1 / 52

9 March 2011

9 March 2011. Algebra 2. Algebraic Operations 3/9. Terms are considered “like” if they have the same variable AND the same powers on the variable. Like Terms. Mathematics.XEI.303: (16-19) Combine like terms. Algebraic Operations 3/9.

candie
Télécharger la présentation

9 March 2011

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 9 March 2011 Algebra 2

  2. Algebraic Operations 3/9 Terms are considered “like” if they have the same variable AND the same powers on the variable. • Like Terms Mathematics.XEI.303: (16-19) Combine like terms

  3. Algebraic Operations 3/9 Terms are considered “like” if they have the same variable AND the same powers on the variable. Example: x2, 2x, 5x3, 8x2 Only x2, 8x2 are like terms • Like Terms Mathematics.XEI.303: (16-19) Combine like terms

  4. Which of the following are like terms? • 2x and2x2 • 3x and 3 • 4x2 and 4x3 • 5x3 and 8x3 • x and xy 60 0 of 30

  5. Algebraic Operations 3/9 When you are combining like terms, add the coefficients. • Like Terms Mathematics.XEI.303: (16-19) Combine like terms

  6. Algebraic Operations 3/9 When you are combining like terms, add the coefficients. Example: 2xy + xy + 5xy = ? • Like Terms Mathematics.XEI.303: (16-19) Combine like terms

  7. Algebraic Operations 3/9 When you are combining like terms, add the coefficients. Example: 2xy + xy + 5xy = ? 2 + 1 + 5 = 8 • Like Terms Mathematics.XEI.303: (16-19) Combine like terms

  8. Algebraic Operations 3/9 When you are combining like terms, add the coefficients. Example: 2xy + xy + 5xy = ? 2 + 1 + 5 = 8, so 2xy + xy + 5xy = 8xy • Like Terms Mathematics.XEI.303: (16-19) Combine like terms

  9. 2a3 + a2 + a + 3a – 4a3 = ? • a9 • 2a7 - 4a3 • 2a3 + a2 + 4a • -2a3 + a2 + 4a 60 0 of 30

  10. 2a3 + a2 + a + 3a – 4a3 = ? 2a3 + a2+ a+ 3a – 4a3= ? Combine like terms -2a3+ a2+ 4a

  11. Like Terms: • Choose any 10 questions from the first 15 • Write the question #, show your work, and write the letter answer choice on your sheet • You have 10 minutes.

  12. 0 0 6 0 0 0 1 8 7 5 4 4 3 2 1 5 4 9 9 6 9 0 8 7 6 5 4 3 2 1 0 3 9 8 7 5 2 0 1 0 9 8 7 6 5 4 3 2 1 0 2 1 9 8 7 3 6 4 5 3 2 1 0 9 8 7 5 4 3 2 1 0 0 6 Time Left Hours Minutes Seconds

  13. Algebraic Operations 3/9 You can multiply or divide the same variable, even if the powers are different. • Exponent Rules Mathematics.NCP.604: (28-32) Apply rules of exponents

  14. Algebraic Operations 3/9 You can multiply or divide the same variable, even if the powers are different. Multiplication: Add exponents Division: Subtract exponents Example: (x2)(x3)(x5)(x7) = ? • Exponent Rules Mathematics.NCP.604: (28-32) Apply rules of exponents

  15. Algebraic Operations 3/9 Example: (x2)(x3)(x5)(x7) = ? • Exponent Rules Mathematics.NCP.604: (28-32) Apply rules of exponents

  16. Algebraic Operations 3/9 Example: (x2)(x3)(x5)(x7) = ? Add all the exponents on ‘x’ 2 + 3 + 5 + 7 = 17 • Exponent Rules Mathematics.NCP.604: (28-32) Apply rules of exponents

  17. Algebraic Operations 3/9 Example: (x2)(x3)(x5)(x7) = ? Add all the exponents on ‘x’ 2 + 3 + 5 + 7 = 17 (x2)(x3)(x5)(x7) = x17 • Exponent Rules Mathematics.NCP.604: (28-32) Apply rules of exponents

  18. Algebraic Operations 3/9 Example 2: • Exponent Rules Mathematics.NCP.604: (28-32) Apply rules of exponents

  19. Algebraic Operations 3/9 Example 2: Larger x is on top, subtract the bottom power from the top power: • Exponent Rules Mathematics.NCP.604: (28-32) Apply rules of exponents

  20. Algebraic Operations 3/9 Example 2: Larger x is on top, subtract the bottom power from the top power: Larger y is on bottom, subtract the top power from the bottom power: • Exponent Rules Mathematics.NCP.604: (28-32) Apply rules of exponents

  21. (xy2)(x3y2) = ? • x3y4 • x2y • x4y4 • xy7 • xy8 60 0 of 30

  22. (xy2)(x3y2) = ? • (xy2)(x3y2) = ? x4

  23. (xy2)(x3y2) = ? • (xy2)(x3y2) = ? x4y4

  24. Algebraic Operations 3/9 If you are raising a variable with an exponent, multiply the powers. Example: (a3)4 • Exponent Rules Mathematics.NCP.604: (28-32) Apply rules of exponents

  25. Algebraic Operations 3/9 If you are raising a variable with an exponent, multiply the powers. Example: (a3)4 3*4 = 12 • Exponent Rules Mathematics.NCP.604: (28-32) Apply rules of exponents

  26. Algebraic Operations 3/9 If you are raising a variable with an exponent, multiply the powers. Example: (a3)4 3*4 = 12 (a3)4 = a12 • Exponent Rules Mathematics.NCP.604: (28-32) Apply rules of exponents

  27. Exponent Rules: • Complete ten questions out of # 16-30 • Write the question #, show your work, and write the letter answer choice on your sheet • You have 10 minutes.

