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CHAPTER 11 – PART A

CHAPTER 11 – PART A

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CHAPTER 11 – PART A

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  1. CHAPTER 11 – PART A Lesson’s Covered: 11.1 11.2 QUIZ COVERING 11.1-11.2 11.4 11.5 QUIZ COVERING 11.4-11.5 Part A TEST

  2. Algebra I – Chapter 11 Daily Warm-Up Factor the Trinomial 1. y² + 5y - 14 Solve the Quadratic Equation by Factoring 2. x² - 9x = -14

  3. 11.1 Ratio and Proportion Objectives: • Write and solve proportions • Use proportions in real life

  4. A ratio is a comparison of two quantities of the same kind, expressed in the same units. • The steepness of a hill can be written as the ratio of its height to its horizontal extent. • Ratios can be expressed as follows: • 2 to 3 • 2:3 • 2/3

  5. 1 4 = 3 12 A proportion is an equation stating that 2 ratios are equal. is a proportion Read: “1 is to 3 as 4 is to 12” Read:

  6. × = × 2 6 3 4 = 5y 6x = ad bc = 3a 30 Cross Product Property: The product of the extremes equals the product of the means. Extremes Means Apply the cross product property to: a = ?

  7. = w 12 9 = y 2 = ± t 5 Solve the proportions: 2w = 24 4y = 18 50 = 2t² 25 = t²

  8. Solve the proportions:

  9. YOUR TURN-Solve the proportions:

  10. Extraneous solution – solution that doesn’t satisfy the original equation. 2(y² - 9) = (y + 3)(y – 3) 2y² - 18 = y² - 9 y² - 9 = 0 (y + 3)(y – 3) = 0 y = ? Remember to check in original equation!! Why not ±3?

  11. YOU TRY-Remember to check for Extraneous Solutions! Extraneous solution – solution that doesn’t satisfy the original equation.

  12. Using Proportions in Real Life You want to make a scale model of a parade float. The float is 5.5 feet long and 10 feet high. Your model will be 14 inches high. How long should it be?

  13. Algebra I – L 11.1 What is present in every paint bucket but absent in every translucent bucket? Clue: it is not paint. Tonight’s Homework: Pages 646-647 #’s 17-18, 27-28, 30-31, 44

  14. Algebra I – Chapter 11 Daily Warm-Up

  15. 11.2 Percents Goal: Use equations to solve percent problems Use percents in real-life problems

  16. What is 50% of 90? Percent Equation: Percent Proportion: a = p * b a/b = p/100 a = b = p = of =. (multiplication) % = decimal (move 2 to the left) – For Equation ONLY! Is = “=“

  17. Let’s Solve for a, p, or b? 131 is what % of 255? What is 150% of $200? 9.6 is 12% of what number?

  18. Your Turn. Solve each % Problem. 18 is what percent of 60? 52 is 12.5% of what number? What distance is 24% of 710 miles? $4 is 2.5% of what number? 2 is what percent of 40 feet? 9 people is what percent of 60 people? 85% of 300 is what number?

  19. The graph shows the results of a poll of student taken to find out the average amount of time spent on various activities in a 24 hour period. How many hours on average spent sleeping? How many hours watching TV?

  20. Algebra I – L 11.2 1-2-3-4-5-6I am a 6 letter word.Letters 6-5-2 spell out a drink.Letters 4-5-2-3 spell out a fruit.Letters 1-2-6 spell out a pet.Letters 3-2-6 spell out a pest, which often gets eaten by 1-2-6. What am I? Tonight’s Homework: Page 653 #’s 10-20, 33

  21. Algebra I – Chapter 11 Daily Warm-Up • What number is 54% of $88? • 631 feet is what percent of 1,281 feet?

  22. 11.4 Simplifying Rational Expressions Goals: Simplify a rational expression Use rational expressions to find geometric probability

  23. Rational number = a number that can be written as a quotient of 2 integers (fraction)

  24. Rational expressions = an expression number that can be written as a fraction of 2 nonzero polynomials

  25. Simplify Rational Expressions: • Factor out a GCF, if possible • Factor if it is quadratic, if possible • Reduce the numerical part, if possible • Cancel out common factors (blocks)

  26. Simplify Rational Expressions: • Factor out a GCF, if possible • Factor if it is quadratic, if possible • Reduce the numerical part, if possible • Cancel out common factors (blocks) = = What values for x would make these expressions undefined?

