1. The Distributive Property

2. The distributive property is mental math strategy that can be used when multiplying.
43 x 5 =?

3. Break apart the double-digit number.
43 x 5 =? +

4. Then multiply each part by 5.
43 x 5 =? +
x 5 x 5

5. Then multiply each part by 5.
43 x 5 =? +
x 5 x 5

6. Finally, sum your two products
43 x 5 =215 +
x 5 x 5 +
= 215

7. Let’s look at another example.

8. Break apart the double-digit number.
53 x 6 = ?

9. Break apart the double-digit number.
53 x 6 = ? +

10. Multiply each part by 6.
53 x 6 = ? +
x x 6

11. Multiply each part by 6.
53 x 6 = ? +
x x 6

12. Sum the two products.
53 x 6 = 318 +
x x 6
= 318

13. There are three steps to the distributive property.
4 x 28 =

14. There are three steps to the distributive property.
4 x 28 =
1) Break apart the double-digit number.

15. There are three steps to the distributive property.
4 x 28 = 4 x (20 + 8)
1) Break apart the double-digit number.

16. There are three steps to the distributive property.
4 x 28 = 4 x (20 + 8)
Break apart the double-digit number.
Multiply each part by 4. (distribute the 4)

17. There are three steps to the distributive property.
4 x 28 = 4 x (20 + 8) = (4 x 20) + (4 x 8)
Break apart the double-digit number.
Multiply each part by 4. (distribute the 4)

18. There are three steps to the distributive property.
4 x 28 = 4 x (20 + 8) = (4 x 20) + (4 x 8)
Break apart the double-digit number.
Multiply each part by 4. (distribute the 4)
Sum the two products.

19. There are three steps to the distributive property.
4 x 28 = 4 x (20 + 8) = (4 x 8)
Break apart the double-digit number.
Multiply each part by 4. (distribute the 4)
Sum the two products.

20. There are three steps to the distributive property.
4 x 28 = 4 x (20 + 8) =
Break apart the double-digit number.
Multiply each part by 4. (distribute the 4)
Sum the two products.

21. There are three steps to the distributive property.
4 x 28 = 4 x (20 + 8) = = 112
Break apart the double-digit number.
Multiply each part by 4. (distribute the 4)
Sum the two products.

22. The word “distribute” means “to give out.”

23. Distribute the cubes to the girls.

24. Distribute the cubes to the girls.

25. Distribute the cubes to the girls.

26. Distribute the cubes to the girls.

27. Distribute the cubes to the girls.

28. Distribute the cubes to the girls.

29. In this example, the 5 was distributed.
5 x 38 = 5 x (30 + 8) = (5 x 30) + (5 x 8)

30. In this example, the 7 was distributed.
7 x 46 = 7 x (40 + 6) = (7 x 40) + (7 x 6)

31. Find the area of the rectangle. Area = length x width

32. Find the area of the rectangle. Area = length x width

33. Find the area of the rectangle. Area = length x width
20 ft ft

34. Find the area of the rectangle. Area = length x width
20 ft ft

35. Find the area of the rectangle. Area = length x width
20 ft ft

36. Find the area of the rectangle. Area = length x width
Find the area of each rectangle.
6 ft
6 ft
20 ft ft

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

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

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

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

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

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

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

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

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

46. Break the pool into a deep end and a shallow end.
deepwater
8 yds
8 yds
shallow water
10 yds
5 yds

47. Find the area of the deep end.
deepwater
8 yds
8 yds
shallow water
10 yds
5 yds

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

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

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

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

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

53. = 120 square yards 40 80
8 yds
5 yds
10 yds

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

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

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

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

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

59. (9 x 5) + (9 x 20) = area
9 yds
(9 x 5)
(9 x 20)
5 yds
20 yds

60. Practice Time

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

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

63. 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)

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

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

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

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

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

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

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

71. 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

72. 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

73. 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

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

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

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

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

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

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

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

81. 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

82. 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

83. 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

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

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

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

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

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

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

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

91. 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

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

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

94. 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

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

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

97. 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

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

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

100. 11) Which expression is equivalent to 3(x + 7)?

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

102. 12) Which expression is equivalent to 4(x + 5)?

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

104. 13) Which expression is equivalent to 8(x + 2)?

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

106. 14) Which expression is equivalent to 2(x + 3)?

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

108. The End.