Bell Work1. 62 + 132 + (–62)2. 22 + 49 + 283.

4.

5. 4 × 8 × 5

8

5

11

7

8

3

3623

1

132

99

62

160

11

71

THE DISTRIBUTIVE PROPERTY

The Distributive PropertyThe product of a and

(b+c):

a(b+c) = ab + ac

ex: 5(x + 2) = 5(x) + 5(2)

5x + 10

The product of a and (b-c):

a(b-c) = ab – ac

ex: 4(x –7)= 4(x) – 4(7)

4x –28

Sharing what is Outside the parentheses with EVERYTHING

INSIDE the parentheses.

Find the total area of the rectangles.Area = length x width

6 ft

20 ft + 4 ft

6 ft

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

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

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

6 ft

24 ft

144 sq ft

A Visual Example of the Distributive property

Find the area of this rectangle.

We could say that this is 4(x + 2)

x +2

Or..

x 2

4

x 2

44

)2(44 x 84 x

So we can say that

4(x+2) = 4x+8

Example using the distributive property

)5(2 x )(2 x )5(2

102 x

Another Example

)4(2 x )(2 x

82 x

)4(2

)4(3 x )(3 x

123 x

Another Example

)4)(3(

)12(3 xOr

)5(4 y )(4 y

204 y

Another Example

)5)(4(

)20(4 yOr

A swimming pool has a shallow end and a deep end. Find the surface area of the pool.

shallow waterDeep

water8 yds

5 yds 10 yds

80 408 yds

5 yds 10 yds

40 + 80 = 120 square yards

Write an expression that shows two ways on how to find the area of the rectangle.

(use the distributive property)

9 yds

5 yds 20 yds

(9 x 5) + (9 x 20) = area0r

9(5+20)=area

9 yds

5 yds 20 yds

(9 x 5) (9 x 20)

1) Which of the following expressions shows the distributive property for

5(3 + 7)?

(5 x 3) + (5 x 7)

(5 x 3) x (5 x 7)

(5 + 3) x (5 + 7)

Which of the following expressions shows the distributive property for

3(9 + 4) ?

(3 x 9) + (3 x 4)

(3 + 9) + (3 + 4)

(3 + 9) x (3 + 4)

Which of the following expressions is equivalent to:2( 3) + 2( 3)

2 (3 + 3)

2 + 2 + 3 + 3

3(2 + 3)

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)

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)

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

3x + 7

x + 21

x + 10

3x + 21

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

4x + 5

4x + 20

x + 9

9x

13) Which expression is equivalent to 8(x – 2)?

8x – 16

8x – 2

10x

8x – 10

Which expression is equivalent to 2(x – 3)?

2x – 3

2x – 5

2x – 6

2x – 2

Practice:Worksheet 61

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