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The Distributive Property

The distributive property is a powerful mental math strategy that simplifies multiplication, especially for double-digit numbers. For example, to calculate 43 x 5, we break 43 into 40 and 3, multiplying each by 5 to get 200 and 15, which sums to 215. Similarly, for 53 x 6, we separate 53 into 50 and 3, leading to a product of 318. This guide outlines the three essential steps of the distributive property and illustrates its applications through various examples. Perfect for students and learners eager to enhance their math skills!

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The Distributive Property

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  1. The Distributive Property

  2. The distributive property is mental math strategy that can be used when multiplying. 43 x 5 =?

  3. Break apart the double-digit number. 43 x 5 =? 40 3 +

  4. Then multiply each part by 5. 43 x 5 =? 40 3 + x 5x 5

  5. Then multiply each part by 5. 43 x 5 =? 40 3 + x 5x 5 200 15

  6. Finally, sum your two products 43 x 5 =215 40 3 + x 5x 5 200 15 + = 215

  7. Let’s look at another example. 53 x 6 = ?

  8. Break apart the double-digit number. 53 x 6 = ?

  9. Break apart the double-digit number. 53 x 6 = ? 50 3 +

  10. Multiply each part by 6. 53 x 6 = ? 50 3 + x 6x 6

  11. Multiply each part by 6. 53 x 6 = ? 50 3 + x 6x 6 300 18

  12. Sum the two products. 53 x 6 = 318 50 3 + x 6x 6 300 + 18 = 318

  13. There are three steps to the distributive property. 4 x 28 =

  14. There are three steps to the distributive property. 4 x 28 = 1) Break apart the double-digit number.

  15. There are three steps to the distributive property. 4 x 28 = 4 x (20 + 8) 1) Break apart the double-digit number.

  16. There are three steps to the distributive property. 4 x 28 = 4 x (20 + 8) • Break apart the double-digit number. • Multiply each part by 4. (distribute the 4)

  17. There are three steps to the distributive property. 4 x 28 = 4 x (20 + 8) = (4 x 20) + (4 x 8) • Break apart the double-digit number. • Multiply each part by 4. (distribute the 4)

  18. There are three steps to the distributive property. 4 x 28 = 4 x (20 + 8) = (4 x 20) + (4 x 8) • Break apart the double-digit number. • Multiply each part by 4. (distribute the 4) • Sum the two products.

  19. There are three steps to the distributive property. 4 x 28 = 4 x (20 + 8) = 80 + (4 x 8) • Break apart the double-digit number. • Multiply each part by 4. (distribute the 4) • Sum the two products.

  20. There are three steps to the distributive property. 4 x 28 = 4 x (20 + 8) = 80 + 32 • Break apart the double-digit number. • Multiply each part by 4. (distribute the 4) • Sum the two products.

  21. There are three steps to the distributive property. 4 x 28 = 4 x (20 + 8) = 80 + 32 = 112 • Break apart the double-digit number. • Multiply each part by 4. (distribute the 4) • Sum the two products.

  22. The word “distribute” means “to give out.”

  23. Distribute the cubes to the girls.

  24. Distribute the cubes to the girls.

  25. Distribute the cubes to the girls.

  26. Distribute the cubes to the girls.

  27. Distribute the cubes to the girls.

  28. Distribute the cubes to the girls.

  29. In this example, the 5 was distributed. 5 x 38 = 5 x (30 + 8) = (5 x 30) + (5 x 8)

  30. In this example, the 7 was distributed. 7 x 46 = 7 x (40 + 6) = (7 x 40) + (7 x 6)

  31. Find the area of the rectangle.Area = length x width 6 ft 24 ft

  32. Find the area of the rectangle.Area = length x width 6 ft 24 ft

  33. Find the area of the rectangle.Area = length x width 6 ft 20 ft + 4 ft

  34. Find the area of the rectangle.Area = length x width 6 ft 20 ft + 4 ft

  35. Find the area of the rectangle.Area = length x width 6 ft 6 ft 20 ft + 4 ft

  36. Find the area of the rectangle.Area = length x width Find the area of each rectangle. 6 ft 6 ft 20 ft + 4 ft

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

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

  39. 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

  40. Find the area of the rectangle.Area = length x width Now put the two rectangles back together. 6 ft 6 ft 120 sq ft 24 sq ft 20 ft + 4 ft

  41. 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 20 ft + 4 ft

  42. 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 20 ft + 4 ft

  43. 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

  44. Find the area of the rectangle.Area = length x width Now put the two rectangles back together. 6 ft 144 sq ft 24 ft

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

  46. Break the pool into a deep end and a shallow end. deepwater 8 yds 8 yds shallow water 10 yds 5 yds

  47. Find the area of the deep end. deepwater 8 yds 8 yds shallow water 10 yds 5 yds

  48. Find the area of the deep end. 8 x 5 = 40 8 yds 8 yds shallow water 10 yds 5 yds

  49. Find the area of the shallow end. 8 x 5 = 40 8 yds 8 yds shallow water 10 yds 5 yds

  50. Find the area of the shallow end. 8 x 5 = 40 8 yds 8 yds 8 x 10 = 80 10 yds 5 yds

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