1. 3/19/2016Math 120 - KM1 Chapter 7: Rational Equations, Expressions, and Functions 7.1 Multiplication and Division 7.2 Addition and Subtraction 7.3 Division of Polynomials 7.4 Complex Rational Expressions.4 Complex Rational Expressions 7.5 Solving Rational Equations.5 Solving Rational Equations 7.6 Applications and Proportions.6 Applications and Proportions 7.7 Formulas and Applications.7 Formulas and Applications 7.8 Variation and Applications.8 Variation and Applications

2. 3/19/2016Math 120 - KM2 7.1

3. 3/19/2016Math 120 - KM3 Simplify a Rational Expression Factor each polynomial Like Factors reduce to 1 Opposite Factors reduce to -1 7.1

4. 3/19/2016Math 120 - KM4 How about Opposite Factors? Factor each polynomial Like Factors reduce to 1 Opposite Factors reduce to -1 7.1

5. 3/19/2016Math 120 - KM5 How about another one? Factor each Polynomial Like Factors reduce to 1 Opposite Factors reduce to -1 7.1

6. 3/19/2016Math 120 - KM6 Okay, one more to be sure! Factor each Polynomial Like Factors reduce to 1 Opposite Factors reduce to -1 7.1

7. 3/19/2016Math 120 - KM7 Oh, don’t forget ones like this! Factor each Polynomial Like Factors reduce to 1 Opposite Factors reduce to -1 7.1

8. 3/19/2016Math 120 - KM8 Multiply Straight Across Factor each Polynomial Like Factors reduce to 1 Opposite Factors reduce to -1 7.1

9. 3/19/2016Math 120 - KM9 Polynomials TOO! Factor each Polynomial Like Factors reduce to 1 Opposite Factors reduce to -1 7.1

10. 3/19/2016Math 120 - KM10 Divide: Multiply by the Reciprocal 7.1

11. 3/19/2016Math 120 - KM11 Polynomials too! 7.1

12. 3/19/2016Math 120 - KM12 7.2

13. 3/19/2016Math 120 - KM13 Addition & Subtraction LCD Higher Terms Reduce + or - 7.2

14. 3/19/2016Math 120 - KM14 Addition & Subtraction: Ex 1 LCD Higher TermsReduce+ or - 7.2

15. 3/19/2016Math 120 - KM15 Addition & Subtraction: Ex 2 LCD Higher TermsReduce+ or - 7.2

16. 3/19/2016Math 120 - KM16 Addition & Subtraction: Ex 3 LCD Higher TermsReduce+ or - 7.2

17. 3/19/2016Math 120 - KM17 Addition & Subtraction: Ex 4 LCD Higher TermsReduce+ or - 7.2

18. 3/19/2016Math 120 - KM18 7.3

19. 3/19/2016Math 120 - KM19 Short Division Distribute the monomial divisor Simplify each term. 7.3

20. 3/19/2016Math 120 - KM20 Long Division Divisor Quotient Remainder Dividend Division Symbol Equal Symbol 7.3

21. 3/19/2016Math 120 - KM21 Long Division Divisor Quotient Fractional Remainder Dividend Division Symbol 7.3

22. 3/19/2016Math 120 - KM22 Long Division 3 34 4 12417 36 57 48 9 7.3

23. 3/19/2016Math 120 - KM23 Try Polynomials? X-11 7.3

24. 3/19/2016Math 120 - KM24 Just a little Harder 4x + 7 7.3

25. 3/19/2016Math 120 - KM25 Tricky? 2x 2 – 9x + 10 7.3

26. 3/19/2016Math 120 - KM26 Trinomial Divisor? x 2 + 3x + 4 + (6x+6)/(x 2 – x – 1) 7.3

27. 3/19/2016Math 120 - KM27 Synthetic Division 7.3

28. 3/19/2016Math 120 - KM28 Synthetic Division: Ex 1 3x + 2 7.3

29. 3/19/2016Math 120 - KM29 Synthetic Division: Ex 2 7.3

30. 3/19/2016Math 120 - KM30 Synthetic Division: Ex 3 7.3

31. 3/19/2016 Math 120 - KM31 7.4

32. 3/19/2016Math 120 - KM32 Use the LCM or LCD 7.4

33. 3/19/2016Math 120 - KM33 LCD is EZ to use! 7.4

34. 3/19/2016Math 120 - KM34 Work Smart! 7.4

35. 3/19/2016Math 120 - KM35 Do this in your HEAD! 7.4

36. 3/19/2016Math 120 - KM36 You CAN do this! 7.4

37. 3/19/2016Math 120 - KM37 You Have the Power! 7.4

38. 3/19/2016Math 120 - KM38 Careful with the signs! 7.4

39. 3/19/2016Math 120 - KM39 Calculus Anyone? 7.4

40. 3/19/2016Math 120 - KM40 7.5

41. 3/19/2016Math 120 - KM41 Strategy 7.5

42. 3/19/2016Math 120 - KM42 Start with an EZ one? 25/14 7.5

43. 3/19/2016Math 120 - KM43 A little harder? 1,4 7.5

44. 3/19/2016Math 120 - KM44 What’s the LCD? 7/2 7.5

45. 3/19/2016Math 120 - KM45 7.6 Proportions and Work Problems 7.6

46. 3/19/2016Math 120 - KM46 Work it … out! Distance = rate  time Part of job completed = rate of work  time worked 7.6

47. 3/19/2016Math 120 - KM47 Think about it! Her rate is 1/8 th of the room per hour Maria can paint a room in 8 hours If she works for 6 hours, she can finish 6 x 1/8 or 3/4ths of the room 7.6

