# 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

4 yds3 yds 9 yds

4 yds

4 yds3 yds 9 yds

4 yds

4 x 3

4 yds3 yds 9 yds

4 yds

4 x 34 x 9

4 yds3 yds 9 yds

4 yds

4 x 34 x 9

4 yds3 yds 9 yds

4 x 34 x 9

4 yds3 yds 9 yds

4 x 34 x 9

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

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