Int Math 2 Section 2-5 1011
- 1. Section 2-5 Multiply and Divide Variable Expressions
- 2. Essential Questions How are variable expressions simplified? How are variable expressions evaluated? Where you’ll see this: Part-time job, weather, engineering, spreadsheets
- 3. Vocabulary 1. Property of the Opposite of a Sum: 2. Distributive Property:
- 4. Vocabulary 1. Property of the Opposite of a Sum: The negative outside the parentheses makes everything inside it opposite 2. Distributive Property:
- 5. Vocabulary 1. Property of the Opposite of a Sum: The negative outside the parentheses makes everything inside it opposite 2. Distributive Property: Multiply each term inside the parentheses by the term outside
- 6. Example 1 Simplify. a. − 2(n − 5) b. .3( x + .7) c. -(2ab + 9ac) d. 2x(4 x + 7y )
- 7. Example 1 Simplify. a. − 2(n − 5) b. .3( x + .7) c. -(2ab + 9ac) d. 2x(4 x + 7y )
- 8. Example 1 Simplify. a. − 2(n − 5) b. .3( x + .7) −2n c. -(2ab + 9ac) d. 2x(4 x + 7y )
- 9. Example 1 Simplify. a. − 2(n − 5) b. .3( x + .7) −2n c. -(2ab + 9ac) d. 2x(4 x + 7y )
- 10. Example 1 Simplify. a. − 2(n − 5) b. .3( x + .7) −2n +10 c. -(2ab + 9ac) d. 2x(4 x + 7y )
- 11. Example 1 Simplify. a. − 2(n − 5) b. .3( x + .7) −2n +10 c. -(2ab + 9ac) d. 2x(4 x + 7y )
- 12. Example 1 Simplify. a. − 2(n − 5) b. .3( x + .7) −2n +10 .3x c. -(2ab + 9ac) d. 2x(4 x + 7y )
- 13. Example 1 Simplify. a. − 2(n − 5) b. .3( x + .7) −2n +10 .3x c. -(2ab + 9ac) d. 2x(4 x + 7y )
- 14. Example 1 Simplify. a. − 2(n − 5) b. .3( x + .7) −2n +10 .3x +.21 c. -(2ab + 9ac) d. 2x(4 x + 7y )
- 15. Example 1 Simplify. a. − 2(n − 5) b. .3( x + .7) −2n +10 .3x +.21 c. -(2ab + 9ac) d. 2x(4 x + 7y )
- 16. Example 1 Simplify. a. − 2(n − 5) b. .3( x + .7) −2n +10 .3x +.21 c. -(2ab + 9ac) d. 2x(4 x + 7y ) −2ab
- 17. Example 1 Simplify. a. − 2(n − 5) b. .3( x + .7) −2n +10 .3x +.21 c. -(2ab + 9ac) d. 2x(4 x + 7y ) −2ab
- 18. Example 1 Simplify. a. − 2(n − 5) b. .3( x + .7) −2n +10 .3x +.21 c. -(2ab + 9ac) d. 2x(4 x + 7y ) −2ab −9ac
- 19. Example 1 Simplify. a. − 2(n − 5) b. .3( x + .7) −2n +10 .3x +.21 c. -(2ab + 9ac) d. 2x(4 x + 7y ) −2ab −9ac
- 20. Example 1 Simplify. a. − 2(n − 5) b. .3( x + .7) −2n +10 .3x +.21 c. -(2ab + 9ac) d. 2x(4 x + 7y ) −2ab −9ac 8x 2
- 21. Example 1 Simplify. a. − 2(n − 5) b. .3( x + .7) −2n +10 .3x +.21 c. -(2ab + 9ac) d. 2x(4 x + 7y ) −2ab −9ac 8x 2
- 22. Example 1 Simplify. a. − 2(n − 5) b. .3( x + .7) −2n +10 .3x +.21 c. -(2ab + 9ac) d. 2x(4 x + 7y ) −2ab −9ac 8 x +14 xy 2
- 24. Dividing Variable Expressions Divide each term in numerator by denominator
- 25. Dividing Variable Expressions Divide each term in numerator by denominator Rewrite as distribution
- 26. Dividing Variable Expressions Divide each term in numerator by denominator Rewrite as distribution 3− x 2
- 27. Dividing Variable Expressions Divide each term in numerator by denominator Rewrite as distribution 3− x 1 3− x i 2 2 1
- 28. Dividing Variable Expressions Divide each term in numerator by denominator Rewrite as distribution 3− x 1 3− x i 1 2 (3 − x) 2 2 1
- 29. Dividing Variable Expressions Divide each term in numerator by denominator Rewrite as distribution 3− x 1 3− x i 1 2 (3 − x) 2 2 1 3 2 − x 1 2
- 30. Dividing Variable Expressions Divide each term in numerator by denominator Rewrite as distribution 3− x 1 3− x i 1 2 (3 − x) 2 2 1 3 2 − x 1 2 − x+ 1 2 3 2