48. 3/19/2016Math 120 - KM48 Teamwork! Renee can build a wall in 10 hours. Sean can build the wall in 15 hours. How long will it take to build the wall if they work together? 6 hours 7.6

49. 3/19/2016Math 120 - KM49 Higher Math? 16 hours Jacob requires 8 hours to shingle a roof by himself. Jacob and Trisha work on a roof for 2 hours, then Jacob leaves for another job. Trisha takes 10 more hours to finish the job. How long would it take Trisha to do the job working alone? 7.6

50. 3/19/2016Math 120 - KM50 Don’t Dive In Yet! A large pump can fill a pool in 6 hours while a small pump would take 15 hours. How long will it take if both pumps work together? 4 hours 17 minutes 7.6

51. 3/19/2016Math 120 - KM51 Oh no, a leak! 7 hours A large pipe can fill a tank in 10 hours while a small pipe could fill it in 14 hours. Inadvertently, a drain is left open which can empty the tank in 35 hours. If the tank starts out empty and both inlets and the drain are working, when will the tank be full? (just before it starts to overflow) 7.6

52. 3/19/2016Math 120 - KM52 A RATIO is the quotient of two quantities that have the same units. 7.6

53. 3/19/2016Math 120 - KM53 A Space Shuttle Ratio On average, the shuttle loses 50 of its 24,000 heat protection tiles during each trip. http://www.ed.arizona.edu/ward/Shuttle/shuttle.html 7.6

54. 3/19/2016Math 120 - KM54 A RATE is the quotient of two quantities that have different units. 7.6

55. 3/19/2016Math 120 - KM55 A UNIT RATE is a rate with a denominator of 1. 7.6

56. 3/19/2016Math 120 - KM56 Starbucks  Yum! http://www.starbucks.com A 16 ounce White Chocolate Mocha has 470 calories. This is a UNIT rate 7.6

57. 3/19/2016Math 120 - KM57 A PROPORTION is the equality of two ratios or rates. 7.6

58. 3/19/2016Math 120 - KM58 Parts of a PROPORTION a is to b as c is to d a:b = c:d 7.6

59. 3/19/2016Math 120 - KM59 Solve This? 7.6

60. 3/19/2016Math 120 - KM60 What if ? 7.6

61. 3/19/2016Math 120 - KM61 Similar Figures? 7.6

62. 3/19/2016Math 120 - KM62 OK…try this one! 7.6

63. 3/19/2016Math 120 - KM63 Trouble Parking? A theatre that can seat 1500 people has a parking lot with 600 spaces. At the same rate, how many parking spaces should a new theatre with 2200 seats create? 7.6

64. 3/19/2016Math 120 - KM64 Time to Vote? A survey showed that 5 out of every 8 voters would vote in a special election. At this rate, how many people would be expected to vote in a city of 180,000 voters ? 7.6

65. 3/19/2016Math 120 - KM65 7.7

66. 3/19/2016Math 120 - KM66 Literally, Solve It! 7.7

67. 3/19/2016Math 120 - KM67 One More! 7.7

68. 3/19/2016Math 120 - KM68 7.8

69. 3/19/2016Math 120 - KM69 Direct Variation y varies directly as x y = kx k is a constant The harder he hits, the higher it goes! 7.8

70. 3/19/2016Math 120 - KM70 Inverse Variation As the elevation increases, the oxygen concentration decreases! y varies inversely as x 7.8

71. 3/19/2016Math 120 - KM71 Types of Variation y varies inversely as x y varies directly as x y = kx z varies jointly as x and y z = kxy k is the constant of proportionality or the constant of variation combined variation 7.8

72. 3/19/2016Math 120 - KM72 DIRECT multiplication 1152 I varies directly as h. If I = 256 when h = 8, determine I when h = 36. 7.8

73. 3/19/2016Math 120 - KM73 Direct again? 211.75 s varies directly as the square of v. If v = 30 when s = 63, determine s when v = 55. 7.8

74. 3/19/2016Math 120 - KM74 Inverse Divide 4.23077 t is inversely proportional to r. If t=5 when r = 55, determine t when r = 65. 7.8

75. 3/19/2016Math 120 - KM75 Force Yourself to Try this one! 80 lbs. The repulsive force, f, between the north poles of two magnets is inversely proportional to the square of the distance, d, between them. If the repulsive force is 20 lbs. when the distance is 4 inches, find the repulsive force when the distance is 2 inches. 7.8

76. 3/19/2016 6:52 PM krm Variation Problems If the voltage, V, in an electric circuit is held constant, the current, I, is inversely proportional to the resistance R. If the current is 40 amperes when the resistance is 270 ohms, find the current when the resistance is 150 ohms. 10800 = k 72 amps Ohm’s Law 7.8

77. 3/19/2016 6:52 PM krm Variation Problems The number of cars manufactured on an assembly line varies jointly as the number of workers and the time they work. 200 workers can produce 60 cars in 2 hours. Determine how many cars 240 workers should be able to produce in 3 hours. kv = 3/20 108 cars Assembly Line 7.8

78. 3/19/2016 6:52 PM krm Variation Problems The cephalic index, C, varies directly as the skull width, w, and inversely as the length of the skull, n. The cephalic index is 70 for a width of 7 and a length of 10. Find the index for a skull with a width of 6 and a length of 8. 75 Anthropology 7.8

79. 3/19/2016Math 120 - KM79 That’s All For Now!