Section 2-5
Multiply and Divide Variable Expressions
Essential Questions

 How are variable expressions simplified?
 How are variable expressions evaluated?


 Where you’ll see...
Vocabulary
1. Property of the Opposite of a Sum:




2. Distributive Property:
Vocabulary
1. Property of the Opposite of a Sum: The negative
    outside the parentheses makes everything inside
    it o...
Vocabulary
1. Property of the Opposite of a Sum: The negative
    outside the parentheses makes everything inside
    it o...
Example 1
                  Simplify.

a. − 2(n − 5)                 b. .3( x + .7)




c. -(2ab + 9ac)               d. 2...
Example 1
                  Simplify.

a. − 2(n − 5)                 b. .3( x + .7)




c. -(2ab + 9ac)               d. 2...
Example 1
                  Simplify.

a. − 2(n − 5)                 b. .3( x + .7)
    −2n


c. -(2ab + 9ac)             ...
Example 1
                  Simplify.

a. − 2(n − 5)                 b. .3( x + .7)
    −2n


c. -(2ab + 9ac)             ...
Example 1
                  Simplify.

a. − 2(n − 5)                 b. .3( x + .7)
    −2n +10


c. -(2ab + 9ac)         ...
Example 1
                  Simplify.

a. − 2(n − 5)                 b. .3( x + .7)
    −2n +10


c. -(2ab + 9ac)         ...
Example 1
                  Simplify.

a. − 2(n − 5)                 b. .3( x + .7)
    −2n +10                      .3x

...
Example 1
                  Simplify.

a. − 2(n − 5)                 b. .3( x + .7)
    −2n +10                      .3x

...
Example 1
                  Simplify.

a. − 2(n − 5)                 b. .3( x + .7)
    −2n +10                      .3x +...
Example 1
                  Simplify.

a. − 2(n − 5)                 b. .3( x + .7)
    −2n +10                      .3x +...
Example 1
                  Simplify.

a. − 2(n − 5)                 b. .3( x + .7)
    −2n +10                      .3x +...
Example 1
                  Simplify.

a. − 2(n − 5)                 b. .3( x + .7)
    −2n +10                      .3x +...
Example 1
                  Simplify.

a. − 2(n − 5)                 b. .3( x + .7)
    −2n +10                      .3x +...
Example 1
                  Simplify.

a. − 2(n − 5)                 b. .3( x + .7)
    −2n +10                      .3x +...
Example 1
                  Simplify.

a. − 2(n − 5)                 b. .3( x + .7)
    −2n +10                      .3x +...
Example 1
                  Simplify.

a. − 2(n − 5)                 b. .3( x + .7)
    −2n +10                      .3x +...
Example 1
                  Simplify.

a. − 2(n − 5)                 b. .3( x + .7)
    −2n +10                      .3x +...
Dividing Variable
Expressions
Dividing Variable
Expressions
 Divide each term in numerator by denominator
Dividing Variable
Expressions
 Divide each term in numerator by denominator
 Rewrite as distribution
Dividing Variable
Expressions
 Divide each term in numerator by denominator
 Rewrite as distribution
         3− x
       ...
Dividing Variable
Expressions
 Divide each term in numerator by denominator
 Rewrite as distribution
         3− x        ...
Dividing Variable
Expressions
 Divide each term in numerator by denominator
 Rewrite as distribution
         3− x        ...
Dividing Variable
Expressions
 Divide each term in numerator by denominator
 Rewrite as distribution
         3− x        ...
Dividing Variable
Expressions
 Divide each term in numerator by denominator
 Rewrite as distribution
         3− x        ...
Example 2
Simplify. Practice both methods of division to see
               which one you prefer.

     6x + 3            ...
Example 2
Simplify. Practice both methods of division to see
               which one you prefer.

     6x + 3            ...
Example 2
Simplify. Practice both methods of division to see
               which one you prefer.

     6x + 3            ...
Example 2
Simplify. Practice both methods of division to see
               which one you prefer.

     6x + 3            ...
Example 2
Simplify. Practice both methods of division to see
               which one you prefer.

     6x + 3            ...
Example 2
Simplify. Practice both methods of division to see
               which one you prefer.
     1.6 − .8 z         ...
Example 2
Simplify. Practice both methods of division to see
               which one you prefer.
     1.6 − .8 z         ...
Example 2
Simplify. Practice both methods of division to see
               which one you prefer.
     1.6 − .8 z         ...
Example 2
Simplify. Practice both methods of division to see
               which one you prefer.
     1.6 − .8 z         ...
Example 2
Simplify. Practice both methods of division to see
               which one you prefer.
     1.6 − .8 z         ...
Example 2
Simplify. Practice both methods of division to see
               which one you prefer.
     1.6 − .8 z         ...
Example 3
      Evaluate when x = 2 and y = -4.
  a. − 3( x + 1)
          2
                            b. − 4 6 − y
Example 3
      Evaluate when x = 2 and y = -4.
  a. − 3( x + 1)
            2
                            b. − 4 6 − y

 ...
Example 3
      Evaluate when x = 2 and y = -4.
  a. − 3( x + 1)
             2
                            b. − 4 6 − y

...
Example 3
      Evaluate when x = 2 and y = -4.
  a. − 3( x + 1)
             2
                            b. − 4 6 − y

...
Example 3
      Evaluate when x = 2 and y = -4.
  a. − 3( x + 1)
             2
                            b. − 4 6 − y

...
Example 3
      Evaluate when x = 2 and y = -4.
  a. − 3( x + 1)
             2
                            b. − 4 6 − y

...
Example 3
      Evaluate when x = 2 and y = -4.
  a. − 3( x + 1)
             2
                            b. − 4 6 − y

...
Example 3
      Evaluate when x = 2 and y = -4.
  a. − 3( x + 1)
             2
                            b. − 4 6 − y

...
Example 3
      Evaluate when x = 2 and y = -4.
  a. − 3( x + 1)
             2
                            b. − 4 6 − y

...
Example 3
      Evaluate when x = 2 and y = -4.
  a. − 3( x + 1)
             2
                            b. − 4 6 − y

...
Example 3
      Evaluate when x = 2 and y = -4.
  a. − 3( x + 1)
             2
                            b. − 4 6 − y

...
Example 3
    Evaluate when x = 2 and y = -4.
            y-x
       c.
            x-y
Example 3
    Evaluate when x = 2 and y = -4.
             y-x
       c.
             x-y

            −4 − 2
            ...
Example 3
    Evaluate when x = 2 and y = -4.
             y-x
       c.
             x-y

            −4 − 2
            ...
Example 3
    Evaluate when x = 2 and y = -4.
             y-x
       c.                    6
             x-y
           ...
Example 3
    Evaluate when x = 2 and y = -4.
             y-x
       c.                    6
             x-y
           ...
Problem Set
Problem Set


                p. 74 #1-47 odd




“Nobody got anywhere in the world by simply being
           content.” -...
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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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