265): a ratio of two measurements having different kindsof units.Ex) 65 miles in 3 hours miles and hours aredifferent kinds of units$16 for 2 pounds Dollars and pounds are
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 poundExample Uno: Write Ratios as FractionsExpress the ratio 9 goldfish out of 15 fish in simplest form9 = Divide the numerator and denominatorby the GCF, 3The ratio of goldfish to fish is 3 to 5. This means that for every5 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 FractionsExpress the ratio 3 feet to 16 inches as a fraction in simplest form.3 feet = inches Here we convert feet to inches16 inches inchesSimplify: inches = 9 inches We divide the numerator16 inches inches & denominator by theGCF 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 of30 recordable CDs costs $28. Which package has the lowercost per CD?Recall the definition of Unit Rate (265): when a rate issimplified so that it has a denominator of 1.Ex) $5 per pound, which means $5 per 1 pound18 dollars = Divide the numerator and20 CDs 1 CD denominator of 18 by 20 so the20new denominator will = 1Do the same with the second rate:28 dollars = Divide the numerator & denomintor30 CDs 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 lowercost 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 throughouta computation.Example Cuatro: Convert RatesA grizzly bear can run 30 miles in 1 hour. How manyfeet is this per second?You need to convert 30 miles to ft1 hr sThere 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 seconds1 hr hr mi hr= 30 mi ft 1 hr Remember, use the reciprocal when1 hr mi s dividing fractions= 30 mi 5280 ft 1 hr1 hr mi s Divide the common factors and units
8 441= 30 mi 5280 ft 1 hr1 hr mi s Divide the common factors and units= 44 ftsSo, 30 miles per hour is equivalent to 44 feet per second.When working on problems like this, work carefully andlogically think through what you are doing!!1201
9 Your Turn!!Express each ratio as a fraction in simplest form.18 cups to 45 cups9 pounds to 16 tons (2000 pounds/ton)155 apples to 75 orangesExpress each ratio as a unit rate, round to nearest tenth if needed$3 for 6 cans of tuna68 meters in 15 seconds236.7 miles in 4.5 days18 = 6 = 29 = 9,000155 = 31$0.50/can4.5 m/sec52.6 mi/day
10 Take a practice sheet & see me during study hall if you have questions !!