1. Solve the following equations: 6(4+8) 6 4 +6 8 −10 9−10 −10×9− −10 ×10
Bell Work
Solve the following equations:
6(4+8)
−10 9−10
−10×9− −10 ×10

2. The Distributive
Property

3. The Distributive Property
We use the distributive property to multiply a number by a sum or a difference.
For example: 5(3+9)
So we multiply each term in parentheses by the number outside the parentheses.
5 3 +5(9)
Sharing what is Outside the parentheses with EVERYTHING INSIDE the parentheses.

4. The Distributive Property
The product of a and (b+c)
a(b+c) = ab + ac
ex: 5(4 + 2) = 5(4) + 5(2)
The product of a and (b-c)
a(b-c) = ab – ac
ex: 4(3 –7)= 4(3) – 4(7)
12 –28
Sharing what is Outside the parentheses with EVERYTHING INSIDE the parentheses.

5. The Distributive Property
To help see this better we can use what is called “the array model” or the “area model”.

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

7. Find the area of each rectangle.
One Way:
6(20) +6(4)
Find the area of each rectangle.
6 ft
6 ft
120 sq ft
24 sq ft
20 ft ft

8. Now put the two rectangles back together.
6(20) +6(4)
= 144 sq ft
Now put the two rectangles back together.
6 ft
120 sq ft
+ 24 sq ft
24 ft

9. Put the two rectangles together
Second way:
Put the two rectangles together
6 ft
6 ft
20 ft ft

10. Second way:
6(20+4)
6(24) = 144 ft2
6 ft
144 sq ft
20 ft + 4 ft

11. The Distributive Property
We can do this when we have variables also.
Having a variable means we don’t know all the dimensions of our rectangles.

12. Working Backwards with the Distributive Propertyx 2 4
Find the area of this rectangle.
x +2
We could say that this is 4(x + 2)
Or..

13. 2 4 4 x
So we can say that
4(x+2) = 4x+8

14. Example using the distributive property

15. Another Example

16. Another Example Or

17. Another Example Or

18. Another Example Or

19. A swimming pool has a shallow end and a deep end
A swimming pool has a shallow end and a deep end. Find the area of the pool.
Deep
water
8 yds
shallow water
5 yds
10 yds

20. 40 + 80 = 120 square yards Or 8 ×15 = 120 square yards 8 yds 5 yds

21. You Try: Write two expressions that show how to find the total area of the rectangle, then solve. (use the distributive property)
9 yds
5 yds
20 yds

22. Or (9 x 5) + (9 x 20) 0r 9(5+20) 9 yds 5 yds 20 yds 45+ 180 = 225 yds2