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Splash Screen. Five-Minute Check (over Lesson 8–1) CCSS Then/Now Example 1: LCM of Monomials and Polynomials Key Concept: Adding and Subtracting Rational Expressions Example 2: Monomial Denominators Example 3: Polynomial Denominators Example 4: Complex Fractions with Different LCDs

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Splash Screen

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  1. Splash Screen

  2. Five-Minute Check (over Lesson 8–1) CCSS Then/Now Example 1: LCM of Monomials and Polynomials Key Concept: Adding and Subtracting Rational Expressions Example 2: Monomial Denominators Example 3: Polynomial Denominators Example 4: Complex Fractions with Different LCDs Example 5: Complex Fractions with Same LCD Lesson Menu

  3. A. –3rt B. –3r C. 3rt2 D. 4r 5-Minute Check 1

  4. A. –3rt B. –3r C. 3rt2 D. 4r 5-Minute Check 1

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

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

  7. A. B. C. D. 5-Minute Check 3

  8. A. B. C. D. 5-Minute Check 3

  9. A. B. C. D. 5-Minute Check 4

  10. A. B. C. D. 5-Minute Check 4

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

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

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

  14. A. B. C. D. 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 3 Construct viable arguments and critique the reasoning of others. CCSS

  16. You added and subtracted polynomial expressions. • Determine the LCM of polynomials. • Add and subtract rational expressions. Then/Now

  17. LCM of Monomials and Polynomials A. Find the LCM of 15a2bc3, 16b5c2, and 20a3c6. 15a2bc3 = 3 ● 5 ● a2 ● b ● c3 Factor the first monomial. 16b5c2 = 24● b5 ● c2 Factor the second monomial. 20a3c6 = 22● 5 ● a3 ● c6 Factor the third monomial. LCM = 3 ● 5 ● 24● a3 ● b5 ● c6 Use each factor thegreatest number of timesit appears. Example 1A

  18. LCM of Monomials and Polynomials = 240a3b5c6 Simplify. Answer: Example 1A

  19. LCM of Monomials and Polynomials = 240a3b5c6 Simplify. Answer: 240a3b5c6 Example 1A

  20. LCM of Monomials and Polynomials B. Find the LCM of x3 – x2– 2x and x2– 4x + 4. x3 – x2– 2x = x(x + 1)(x – 2) Factor the first polynomial. x2 – 4x + 4 = (x – 2)2 Factor the second polynomial. LCM = x(x + 1)(x – 2)2 Use each factor the greatest number of times it appears as a factor. Answer: Example 1B

  21. LCM of Monomials and Polynomials B. Find the LCM of x3 – x2– 2x and x2– 4x + 4. x3 – x2– 2x = x(x + 1)(x – 2) Factor the first polynomial. x2 – 4x + 4 = (x – 2)2 Factor the second polynomial. LCM = x(x + 1)(x – 2)2 Use each factor the greatest number of times it appears as a factor. Answer:x(x + 1)(x – 2)2 Example 1B

  22. A. Find the LCM of 6x2zy3, 9x3y2z2, and 4x2z. A.x2z B. 36x2z C. 36x3y3z2 D. 36xyz Example 1A

  23. A. Find the LCM of 6x2zy3, 9x3y2z2, and 4x2z. A.x2z B. 36x2z C. 36x3y3z2 D. 36xyz Example 1A

  24. B. Find the LCM of x3 + 2x2 – 3x and x2 + 6x + 9. A.x(x + 3)2(x – 1) B.x(x + 3)(x – 1) C.x(x – 1) D. (x + 3)(x – 1) Example 1B

  25. B. Find the LCM of x3 + 2x2 – 3x and x2 + 6x + 9. A.x(x + 3)2(x – 1) B.x(x + 3)(x – 1) C.x(x – 1) D. (x + 3)(x – 1) Example 1B

  26. Concept

  27. Simplify . Monomial Denominators The LCD is 42a2b2. Simplify each numerator and denominator. Add the numerators. Example 2

  28. Monomial Denominators Answer: Example 2

  29. Answer: Monomial Denominators Example 2

  30. Simplify . A. B. C. D. Example 2

  31. Simplify . A. B. C. D. Example 2

  32. Simplify . The LCD is 6(x – 5). Polynomial Denominators Factor the denominators. Subtract the numerators. Example 3

  33. Distributive Property Combine like terms. Simplify. Polynomial Denominators Simplify. Answer: Example 3

  34. Distributive Property Combine like terms. Simplify. Answer: Polynomial Denominators Simplify. Example 3

  35. Simplify . A. B. C. D. Example 3

  36. Simplify . A. B. C. D. Example 3

  37. Simplify . Complex Fractions with Different LCDs The LCD of the numerator is ab. The LCD of the denominator is b. Example 4

  38. Write as a division expression. Complex Fractions with Different LCDs Simplify the numerator and denominator. Multiply by the reciprocal of the divisor. Simplify. Example 4

  39. Complex Fractions with Different LCDs Answer: Example 4

  40. Answer: Complex Fractions with Different LCDs Example 4

  41. Simplify . A. B. –1 C.D. Example 4

  42. Simplify . A. B. –1 C.D. Example 4

  43. Simplify The LCD of all of the denominators is xy. Multiply by Complex Fractions with Same LCD Distribute xy. Example 5

  44. Complex Fractions with Same LCD Answer: Example 5

  45. Complex Fractions with Same LCD Answer: Example 5

  46. Simplify A.B. C.D. Example 5

  47. Simplify A.B. C.D. Example 5

  48. End of the Lesson

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