Rational Expressions

Transcription

1 Algebra Assignment Sheet Name: Date: Period: # Rational Expressions (1) Page 183 #11 22 all (2) Page 646 #2 7 and #9 14 (3) Page 646 #17 38 LEFT (4) Page 646 #19 40 RIGHT (5) Page 653 #10 30 Even *******Quiz tomorrow******* (6) Page 667 #9 27 left (7) Page 667 #11 29 right (8) page 673 #12 33 left (9) page 673 #14 34 right *******Quiz tomorrow******* (10) page 679 #4 9 (11) page 679 #10 18 (12) page 679 #19-27 (13) page 679 #28-31 (14) Worksheet (15) chapter review page 192 #32 34; page #2 8 even, #11 21 odd (16) practice chapter test *******test tomorrow******* (17) page #1 5; 10 13

2 3.8 Rates and Ratios (R,E/1) Rates, Ratios and Percents If a and b are two quantities measured in different units, then the is. Rates are often express as unit rates. A is a rate per one given unit, such as 60 miles per 1 gallon. E1) How can you relate this information to individual spending (total population was about 266 million in 1996)? Estimated Spending for Clothes and Food in the United States in 1996 Clothing and Shoes Restaurants Food at home $183 billion $190 billion $300 billion E2) Mileage: You have recorded your car mileage and gasoline use for 2 months. Estimate the number of miles you can drive on a full 18-gallon tank of gasoline. Number of miles Number of gallons E3) a. You are visiting Mexico and you want to exchange $180 for pesos. The rate of currency exchange is pesos per United States dollar. You want to find out how many pesos you will receive. b. When you leave Mexico, you are surprised to find that you have exactly 180 pesos left. You want to find out how many United States dollars you will receive. The rate of currency is now pesos per dollar.

3 E4) Tulips: You tested a sample of 50 tulip bulbs from a shipment of 4500 bulbs for resistance to a type of mold. You found that 32 of the bulbs had a natural resistance, and 18 did not. Use these results to estimate the number of bulbs in the shipment that will have a natural resistance to the mold. E5) What percent of year-olds said that they are dating? A Survey of Teen Dating Age Group Number Surveyed Number Who Are Dating year olds year olds year olds E6) Glass Recycling: The circle graph shows the percent of glass containers recycled in the United States in a recent year. About 3.2 million tons of glass containers were recycled. Estimate the total weight of glass containers used that year. Glass Containers Recycled 29% Not recycled 71%

4 11.1 Ratios and Proportions (R,E/3) Ratio and Proportion An equation that states that two ratios are equal is a. where b and d are nonzero This proportion is read as a is to b as c is to d. When the ratios are written in this order, the numbers a and d are the of the proportion and the numbers b and c are the of the proportion. Properties of proportions 1) Reciprocal Property states: If, then. 2) Cross Product Property states: If, then ad = bc. When a proportion involves a single variable, finding the value of the variable is called. Watch out for solutions. Extraneous solutions are trial solution that do not satisfy the original equation. E1) Solve the proportion P1) Solve the proportion E2) Solve the proportion P2) Solve the proportion E3) Solve the proportion P3) Solve the proportion E4) You want to make a scale model of one of the clay horses found in the tomb. The clay horse is 1.5 meters tall and 2 meters long. Your scale model will be 18 inches long. How tall should it be? P4) You want to make a scale model of a parade float. The float is 5.5 feet high and 10 feet long. Your model will be 14 inches long. How tall should it be

5 11.2 Percents (R,E/1) Percents E1) What is 30% of 70 feet? E2) Fourteen dollars is 25% of what amount of money? E3) One hundred thirty-five is what percent of 27? E4) Science: There are about 170,000 species of butterflies and moths world-wide. Butterflies and moths make up about 17% of all classified insect species. Estimate how many insect species have been classified. Insect Species in North America Diptera (true flies), 20% Other, 16% Lepidoptera(butt erflies and moths), 13% Hymenoptera (includes bees and ants), 18% Coleoptera (beetles), 33% E5) The circle graph shows the average costs (in percents) of owning an automobile in Suppose that in 1996 a car owner spent $650 on gasoline for a car whose total costs were $3750. Was the percent spent on gasoline about the same as the national average? Automobile Ownership Costs Maintena nce 7.70% Insurance 14.10% Tires 3.60% Gasoline 17.10% Other 4.60% Depreciati on and Interest 52.90%

6 11.4 Simplyfing Rational Expressions with Excluded Domain Values (I,E/2) Simplifying Rational Expressions A rational expression is if its numerator and denominator have no factors in common (other than 1). E1) Simplify the expression a. b. c. P1) Simplify the expression a. b. c. E2) Simplify P2) Simplify E3) Simplify P3) Simplify E4) In Examples 2 and 3, are the original expression and the simplified expression defined for the same values of the variable? P4) In Practice 2 and 3, are the original expression and the simplified expression defined for the same values of the variable?

7 11.5 Multiplying and Dividing Rational Expressions (I,E/2) Multiplying and Dividing Rational Expressions E1)Simplify P1)Simplify E2) Simplify P2) Simplify E3) Simplify P3) Simplify E4) Simplify P4) Simplify E5) Simplify P5) Simplify

8 11.6 Adding and Subtracting Rational Expressions (I,E/5) Adding and Subtracting Rational Expressions E1) Simplify a. b. P1) Simplify a. b. E2) Simplify P2) Simplify E3) Simplify P3) Simplify E4) Simplify P4) Simplify