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Mastering the Distributive Property in Math

Learn how to apply the distributive property in mathematical calculations to simplify expressions and find the total areas of rectangles. Practice with examples and worksheets.

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Mastering the Distributive Property in Math

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  1. 132 99 62 160 Bell Work 1. 62 + 132 + (–62) 22 + 49 + 28 3. 4. 5. 4 × 8 × 5

  2. The Distributive Property

  3. 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.

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

  5. Find the area of the rectangle.Area = length x width Find the area of each rectangle. 6 ft 6 ft 120 sq ft 24 sq ft 20 ft + 4 ft

  6. Find the area of the rectangle.Area = length x width Now put the two rectangles back together. 6 ft 120 sq ft + 24 sq ft 24 ft

  7. Find the area of the rectangle.Area = length x width 6 ft 144 sq ft 24 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 40 80 8 yds 5 yds 10 yds

  16. 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

  17. (9 x 5) + (9 x 20) = area 0r 9(5+20)=area 9 yds (9 x 5) (9 x 20) 5 yds 20 yds

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

  19. 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)

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

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

  22. Which of the following expressions is equivalent to:(5 x 9) – (5 x 3) ? 3 x (9 – 5) 5 x (9 – 3) 9 x (3 – 5)

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

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

  25. 13) Which expression is equivalent to 8(x – 2)? 10x 8x – 2 8x – 16 8x – 10

  26. Which expression is equivalent to 2(x – 3)? 2x – 6 2x – 5 2x – 3 2x – 2

  27. Practice: Worksheet 61 Go Broncos

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