  28. 0 1 9 0 0 0 5 3 8 6 5 4 3 2 1 7 0 9 5 1 8 7 6 5 4 3 2 3 0 4 9 8 7 6 5 4 4 2 3 9 8 7 6 5 4 2 7 1 0 2 1 9 8 6 1 5 0 0 3 2 1 0 4 8 9 6 5 4 3 2 1 0 7 Time Left: Hours Minutes Seconds

  29. Algebraic Operations 3/9 If you are adding two fractions with the SAME denominator: • Adding Fractions Mathematics.NCP.201: (13-15) Recognize equivalent fractions

  30. Algebraic Operations 3/9 If you are adding two fractions with the SAME denominator: Add the numerators together. • Adding Fractions Mathematics.NCP.201: (13-15) Recognize equivalent fractions

  31. Algebraic Operations 3/9 If you are adding two fractions with the SAME denominator: Add the numerators together. 4 + 6 = 10 • Adding Fractions Mathematics.NCP.201: (13-15) Recognize equivalent fractions

  32. Algebraic Operations 3/9 If you are adding two fractions with the SAME denominator: Add the numerators together. 4 + 6 = 10 • Adding Fractions Mathematics.NCP.201: (13-15) Recognize equivalent fractions

  33. . • 7x/6 • 7x/3 • 10x/9 • 10x/6 • 10x/3 60 0 of 30

  34. Algebraic Operations 3/9 If you are adding two fractions with a different denominator: • Adding Fractions Mathematics.NCP.501: (24-27) Find and use the least common multiple

  35. Algebraic Operations 3/9 If you are adding two fractions with a different denominator: Multiply the denominators: • Adding Fractions Mathematics.NCP.501: (24-27) Find and use the least common multiple

  36. Algebraic Operations 3/9 If you are adding two fractions with a different denominator: Cross Multiply • Adding Fractions Mathematics.NCP.501: (24-27) Find and use the least common multiple

  37. Adding Fractions: • Complete # 31-40 • Write the question #, show your work, and write the letter answer choice on your sheet • You have 10 minutes.

  38. 0 0 6 0 0 0 1 8 7 5 4 4 3 2 1 5 4 9 9 6 9 0 8 7 6 5 4 3 2 1 0 3 9 8 7 5 2 0 1 0 9 8 7 6 5 4 3 2 1 0 2 1 9 8 7 3 6 4 5 3 2 1 0 9 8 7 5 4 3 2 1 0 0 6 Time Left Hours Minutes Seconds

  39. Simplifying Expressions 3/8 Simplify 3(2q + r) Mathematics.XEI.402: (20-23) Add and subtract simple algebraic expressions

  40. Simplifying Expressions 3/8 Simplify 3(2q + r) 6q + 3r + 20q – 35r Mathematics.XEI.402: (20-23) Add and subtract simple algebraic expressions

  41. Simplifying Expressions 3/8 Simplify 3(2q + r) 6q + 3r + 20q – 35r Mathematics.XEI.402: (20-23) Add and subtract simple algebraic expressions

  42. Notes: Multiplying Binomials 3/8 You can use the box method to multiply two binomials: Example 1: (x + 4)(x – 3) Make a 2x2 square box Box Method XEI.405:Multiply 2 Binomials

  43. Notes: Multiplying Binomials 3/8 You can use the box method to multiply two binomials: Example 1: (x + 4)(x – 3) Write the first binomial across the top x +4 Box Method XEI.405:Multiply 2 Binomials

  44. Notes: Multiplying Binomials 3/8 You can use the box method to multiply two binomials: Example 1: (x + 4)(x – 3) Write the second binomial going down x +4 x -3 Box Method XEI.405:Multiply 2 Binomials

  45. Notes: Multiplying Binomials 3/8 You can use the box method to multiply two binomials: Example 1: (x + 4)(x – 3) Multiply x*x x +4 x x2 -3 Box Method XEI.405:Multiply 2 Binomials

  46. Notes: Multiplying Binomials 3/8 You can use the box method to multiply two binomials: Example 1: (x + 4)(x – 3) Multiply x*4 x +4 x x2 +4x -3 Box Method XEI.405:Multiply 2 Binomials

  47. Notes: Multiplying Binomials 3/8 You can use the box method to multiply two binomials: Example 1: (x + 4)(x – 3) Multiply -3*x x +4 x x2 +4x -3 -3x Box Method XEI.405:Multiply 2 Binomials

  48. Notes: Multiplying Binomials 3/8 You can use the box method to multiply two binomials: Example 1: (x + 4)(x – 3) Multiply -3*4 x +4 x x2 +4x -3 -3x -12 Box Method XEI.405:Multiply 2 Binomials

  49. Notes: Multiplying Binomials 3/8 You can use the box method to multiply two binomials: Example 1: (x + 4)(x – 3) List each term inside the box x +4 x x2 +4x -3 -3x -12 x2 + 4x – 3x - 12 Box Method XEI.405:Multiply 2 Binomials

  50. Notes: Multiplying Binomials 3/8 You can use the box method to multiply two binomials: Example 1: (x + 4)(x – 3) Simplify x +4 x x2 +4x -3 -3x -12 x2 + 4x – 3x – 12 = x2 + x - 12 Box Method XEI.405:Multiply 2 Binomials

More Related