  27. Simplify Rational Expressions: • Factor out a GCF, if possible • Factor if it is quadratic, if possible • Reduce the numerical part, if possible • Cancel out common factors (blocks) = x ≠ 0, 1/2 = What values for x would make these expressions undefined?

  28. Simplify Rational Expressions: • Factor out a GCF, if possible • Factor if it is quadratic, if possible • Reduce the numerical part, if possible • Cancel out common factors (blocks)

  29. Simplify Rational Expressions: • Factor out a GCF, if possible • Factor if it is quadratic, if possible • Reduce the numerical part, if possible • Cancel out common factors (blocks)

  30. Simplify Rational Expressions: • Factor out a GCF, if possible • Factor if it is quadratic, if possible • Reduce the numerical part, if possible • Cancel out common factors (blocks)

  31. Algebra I – L 11.4 There were four brothers who were born in this world together. One runs but is never weary, One eats but is never full, One drinks but is never thirsty, One sings a song that is never good. Who are they? Tonight’s Homework: Page 667 #’s 9-11, 18-20, 25-26

  32. Algebra I – Chapter 11 Daily Warm-Up

  33. 11.5 Multiplying and Dividing Rational Expressions Goals: Multiply and divide rational expressions Use rational expressions in real-life models

  34. Change Keep Flip Multiply fractions: Divide fractions:

  35. Multiply/Divide Rational Expressions: • If Division, change to Multiplication • GCF & factor quadratics if possible • Cancel all common factors (blocks)

  36. + 2x 1 × - (2x 3) 2 - - 2x x 3 • Multiply/Divide Rational Expressions: • If Division, change to Multiplication • GCF & factor quadratics if possible • Cancel all common factors (blocks) 1 (2x-3)(x+1)

  37. Multiply/Divide Rational Expressions: • If Division, change to Multiplication • GCF & factor quadratics if possible • Cancel all common factors (blocks)

  38. Multiply/Divide Rational Expressions: • If Division, change to Multiplication • GCF & factor quadratics if possible • Cancel all common factors (blocks)

  39. n - 2 n + 5 • = - 2n n 2 • Multiply/Divide Rational Expressions: • If Division, change to Multiplication • GCF & factor quadratics if possible • Cancel all common factors (blocks) n+5 2n = keep flip change

  40. 5x² - 20x ¸ (x - 4) + x 5 • Multiply/Divide Rational Expressions: • If Division, change to Multiplication • GCF & factor quadratics if possible • Cancel all common factors (blocks) =

  41. Now you try:

  42. Algebra I – L 11.5 Remove six letters from this sequence to reveal a familiar English word. BSAINXLEATNTEARS If you drop me I'm sure to crack but give me a smile and I'll always smile back Tonight’s Homework: Page 673 #’s 12, 15, 18, 22, 32

  43. CHAPTER 11 – PART B Lesson’s Covered: 11.6 11.7 QUIZ COVERING 11.6-11.7 11.8 Part B TEST

  44. 11-6 Adding and Subtracting Rational Expressions Goal: Add & subtract rational expressions with like and unlike denominators.

  45. Vocabulary • LCD – Least common denominator is the least common multiple of the denominators of two or more fractions.

  46. Adding and Subtracting with Like Denominators • Let a, b, and c be polynomials, with c ≠0. • To add, add numerators: a + b = a + b c c c • To subtract, subtract the numerators. a – b = a – b c c c

  47. Ex 1 – Common Denominators 7 + 2x -7 = 7 +(2x – 7) = 2x = 2x 2x 2x 2x 5 - 2m = 5 – 2m 3m – 4 3m – 4 3m - 4 1

  48. Now you try: • 5 + x – 6 = 3x 3x • 9 - 4n = 2n – 1 2n - 1

  49. Ex 2 – Common Denominators 3x - x + 1 = 3x – ( x + 1) 2x² + 3x - 2 2x² + 3x - 2 2x² + 3x – 2 = 2x – 1 Factor and divide out common factors (2x – 1) ( x + 2) = 1 x + 2 Simplified form

  50. Add or Subtract and Simplify