The document explains the distributive property for multiplying two numbers. It provides examples of breaking apart double-digit numbers and then multiplying each part. There are three steps: 1) break apart the double-digit number, 2) multiply each part by the other number, 3) sum the products. It also applies this to finding the area of rectangles by breaking them into individual rectangles and then adding the areas.

1. The Distributive Property
http://www.slideshare.net/anthonymaiorano/5-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 =?
40 3+

4. Then multiply each part by 5.
43 x 5 =?
40 3
x 5 x 5
+

5. Then multiply each part by 5.
43 x 5 =?
40 3
x 5 x 5
200 15
+

6. Finally, sum your two products
43 x 5 =215
40 3
x 5 x 5
200 15+ = 215
+

7. Let’s look at another example.
53 x 6 = ?

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

9. Break apart the double-digit number.
53 x 6 = ?
50 3+

10. Multiply each part by 6.
53 x 6 = ?
50 3
x 6 x 6
+

11. Multiply each part by 6.
53 x 6 = ?
50 3
x 6 x 6
300 18
+

12. Sum the two products.
53 x 6 = 318
50 3
x 6 x 6
300 + 18 = 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)
1) Break apart the double-digit number.
2) 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)
1) Break apart the double-digit number.
2) 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)
1) Break apart the double-digit number.
2) Multiply each part by 4. (distribute the 4)
3) Sum the two products.

19. There are three steps to the distributive
property.
4 x 28 = 4 x (20 + 8) = 80 + (4 x 8)
1) Break apart the double-digit number.
2) Multiply each part by 4. (distribute the 4)
3) Sum the two products.

20. There are three steps to the distributive
property.
4 x 28 = 4 x (20 + 8) = 80 + 32
1) Break apart the double-digit number.
2) Multiply each part by 4. (distribute the 4)
3) Sum the two products.

21. There are three steps to the distributive
property.
4 x 28 = 4 x (20 + 8) = 80 + 32 = 112
1) Break apart the double-digit number.
2) Multiply each part by 4. (distribute the 4)
3) 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
6 ft
24 ft

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

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

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

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

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

37. 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

38. 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

39. 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

40. 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

41. 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

42. 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

43. 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

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

45. A swimming pool has a shallow end
and a deep end. Find the surface
area of the pool.
shallow water
deep
water8
yds
5 yds 10 yds

46. shallow water
deep
water8
yds
5 yds 10 yds
8
yds
Break the pool into a deep end and a
shallow end.

47. shallow water
deep
water8
yds
5 yds 10 yds
8
yds
Find the area of the deep end.

48. shallow water8 x 5
= 40
8
yds
5 yds 10 yds
8
yds
Find the area of the deep end.

49. shallow water8 x 5
= 40
8
yds
5 yds 10 yds
8
yds
Find the area of the shallow end.

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

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

52. 80408
yds
5 yds 10 yds
Now sum the two areas together.
+

53. 80408
yds
5 yds 10 yds
40 + 80 = 120 square yards

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
5 yds 20 yds
(9 x 5)

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

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

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

60. Practice Time

61. 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)

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

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:
2 + 3 + 2 + 3
and shows the distributive property.
2 x (2 + 3)
2 + 2 + 3 + 3
3 x (2 + 3)

66. 3) Which of the following expressions is equivalent to:
2 + 3 + 2 + 3
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) ?
4 x (3 + 8)
8 x (3 + 4)
3 x (4 + 8)

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

69. 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)

70. 5) Which of the following expressions is equivalent to:
(5 x 9) + (5 x 3) ?
5 x (9 + 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
3 yds 9 yds
4
yds

75. 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
yds
4 x 3

76. 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
yds
4 x 3 4 x 9

77. 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
yds
4 x 3 4 x 9

78. 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

79. 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

80. 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

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
4 yds 8 yds
6
yds

85. 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

86. 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 6 x 8

87. 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 6 x 8

88. 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

89. 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

90. 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

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
2 yds 10 yds
5 x 2 5 x 10

93. 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

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
3 yds 5 yds
8 x 3 8 x 5

96. 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

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
x yds 10 yds
5x 5 ∙ 10

99. 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

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

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

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

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

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

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

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

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

108. The End.