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The Distributive Property

The Distributive Property. The Distributive Property. The 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.

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The Distributive Property

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  1. The Distributive Property

  2. The Distributive Property The 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 Outsidethe parentheses with EVERYTHING INSIDE the parentheses.

  3. Find the total area of the rectangles.Area = length x width 6 ft 6 ft 20 ft + 4 ft

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

  5. 6(20) +6(4) 120 +24 = 144 sqft Now put the two rectangles back together. 6 ft 120 sq ft + 24 sq ft 24 ft

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

  7. Second way: 6(20+4) 6(24) = 144 ft2 6 ft 144 sqft 20 ft + 4 ft

  8. 4 x 2 x +2 A Visual Example of the Distributive property Find the area of this rectangle. We could say that this is 4(x + 2) Or..

  9. 4 2 4 x So we can say that 4(x+2) = 4x+8

  10. Example using the distributive property

  11. Another Example

  12. Another Example Or

  13. Another Example Or

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

  15. 40 + 80 = 120 square yards Or 8 ×15 = 120 square yards 40 80 8 yds 5 yds 10 yds

  16. 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

  17. 45+ 180 = 225 yds2 Or 9(25) = 225 yds2 (9 x 5) + (9 x 20) 0r 9(5+20) 9 yds (9 x 5) (9 x 20) 5 yds 20 yds

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