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Splash Screen. Five-Minute Check (over Chapter 7) CCSS Then/Now New Vocabulary Example 1: Simplify a Rational Expression Example 2: Standardized Test Example: Undefined Values Example 3: Simplify Using –1 Key Concept: Multiplying Rational Expressions

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  1. Splash Screen

  2. Five-Minute Check (over Chapter 7) CCSS Then/Now New Vocabulary Example 1: Simplify a Rational Expression Example 2: Standardized Test Example: Undefined Values Example 3: Simplify Using –1 Key Concept: Multiplying Rational Expressions Example 4: Multiply and Divide Rational Expressions Example 5: Polynomials in the Numerator and Denominator Example 6: Simplify Complex Fractions Lesson Menu

  3. Evaluate log12 7. A. 2.4849 B. 1.9459 C. 0.7831 D. 0.5389 5-Minute Check 1

  4. Evaluate log12 7. A. 2.4849 B. 1.9459 C. 0.7831 D. 0.5389 5-Minute Check 1

  5. A. B. C. D. 5-Minute Check 2

  6. A. B. C. D. 5-Minute Check 2

  7. Solve log3 (x2 – 12) = log3 4x. A. 6 B. 7 C. 8 D. 9 5-Minute Check 3

  8. Solve log3 (x2 – 12) = log3 4x. A. 6 B. 7 C. 8 D. 9 5-Minute Check 3

  9. Solve 5ex – 3 = 0. A. –0.5108 B. –0.2197 C. 0.2197 D. 0.4979 5-Minute Check 4

  10. Solve 5ex – 3 = 0. A. –0.5108 B. –0.2197 C. 0.2197 D. 0.4979 5-Minute Check 4

  11. Suppose $200 was deposited in a bank account and it is now worth $1100. If the annual interest rate was 5% compounded continuously, how long ago was the account started? Use the formula A = Pert. A. about 42 years ago B. about 34 years ago C. exactly 29 years ago D. about 24 years ago 5-Minute Check 5

  12. Suppose $200 was deposited in a bank account and it is now worth $1100. If the annual interest rate was 5% compounded continuously, how long ago was the account started? Use the formula A = Pert. A. about 42 years ago B. about 34 years ago C. exactly 29 years ago D. about 24 years ago 5-Minute Check 5

  13. Suppose the population of New York State grows at a rate of 0.3% compounded continuously. In 2006, the population was 19.3 million. Write an equation that represents the population and predict the population in after t years 2020. A.y = 19.3e(0.003)t; about 20.1 million B.y = 19.3e(0.03)t; about 29.4 million C.y = 19.3e(1.003)t; about 52.6 million D.y = 19.3e(1.3)t; about 70.8 million 5-Minute Check 6

  14. Suppose the population of New York State grows at a rate of 0.3% compounded continuously. In 2006, the population was 19.3 million. Write an equation that represents the population and predict the population in after t years 2020. A.y = 19.3e(0.003)t; about 20.1 million B.y = 19.3e(0.03)t; about 29.4 million C.y = 19.3e(1.003)t; about 52.6 million D.y = 19.3e(1.3)t; about 70.8 million 5-Minute Check 6

  15. Content Standards A.APR.7 Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions. Mathematical Practices 8 Look for and express regularity in repeated reasoning. CCSS

  16. You factored polynomials. • Simplify rational expressions. • Simplify complex fractions. Then/Now

  17. rational expression • complex fraction Vocabulary

  18. A. Simplify . Eliminate common factors. ● Simplify a Rational Expression Look for common factors. Simplify. Answer: Example 1A

  19. A. Simplify . Eliminate common factors. ● Answer: Simplify a Rational Expression Look for common factors. Simplify. Example 1A

  20. B. Under what conditions is the expression undefined? Simplify a Rational Expression Just as with a fraction, a rational expression is undefined if the denominator equals zero. The original factored denominator is (y + 7)(y – 3)(y + 3). Answer: Example 1B

