1. Distributive Property: Advanced Problems It may be necessary to review the basic distributive property problems in the number property introduction PowerPoint presentation

2. Recall the distributive property of multiplication over addition... symbolically: a × (b + c) = a × b + a × c and pictorially (rectangular array area model): a × ba × ca bc

3. An example: 6 x 13 using your mental math skills... symbolically: 6 × (10 + 3) = 6 × 10 + 6 × 3 and pictorially (rectangular array area model): 6 × 106 × 36 103

4. Find the area of the rectangle. Area = length x width 6 ft 24 ft

5. Find the area of the rectangle. Area = length x width 6 ft 20 ft+ 4 ft

6. Find the area of the rectangle. Area = length x width 6 ft 20 ft+ 4 ft

7. Find the area of the rectangle. Area = length x width 6 ft 20 ft+ 4 ft 6 ft

8. Find the area of the rectangle. Area = length x width 6 ft 20 ft+ 4 ft 6 ft Find the area of each rectangle.

9. Find the area of the rectangle. Area = length x width 6 ft 20 ft+ 4 ft 6 ft Find the area of each rectangle. 6 x 20 = 120 sq ft

10. Find the area of the rectangle. Area = length x width 6 ft 20 ft+ 4 ft 6 ft Find the area of each rectangle. 6 x 20 = 120 sq ft 6 x 4 = 24 sq ft

11. Find the area of the rectangle. Area = length x width 6 ft 20 ft+ 4 ft 6 ft Find the area of each rectangle. 120 sq ft 24 sq ft

12. Find the area of the rectangle. Area = length x width 6 ft 20 ft+ 4 ft 6 ft Now put the two rectangles back together. 120 sq ft 24 sq ft

13. Find the area of the rectangle. Area = length x width 6 ft 20 ft+ 4 ft Now put the two rectangles back together. 120 sq ft 24 sq ft

14. Find the area of the rectangle. Area = length x width 6 ft 20 ft+ 4 ft Now put the two rectangles back together. 120 sq ft 24 sq ft

15. Find the area of the rectangle. Area = length x width 6 ft 24 ft Now put the two rectangles back together. 120 sq ft + 24 sq ft

16. Find the area of the rectangle. Area = length x width 6 ft 24 ft Now put the two rectangles back together. 144 sq ft

17. A swimming pool has a shallow end and a deep end. Find the surface area of the pool. shallow water deepw ater 8 yds 5 yds 10 yds

18. shallow water deepw ater 8 yds 5 yds 10 yds 8 yds Break the pool into a deep end and a shallow end.

19. shallow water deepw ater 8 yds 5 yds 10 yds 8 yds Find the area of the deep end.

20. shallow water 8 x 5 = 40 8 yds 5 yds 10 yds 8 yds Find the area of the deep end.

21. shallow water 8 x 5 = 40 8 yds 5 yds 10 yds 8 yds Find the area of the shallow end.

22. 8 x 10 = 80 8 x 5 = 40 8 yds 5 yds 10 yds 8 yds Find the area of the shallow end.

23. 8 x 10 = 80 8 x 5 = 40 8 yds 5 yds 10 yds 8 yds Now sum the two areas together.

24. 80 40 8 yds 5 yds 10 yds Now sum the two areas together. +

25. 80 40 8 yds 5 yds 10 yds 40 + 80 = 120 square yards

26. Write an expression that shows how to find the area of the rectangle and uses the distributive property. 9 yds 5 yds 20 yds

27. Find the areas for each individual rectangle. 9 yds 5 yds 20 yds

28. Find the areas for each individual rectangle. 9 yds 5 yds 20 yds (9 x 5)

29. Find the areas for each individual rectangle. 9 yds 5 yds 20 yds (9 x 5)(9 x 20)

30. Sum the two areas. 9 yds 5 yds 20 yds (9 x 5)(9 x 20) +

31. (9 x 5) + (9 x 20) = area 9 yds 5 yds 20 yds (9 x 5)(9 x 20)

32. Practice Time

33. 1) Which of the following expressions shows the distributive property for 5 x (3 + 7)? (5 x 3) + (5 x 7) (5 x 3) x (5 x 7) (5 + 3) x (5 + 7)

34. 1) Which of the following expressions shows the distributive property for 5 x (3 + 7)? (5 x 3) + (5 x 7) Correct!

