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The Distributive Property

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

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

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

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Then multiply each part by x 5 =? 40 3 x 5 x

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Finally, sum your two products 43 x 5 = x 5 x = 215 +

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

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

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

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Multiply each part by x 6 = ? 50 3 x 6 x 6 +

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Multiply each part by x 6 = ? 50 3 x 6 x

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Sum the two products. 53 x 6 = x 6 x = 318 +

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

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

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

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There are three steps to the distributive property. 4 x 28 = 4 x (20 + 8) 1)Break apart the double-digit number. 2)Multiply each part by 4. (distribute the 4)

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There are three steps to the distributive property. 4 x 28 = 4 x (20 + 8) = (4 x 20) + (4 x 8) 1)Break apart the double-digit number. 2)Multiply each part by 4. (distribute the 4)

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There are three steps to the distributive property. 4 x 28 = 4 x (20 + 8) = (4 x 20) + (4 x 8) 1)Break apart the double-digit number. 2)Multiply each part by 4. (distribute the 4) 3)Sum the two products.

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There are three steps to the distributive property. 4 x 28 = 4 x (20 + 8) = 80 + (4 x 8) 1)Break apart the double-digit number. 2)Multiply each part by 4. (distribute the 4) 3)Sum the two products.

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There are three steps to the distributive property. 4 x 28 = 4 x (20 + 8) = )Break apart the double-digit number. 2)Multiply each part by 4. (distribute the 4) 3)Sum the two products.

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There are three steps to the distributive property. 4 x 28 = 4 x (20 + 8) = = 112 1)Break apart the double-digit number. 2)Multiply each part by 4. (distribute the 4) 3)Sum the two products.

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

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Distribute the cubes to the girls.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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8 x 10 = 80 8 x 5 = 40 8 yds 5 yds 10 yds 8 yds Now sum the two areas together.

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yds 5 yds 10 yds Now sum the two areas together. +

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yds 5 yds 10 yds = 120 square yards

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Write an expression that shows how to find the area of the rectangle and uses the distributive property. 9 yds 5 yds 20 yds

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Find the areas for each individual rectangle. 9 yds 5 yds 20 yds

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Find the areas for each individual rectangle. 9 yds 5 yds 20 yds (9 x 5)

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Find the areas for each individual rectangle. 9 yds 5 yds 20 yds (9 x 5)(9 x 20)

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Sum the two areas. 9 yds 5 yds 20 yds (9 x 5)(9 x 20) +

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(9 x 5) + (9 x 20) = area 9 yds 5 yds 20 yds (9 x 5)(9 x 20)

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Practice Time

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

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

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2) Which of the following expressions shows the distributive property for 3 x (9 + 4) ? (3 x 9) + (3 x 4) (3 + 9) + (3 + 4) (3 + 9) x (3 + 4)

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2) Which of the following expressions shows the distributive property for 3 x (9 + 4) ? (3 x 9) + (3 x 4) Correct!

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3) Which of the following expressions is equivalent to: and shows the distributive property. 2 x (2 + 3) x (2 + 3)

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3) Which of the following expressions is equivalent to: and uses the distributive property. 2 x (2 + 3) Correct!

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

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

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

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5) Which of the following expressions is equivalent to: (5 x 9) + (5 x 3) ? 5 x (9 + 3)Correct!

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6) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 4 yds 3 yds 9 yds

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6) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 4 yds 3 yds 9 yds

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6) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 4 yds 3 yds 9 yds

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6) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 4 yds 3 yds 9 yds 4 yds

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6) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 4 yds 3 yds 9 yds 4 yds 4 x 3

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6) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 4 yds 3 yds 9 yds 4 yds 4 x 34 x 9

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6) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 4 yds 3 yds 9 yds 4 yds 4 x 34 x 9

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6) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 4 yds 3 yds 9 yds 4 x 34 x 9

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6) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 4 yds 3 yds 9 yds 4 x 34 x 9

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6) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 4 yds 3 yds 9 yds 4 x 3 +4 x 9

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7) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 6 yds 4 yds 8 yds

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7) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 6 yds 4 yds 8 yds

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7) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 6 yds 4 yds 8 yds

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7) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 6 yds 4 yds 8 yds 6 yds

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7) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 6 yds 4 yds 8 yds 6 yds 6 x 4

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7) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 6 yds 4 yds 8 yds 6 yds 6 x 46 x 8

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7) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 6 yds 4 yds 8 yds 6 yds 6 x 46 x 8

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7) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 6 yds 4 yds 8 yds 6 x 46 x 8

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7) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 6 yds 4 yds 8 yds 6 x 46 x 8

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7) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 6 yds 4 yds 8 yds 6 x 4 +6 x 8

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8) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 5 yds 2 yds 10 yds

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8) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 5 yds 2 yds 10 yds 5 x 25 x 10

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8) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 5 yds 2 yds 10 yds 5 x 2 +5 x 10

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9) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 8 yds 3 yds 5 yds

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9) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 8 yds 3 yds 5 yds 8 x 38 x 5

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9) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 8 yds 3 yds 5 yds 8 x 3 +8 x 5

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10) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 5 yds x yds 10 yds

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10) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 5 yds x yds 10 yds 5x5 ∙ 10

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10) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 5 yds x yds 10 yds 5x +5 ∙ 10

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

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11) Which expression is equivalent to 3(x + 7)? 3x + 21 Correct!

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

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12) Which expression is equivalent to 4(x + 5)? 4x + 20Correct!

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13) Which expression is equivalent to 8(x + 2)? 8x x x 8x + 10

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13) Which expression is equivalent to 8(x + 2)? 8x + 16Correct!

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14) Which expression is equivalent to 2(x + 3)? 2x + 3 2x + 5 2x + 6 2x + 2

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14) Which expression is equivalent to 2(x + 3)? 2x + 6 Correct!

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The End.

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3) Which of the following expressions is equivalent to: and uses the distributive property This shows the commutative property. Try again.

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Sorry! Try again.

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