- 31. Example 2 Simplify. Practice both methods of division to see which one you prefer. 6x + 3 10 y − 5 a. b. 3 2
- 32. Example 2 Simplify. Practice both methods of division to see which one you prefer. 6x + 3 10 y − 5 a. b. 3 2 6x 3 + 3 3
- 33. Example 2 Simplify. Practice both methods of division to see which one you prefer. 6x + 3 10 y − 5 a. b. 3 2 6x 3 + 3 3 2x + 1
- 34. Example 2 Simplify. Practice both methods of division to see which one you prefer. 6x + 3 10 y − 5 a. b. 3 2 6x 3 + 1 2 (10 y − 5) 3 3 2x + 1
- 35. Example 2 Simplify. Practice both methods of division to see which one you prefer. 6x + 3 10 y − 5 a. b. 3 2 6x 3 + 1 2 (10 y − 5) 3 3 2x + 1 5y − 5 2
- 36. Example 2 Simplify. Practice both methods of division to see which one you prefer. 1.6 − .8 z 9x + 5y c. d. −8 7
- 37. Example 2 Simplify. Practice both methods of division to see which one you prefer. 1.6 − .8 z 9x + 5y c. d. −8 7 1.6 .8 z − −8 −8
- 38. Example 2 Simplify. Practice both methods of division to see which one you prefer. 1.6 − .8 z 9x + 5y c. d. −8 7 1.6 .8 z − −8 −8 −.2 + .1z
- 39. Example 2 Simplify. Practice both methods of division to see which one you prefer. 1.6 − .8 z 9x + 5y c. d. −8 7 1.6 .8 z − −8 −8 −.2 + .1z .1z − .2
- 40. Example 2 Simplify. Practice both methods of division to see which one you prefer. 1.6 − .8 z 9x + 5y c. d. −8 7 1.6 .8 z − 1 (9 x + 5 y ) −8 −8 7 −.2 + .1z .1z − .2
- 41. Example 2 Simplify. Practice both methods of division to see which one you prefer. 1.6 − .8 z 9x + 5y c. d. −8 7 1.6 .8 z − 1 (9 x + 5 y ) −8 −8 7 −.2 + .1z 9 x+ y 5 .1z − .2 7 7
- 42. Example 3 Evaluate when x = 2 and y = -4. a. − 3( x + 1) 2 b. − 4 6 − y
- 43. Example 3 Evaluate when x = 2 and y = -4. a. − 3( x + 1) 2 b. − 4 6 − y −3x − 3 2
- 44. Example 3 Evaluate when x = 2 and y = -4. a. − 3( x + 1) 2 b. − 4 6 − y −3x − 3 2 −3(2) − 3 2
- 45. Example 3 Evaluate when x = 2 and y = -4. a. − 3( x + 1) 2 b. − 4 6 − y −3x − 3 2 −3(2) − 3 2 −3(4) − 3
- 46. Example 3 Evaluate when x = 2 and y = -4. a. − 3( x + 1) 2 b. − 4 6 − y −3x − 3 2 −3(2) − 3 2 −3(4) − 3 −12 − 3
- 47. Example 3 Evaluate when x = 2 and y = -4. a. − 3( x + 1) 2 b. − 4 6 − y −3x − 3 2 −3(2) − 3 2 −3(4) − 3 −12 − 3 −15
- 48. Example 3 Evaluate when x = 2 and y = -4. a. − 3( x + 1) 2 b. − 4 6 − y −3x − 3 2 −4 6 − (−4) −3(2) − 3 2 −3(4) − 3 −12 − 3 −15
- 49. Example 3 Evaluate when x = 2 and y = -4. a. − 3( x + 1) 2 b. − 4 6 − y −3x − 3 2 −4 6 − (−4) −3(2) − 3 2 −4 6 + 4 −3(4) − 3 −12 − 3 −15
- 50. Example 3 Evaluate when x = 2 and y = -4. a. − 3( x + 1) 2 b. − 4 6 − y −3x − 3 2 −4 6 − (−4) −3(2) − 3 2 −4 6 + 4 −3(4) − 3 −4 10 −12 − 3 −15
- 51. Example 3 Evaluate when x = 2 and y = -4. a. − 3( x + 1) 2 b. − 4 6 − y −3x − 3 2 −4 6 − (−4) −3(2) − 3 2 −4 6 + 4 −3(4) − 3 −4 10 −12 − 3 −4(10) −15
- 52. Example 3 Evaluate when x = 2 and y = -4. a. − 3( x + 1) 2 b. − 4 6 − y −3x − 3 2 −4 6 − (−4) −3(2) − 3 2 −4 6 + 4 −3(4) − 3 −4 10 −12 − 3 −4(10) −15 −40
- 53. Example 3 Evaluate when x = 2 and y = -4. y-x c. x-y
- 54. Example 3 Evaluate when x = 2 and y = -4. y-x c. x-y −4 − 2 2 − (−4)
- 55. Example 3 Evaluate when x = 2 and y = -4. y-x c. x-y −4 − 2 2 − (−4) −6 6
- 56. Example 3 Evaluate when x = 2 and y = -4. y-x c. 6 x-y 6 −4 − 2 2 − (−4) −6 6
- 57. Example 3 Evaluate when x = 2 and y = -4. y-x c. 6 x-y 6 −4 − 2 2 − (−4) 1 −6 6
- 58. Problem Set
- 59. Problem Set p. 74 #1-47 odd “Nobody got anywhere in the world by simply being content.” - Louis L'Amour