  21. B. Under what conditions is the expression undefined? Simplify a Rational Expression Just as with a fraction, a rational expression is undefined if the denominator equals zero. The original factored denominator is (y + 7)(y – 3)(y + 3). Answer: The values that would make the denominator equal to 0 are –7, 3, and –3. So the expression is undefined at y = –7, y = 3, and y = –3. Example 1B

  22. A. Simplify . A. B. C. D. Example 1A

  23. A. Simplify . A. B. C. D. Example 1A

  24. B. Under what conditions is the expression undefined? A. x = 4 or x = –4 B.x = –5 or x = 4 C.x = –5, x = 4, or x = –4 D.x = –5 Example 1B

  25. B. Under what conditions is the expression undefined? A. x = 4 or x = –4 B.x = –5 or x = 4 C.x = –5, x = 4, or x = –4 D.x = –5 Example 1B

  26. For what value(s) of p is undefined? A 5 B –3, 5 C 3, –5 D 5, 1, –3 Undefined Values Read the Test Item You want to determine which values of p make the denominator equal to 0. Example 2

  27. Undefined Values Solve the Test Item Look at the possible answers. Notice that the p term and the constant term are both negative, so there will be one positive solution and one negative solution. Therefore, you can eliminate choices A and D. Factor the denominator. p2 – 2p –15 = (p – 5)(p + 3) Factor the denominator. p – 5 = 0 or p + 3 = 0 Zero Product Property p = 5 p = –3 Solve each equation. Answer: Example 2

  28. Undefined Values Solve the Test Item Look at the possible answers. Notice that the p term and the constant term are both negative, so there will be one positive solution and one negative solution. Therefore, you can eliminate choices A and D. Factor the denominator. p2 – 2p –15 = (p – 5)(p + 3) Factor the denominator. p – 5 = 0 or p + 3 = 0 Zero Product Property p = 5 p = –3 Solve each equation. Answer: B Example 2

  29. For what value(s) of p is undefined? A. –5, –3, –2 B. –5 C. 5 D. –5, –3 Example 2

  30. For what value(s) of p is undefined? A. –5, –3, –2 B. –5 C. 5 D. –5, –3 Example 2

  31. Simplify . Simplify Using –1 Factor the numerator and the denominator. b – 2 = –(–b + 2) or –1(2 – b) Simplify. Answer: Example 3

  32. Simplify . Simplify Using –1 Factor the numerator and the denominator. b – 2 = –(–b + 2) or –1(2 – b) Simplify. Answer: –a Example 3

  33. Simplify . A.y – x B.y C.x D. –x Example 3

  34. Simplify . A.y – x B.y C.x D. –x Example 3

  35. Concept

  36. A.Simplify . Multiply and Divide Rational Expressions Simplify. Simplify. Answer: Example 4A

  37. A.Simplify . Answer: Multiply and Divide Rational Expressions Simplify. Simplify. Example 4A

  38. B. Simplify Multiply by the reciprocal of the divisor. Simplify. Multiply and Divide Rational Expressions Example 4B

  39. Simplify. Multiply and Divide Rational Expressions Answer: Example 4B

  40. Answer: Simplify. Multiply and Divide Rational Expressions Example 4B

  41. A. Simplify . A. B. C. D. Example 4A

  42. A. Simplify . A. B. C. D. Example 4A

  43. B. Simplify . A. AnsA B. AnsB C. AnsC D. AnsD Example 4B

  44. B. Simplify . A. AnsA B. AnsB C. AnsC D. AnsD Example 4B

  45. A.Simplify . Factor. Polynomials in the Numerator and Denominator 1 + k = k + 1,1 – k = –1(k – 1) = –1 Simplify. Answer: Example 5A

  46. A.Simplify . Factor. Polynomials in the Numerator and Denominator 1 + k = k + 1,1 – k = –1(k – 1) = –1 Simplify. Answer: –1 Example 5A

  47. B.Simplify . Polynomials in the Numerator and Denominator Multiply by the reciprocal of the divisor. Factor. Example 5B

  48. Polynomials in the Numerator and Denominator Simplify. Answer: Example 5B

  49. Answer: Polynomials in the Numerator and Denominator Simplify. Example 5B

  50. A. Simplify . A. B. C.1 D.–1 Example 5A

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