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# Int Math 2 Section 2-5 1011

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Multiply and divide variable expressions

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### Int Math 2 Section 2-5 1011

1. 1. Section 2-5 Multiply and Divide Variable Expressions
2. 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. 3. Vocabulary 1. Property of the Opposite of a Sum: 2. Distributive Property:
4. 4. Vocabulary 1. Property of the Opposite of a Sum: The negative outside the parentheses makes everything inside it opposite 2. Distributive Property:
5. 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. 6. Example 1 Simplify. a. − 2(n − 5) b. .3( x + .7) c. -(2ab + 9ac) d. 2x(4 x + 7y )
7. 7. Example 1 Simplify. a. − 2(n − 5) b. .3( x + .7) c. -(2ab + 9ac) d. 2x(4 x + 7y )
8. 8. Example 1 Simplify. a. − 2(n − 5) b. .3( x + .7) −2n c. -(2ab + 9ac) d. 2x(4 x + 7y )
9. 9. Example 1 Simplify. a. − 2(n − 5) b. .3( x + .7) −2n c. -(2ab + 9ac) d. 2x(4 x + 7y )
10. 10. Example 1 Simplify. a. − 2(n − 5) b. .3( x + .7) −2n +10 c. -(2ab + 9ac) d. 2x(4 x + 7y )
11. 11. Example 1 Simplify. a. − 2(n − 5) b. .3( x + .7) −2n +10 c. -(2ab + 9ac) d. 2x(4 x + 7y )
12. 12. Example 1 Simplify. a. − 2(n − 5) b. .3( x + .7) −2n +10 .3x c. -(2ab + 9ac) d. 2x(4 x + 7y )
13. 13. Example 1 Simplify. a. − 2(n − 5) b. .3( x + .7) −2n +10 .3x c. -(2ab + 9ac) d. 2x(4 x + 7y )
14. 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. 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. 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. 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. 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. 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. 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. 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. 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
23. 23. Dividing Variable Expressions
24. 24. Dividing Variable Expressions Divide each term in numerator by denominator
25. 25. Dividing Variable Expressions Divide each term in numerator by denominator Rewrite as distribution
26. 26. Dividing Variable Expressions Divide each term in numerator by denominator Rewrite as distribution 3− x 2
27. 27. Dividing Variable Expressions Divide each term in numerator by denominator Rewrite as distribution 3− x 1 3− x i 2 2 1
28. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 42. Example 3 Evaluate when x = 2 and y = -4. a. − 3( x + 1) 2 b. − 4 6 − y
43. 43. Example 3 Evaluate when x = 2 and y = -4. a. − 3( x + 1) 2 b. − 4 6 − y −3x − 3 2
44. 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. 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. 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. 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. 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. 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. 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. 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. 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. 53. Example 3 Evaluate when x = 2 and y = -4. y-x c. x-y
54. 54. Example 3 Evaluate when x = 2 and y = -4. y-x c. x-y −4 − 2 2 − (−4)
55. 55. Example 3 Evaluate when x = 2 and y = -4. y-x c. x-y −4 − 2 2 − (−4) −6 6
56. 56. Example 3 Evaluate when x = 2 and y = -4. y-x c. 6 x-y 6 −4 − 2 2 − (−4) −6 6
57. 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. 58. Problem Set
59. 59. Problem Set p. 74 #1-47 odd “Nobody got anywhere in the world by simply being content.” - Louis L'Amour
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