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) 6 4 +6 8 −10 9−10 −10×9− −10 ×10

The Distributive Property

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.

The Distributive Property The product of a and (b+c) a(b+c) = ab + ac ex: 5(4 + 2) = 5(4) + 5(2) 20 + 10 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.

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

Find the total area of the rectangles. Area = length x width 20 ft + 4 ft

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 + 4 ft

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

Put the two rectangles together Second way: Put the two rectangles together 6 ft 6 ft 20 ft + 4 ft

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

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.

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

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

Example using the distributive property

Another Example

Another Example Or

Another Example Or

Another Example Or

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

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

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

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