The document discusses multiplying and dividing variable expressions. It provides examples of simplifying expressions using the distributive property and the property of the opposite of a sum. It also demonstrates dividing variable expressions by writing the division as a fraction and simplifying. Key steps include distributing terms, dividing each term in the numerator by the denominator, and evaluating expressions for given variable values.

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

23. Dividing Variable
Expressions

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