35. 2) Which of the following expressions shows the distributive property for 3 x (9 + 4) ? (3 x 9) + (3 x 4) (3 + 9) + (3 + 4) (3 + 9) x (3 + 4)

36. 2) Which of the following expressions shows the distributive property for 3 x (9 + 4) ? (3 x 9) + (3 x 4) Correct!

37. 3) Which of the following expressions is equivalent to: 2 + 3 + 2 + 3 and shows the distributive property. 2 x (2 + 3) 2 + 2 + 3 + 3 3 x (2 + 3)

38. 3) Which of the following expressions is equivalent to: 2 + 3 + 2 + 3 and uses the distributive property. 2 x (2 + 3) Correct!

39. 4) Which of the following expressions is equivalent to: (4 x 3) + (4 x 8) ? 4 x (3 + 8) 8 x (3 + 4) 3 x (4 + 8)

40. 4) Which of the following expressions is equivalent to: (4 x 3) + (4 x 8) ? 4 x (3 + 8) Correct!

41. 5) Which of the following expressions is equivalent to: (5 x 9) + (5 x 3) ? 9 x (3 + 5) 5 x (9 + 3) 3 x (9 + 5)

42. 5) Which of the following expressions is equivalent to: (5 x 9) + (5 x 3) ? 5 x (9 + 3)Correct!

43. 6) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 4 yds 3 yds 9 yds

44. 6) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 4 yds 3 yds 9 yds

45. 6) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 4 yds 3 yds 9 yds

46. 6) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 4 yds 3 yds 9 yds 4 yd s

47. 6) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 4 yds 3 yds 9 yds 4 yd s 4 x 3

48. 6) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 4 yds 3 yds 9 yds 4 yd s 4 x 34 x 9

49. 6) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 4 yds 3 yds 9 yds 4 yd s 4 x 34 x 9

50. 6) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 4 yds 3 yds 9 yds 4 x 34 x 9

51. 6) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 4 yds 3 yds 9 yds 4 x 34 x 9

52. 6) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 4 yds 3 yds 9 yds 4 x 3 +4 x 9

53. 7) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 6 yds 4 yds 8 yds

54. 7) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 6 yds 4 yds 8 yds

55. 7) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 6 yds 4 yds 8 yds

56. 7) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 6 yds 4 yds 8 yds 6 yds

57. 7) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 6 yds 4 yds 8 yds 6 yds 6 x 4

58. 7) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 6 yds 4 yds 8 yds 6 yds 6 x 46 x 8

59. 7) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 6 yds 4 yds 8 yds 6 yds 6 x 46 x 8

60. 7) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 6 yds 4 yds 8 yds 6 x 46 x 8

61. 7) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 6 yds 4 yds 8 yds 6 x 46 x 8

62. 7) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 6 yds 4 yds 8 yds 6 x 4 +6 x 8

63. 8) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 5 yds 2 yds 10 yds

64. 8) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 5 yds 2 yds 10 yds 5 x 25 x 10

65. 8) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 5 yds 2 yds 10 yds 5 x 2 +5 x 10

66. 9) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 8 yds 3 yds 5 yds

67. 9) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 8 yds 3 yds 5 yds 8 x 38 x 5

68. 9) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 8 yds 3 yds 5 yds 8 x 3 +8 x 5

69. 10) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 5 yds x yds 10 yds

70. 10) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 5 yds x yds 10 yds 5x5 ∙ 10

71. 10) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 5 yds x yds 10 yds 5x +5 ∙ 10

72. 11) Which expression is equivalent to 3(x + 7)? 3x + 7 x + 21 x + 10 3x + 21

73. 11) Which expression is equivalent to 3(x + 7)? 3x + 21 Correct!

74. 12) Which expression is equivalent to 4(x + 5)? 4x + 5 4x + 20 x + 9 9x

75. 12) Which expression is equivalent to 4(x + 5)? 4x + 20Correct!

76. 13) Which expression is equivalent to 8(x + 2)? 8x + 16 8x + 2 10x 8x + 10

77. 13) Which expression is equivalent to 8(x + 2)? 8x + 16Correct!

78. 14) Which expression is equivalent to 2(x + 3)? 2x + 3 2x + 5 2x + 6 2x + 2

79. 14) Which expression is equivalent to 2(x + 3)? 2x + 6 Correct!

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