Unit 4: Comparing & Scaling Name: key

Transcription

1 Unit 4: Comparing & Scaling Name: key 1.1: Analyzing Comparison Statements Ex: How to write a ratio and percents? a. The ratio of Glen s rock CD s to Nina s Rock CD s: or 3: 4 or 3 to 4 b. The fraction of Classical to Total CD s (Nina and Glen): or 4: 15 or 4 to 15 Classical CDs Rock CDs Other CDs Glen Nina Total CDs% c. The fraction of Glen s CD s that are Rock is d. The percent of Glen s CD s that are Classical is % e. Who has greater percent of other Cd s? Glen : % Nina : % 1.2: Comparing Ratios Ex: Write each comparison of concentrate to water as a ratio. a. The mix is 70% concentrate. 70% concentrate 7 30% water 3 b. The fraction of the mix that is water is 2. 5 or 7: 3 or 7 to % concentrate 40% water 3 2 or 3: 2 or 3 to 2

2 1.3: Scaling Ratios Ex: You have an orange juice recipe that calls for 3 cups of water for each 1 cup of concentrate. Part to Part Ratio (concentrate to water): 1 (concentrate) 3 (water) Part to Whole Ratio (concentrate to whole): 1 (concentrate) 4 (concentrate+water) 1.4: Scaling to Solve Proportions Ex: Among American doctors, the ratio of men outnumber women by a ratio of 12 to 5. If there are about 600,000 American doctors that are men, how many are women? 12 men 600,000 men 5 women? No matter which way you set it up, when you solve using cross product you get: 12x 5 600,000 12x 3,000,000 x 250,000 women

3 Ex: There are 12 cookies in a 30 ounce package. a) Write and solve a proportion to find the number of cookies in a 50 ounce package. 12 cookies? 30 ounces 12 cookies or cookies 30 ounce 50 ounce 50 ounces? b) How many ounces does each cookie weigh? 30 ounces? 12 cookies 1 cookie ounces 2.1: Comparison Strategies Ex: (Problem 2.1 A) The campers at each tables share the pizzas equally. Does a person at a small table get the same amount of pizza as a person sitting at a large table? no Large: % Small: % 2.2: Scaling Rates Ex: Julie can drive her car 400 miles at a steady speed using 16 gallons of gasoline. a) Make a rate table to show the number of miles she can drive her car for 1, 2, 3, 400 miles? miles per gallon 16 gallons 1 gallon Gallons Miles

4 b) How many gallons of gas would you need to go 515 miles? 25 miles 1 gallon 515 miles? gallons 2.3: Unit Rate and Constant of Proportionality Ex: The tram ride at a theme park covers a distance of 3½ miles in ¼ of an hour. a) How many miles per hour does the tram go? miles 3.5 1? hour.25 1 hour 4 b) How far can the tram travel in 5 hours? 14 miles 1 hour? 5 hours m/h miles Ex: Find the cost per rose for both situations below. Which is the better buy (cheaper)? a) 3 roses for $5 b) 7 roses for $9 $5 3 roses $9 7 roses 5 3 $1.67 per rose 9 7 $1.29 per rose

5 Ex: It costs $5.10 for 6 apples. a) What is the constant of proportionality? $ $0.85 per apple 6 apples b) Write an equation that relates the number of apples, a, and the cost, C. 3.1: Proportions with Percents C $0. 85 a Commission: The amount earned, based on the percent of total sales. For example, a car salesperson who earns 10% on car sales and sells $60,000 worth of cars would earn a commission of $6,000 (10% of $60,000). Markup The amount added to the buying price of an item. It is usually a percent of the buying price. Ex: Brian made $52,000 at a job this year. Next year, he is supposed to get a 4% raise. How much will he make next year? 100% 52, % X OR 4% 100% X 52, $54, $54, : Measurement Conversions

6 Ex: Describe what value x represents and solve for x. a) 16 ounces 1 pound x 4.2 pounds b) 1 gallon 16 cups x 24 cups ounces gallons Ex: There are about 11.5 grams of fat in 1 tablespoon of butter. How many grams of fat are in 1 cup of butter? (Note: 16 tablespoons 1 cup) cup 2 cup 16 tbsp? 11.5 grams 1 tbsp? 8 tbsp tbsp grams 3.3: Connecting Ratios, Rates, Percents, and Proportions Ex: You are making a punch that is 40 % pineapple juice and 60% orange juice. If you have a pitcher that can hold 32 ounces, how much orange juice should you put in? 60% orange 100% total? 32 ounces ounces orange Ex: The engine in Kevin s power washer uses an oil-gas mixture. It takes ¼ parts oil with 2 parts gas. Kevin has a 16 ounce container of oil and plans to use all of it. a) How much gas will he need to add? 1 4 oil 2 gas 16 oil? ounces of gas b) How large of a container will he need to hold the mixture? 16 cups 1 gallon 8 ounces 1 cup 128 ounces in a gallon 1 gallon