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

+

Let’s 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 = 318

50 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)

1) Break apart the double-digit number.

2) 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)

1) Break apart the double-digit number.

2) 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)

1) Break apart the double-digit number.

2) Multiply each part by 4. (distribute the 4)

3) Sum the two products.

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.

There are three steps to the distributive property.

4 x 28 = 4 x (20 + 8) = 80 + 32

1) Break apart the double-digit number.

2) Multiply each part by 4. (distribute the 4)

3) Sum the two products.

There are three steps to the distributive property.

4 x 28 = 4 x (20 + 8) = 80 + 32 = 112

1) Break apart the double-digit number.

2) Multiply each part by 4. (distribute the 4)

3) 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 ft

24 ft

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

6 ft

24 ft

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

6 ft

20 ft + 4 ft

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

6 ft

20 ft + 4 ft

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

6 ft

20 ft + 4 ft

6 ft

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

6 ft

20 ft + 4 ft

6 ft

Find the area of each rectangle.

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

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

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

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

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

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

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

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

6 ft

24 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

yds

5 yds 10 yds

shallow waterdeepwater8

yds

5 yds 10 yds

8 yds

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

shallow waterdeepwater8

yds

5 yds 10 yds

8 yds

Find the area of the deep end.

shallow water8 x 5 = 40

8 yds

5 yds 10 yds

8 yds

Find the area of the deep end.

shallow water8 x 5 = 40

8 yds

5 yds 10 yds

8 yds

Find the area of the shallow end.

8 x 10 = 808 x 5 = 40

8 yds

5 yds 10 yds

8 yds

Find the area of the shallow end.

8 x 10 = 808 x 5 = 40

8 yds

5 yds 10 yds

8 yds

Now sum the two areas together.

80 408 yds

5 yds 10 yds

Now sum the two areas together.

+

80 408 yds

5 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 yds

5 yds 20 yds

Find the areas for each individual rectangle.

9 yds

5 yds 20 yds

Find the areas for each individual rectangle.

9 yds

5 yds 20 yds

(9 x 5)

Find the areas for each individual rectangle.

9 yds

5 yds 20 yds

(9 x 5) (9 x 20)

Sum the two areas.

9 yds

5 yds 20 yds

(9 x 5) (9 x 20)+

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

9 yds

5 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 yds

3 yds 9 yds

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

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

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

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

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 4 x 9

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 4 x 9

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

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

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

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

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

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

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

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

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 6 x 8

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 6 x 8

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

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

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

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

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

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

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

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

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

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

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

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

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

3x + 7

x + 21

x + 10

3x + 21

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

3x + 21 Correct!

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

4x + 5

4x + 20

x + 9

9x

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

4x + 20 Correct!

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

8x + 16

8x + 2

10x

8x + 10

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

8x + 16 Correct!

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

2x + 3

2x + 5

2x + 6

2x + 2

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

2x + 6 Correct!

The End.