5 - the distributive property

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  • The Distributive Propertyhttp://www.slideshare.net/anthonymaiorano/5-the-distributive-property

  • The distributive property is mental math strategy that can be used when multiplying.

    43 x 5 =?

  • Break apart the double-digit number.

    43 x 5 =? 40 3+

  • Then multiply each part by 5.

    43 x 5 =? 40 3 x 5 x 5+

  • Then multiply each part by 5.

    43 x 5 =? 40 3 x 5 x 5 200 15+

  • Finally, sum your two products

    43 x 5 =215 40 3 x 5 x 5 200 15+= 215+

  • Lets look at another example.53 x 6 = ?

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

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

  • Multiply each part by 6.53 x 6 = ?50 3 x 6 x 6+

  • Multiply each part by 6.53 x 6 = ?50 3 x 6 x 6 300 18+

  • Sum the two products.53 x 6 = 31850 3 x 6 x 6 300 + 18 = 318+

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

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

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

  • 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)

  • 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)

  • 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.

  • 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.

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

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

  • The word distribute means to give out.

  • Distribute the cubes to the girls.

  • Distribute the cubes to the girls.

  • Distribute the cubes to the girls.

  • Distribute the cubes to the girls.

  • Distribute the cubes to the girls.

  • Distribute the cubes to the girls.

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

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

  • Find the area of the rectangle.Area = length x width

    6 ft24 ft

  • Find the area of the rectangle.Area = length x width

    6 ft24 ft

  • Find the area of the rectangle.Area = length x width6 ft20 ft+ 4 ft

  • Find the area of the rectangle.Area = length x width6 ft20 ft+ 4 ft

  • Find the area of the rectangle.Area = length x width6 ft20 ft+ 4 ft

    6 ft

  • Find the area of the rectangle.Area = length x width6 ft20 ft+ 4 ft

    6 ftFind the area of each rectangle.

  • Find the area of the rectangle.Area = length x width6 ft20 ft+ 4 ft

    6 ftFind the area of each rectangle.6 x 20 = 120 sq ft

  • Find the area of the rectangle.Area = length x width6 ft20 ft+ 4 ft

    6 ftFind the area of each rectangle.6 x 20 = 120 sq ft6 x 4 = 24 sq ft

  • Find the area of the rectangle.Area = length x width6 ft20 ft+ 4 ft

    6 ftFind the area of each rectangle.120 sq ft24 sq ft

  • Find the area of the rectangle.Area = length x width6 ft20 ft+ 4 ft

    6 ftNow put the two rectangles back together.120 sq ft24 sq ft

  • Find the area of the rectangle.Area = length x width6 ft20 ft+ 4 ft

    Now put the two rectangles back together.120 sq ft24 sq ft

  • Find the area of the rectangle.Area = length x width6 ft20 ft+ 4 ft

    Now put the two rectangles back together.120 sq ft24 sq ft

  • Find the area of the rectangle.Area = length x width6 ft24 ft

    Now put the two rectangles back together.

    120 sq ft + 24 sq ft

  • Find the area of the rectangle.Area = length x width6 ft24 ft

    Now put the two rectangles back together.

    144 sq ft

  • A swimming pool has a shallow end and a deep end. Find the surface area of the pool.

    shallow waterdeepwater8 yds5 yds 10 yds

  • shallow waterdeepwater8 yds5 yds 10 yds

    8 yds

    Break the pool into a deep end and a shallow end.

  • shallow waterdeepwater8 yds5 yds 10 yds

    8 yds

    Find the area of the deep end.

  • shallow water8 x 5 = 408 yds5 yds 10 yds

    8 yds

    Find the area of the deep end.

  • shallow water8 x 5 = 408 yds5 yds 10 yds

    8 yds

    Find the area of the shallow end.

  • 8 x 10 = 808 x 5 = 408 yds5 yds 10 yds

    8 yds

    Find the area of the shallow end.

  • 8 x 10 = 808 x 5 = 408 yds5 yds 10 yds

    8 yds

    Now sum the two areas together.

  • 80 408 yds5 yds 10 yds

    Now sum the two areas together.+

  • 80 408 yds5 yds 10 yds

    40 + 80 = 120 square yards

  • Write an expression that shows how to find the area of the rectangle and uses the distributive property.

    9 yds5 yds 20 yds

  • Find the areas for each individual rectangle.

    9 yds5 yds 20 yds

  • Find the areas for each individual rectangle.

    9 yds5 yds 20 yds

    (9 x 5)

  • Find the areas for each individual rectangle.

    9 yds5 yds 20 yds

    (9 x 5)(9 x 20)

  • Sum the two areas.

    9 yds5 yds 20 yds

    (9 x 5)(9 x 20)+

  • (9 x 5) + (9 x 20) = area

    9 yds5 yds 20 yds

    (9 x 5)(9 x 20)

  • Practice Time

  • 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)

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

    (5 x 3) + (5 x 7)Correct!

  • 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)

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

    (3 x 9) + (3 x 4)Correct!

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

    2 x (2 + 3)

    2 + 2 + 3 + 3

    3 x (2 + 3)

  • 3) Which of the following expressions is equivalent to:2 + 3 + 2 + 3 and uses the distributive property.

    2 x (2 + 3)Correct!

  • 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)

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

    4 x (3 + 8) Correct!

  • 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)

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

    5 x (9 + 3) Correct!

  • 6) Write an expression that shows how to find the area of the rectangle and uses the distributive property.

    4 yds3 yds 9 yds

  • 6) Write an expression that shows how to find the area of the rectangle and uses the distributive property.

    4 yds3 yds 9 yds

  • 6) Write an expression that shows how to find the area of the rectangle and uses the distributive property.

    4 yds3 yds 9 yds

  • 6) Write an expression that shows how to find the area of the rectangle and uses the distributive property.

    4 yds3 yds 9 yds

    4 yds

  • 6) Write an expression that shows how to find the area of the rectangle and uses the distributive property.

    4 yds3 yds 9 yds

    4 yds

    4 x 3

  • 6) Write an expression that shows how to find the area of the rectangle and uses the distributive property.

    4 yds3 yds 9 yds

    4 yds

    4 x 34 x 9

  • 6) Write an expression that shows how to find the area of the rectangle and uses the distributive property.

    4 yds3 yds 9 yds

    4 yds

    4 x 34 x 9

  • 6) Write an expression that shows how to find the area of the rectangle and uses the distributive property.

    4 yds3 yds 9 yds

    4 x 34 x 9

  • 6) Write an expression that shows how to find the area of the rectangle and uses the distributive property.

    4 yds3 yds 9 yds

    4 x 34 x 9

  • 6) Write an expression that shows how to find the area of the rectangle and uses the distributive property.

    4 yds3 yds 9 yds

    4 x 3 +4 x 9

  • 7) Write an expression that shows how to find the area of the rectangle and uses the distributive property.

    6 yds4 yds 8 yds

  • 7) Write an expression that shows how to find the area of the rectangle and uses the distributive property.

    6 yds4 yds 8 yds

  • 7) Write an expression that shows how to find the area of the rectangle and uses the distributive property.

    6 yds4 yds 8 yds

  • 7) Write an expressio