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PPT – The Distributive Property PowerPoint presentation | free to view - id: 56f245-ZWM0M

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The Distributive Property

The distributive property is mental math strategy

that can be used when multiplying.

24 x 6 ?

Think of an array with a length of 24 and a width

of 6

6

24

How can you break the array apart to make 24 a

friendlier number?

6

24

Break the length into 20 and 4.

6

20 4

Think of them as separate arrays.

6

20 4

Now you have 6 x 20 and 6 times 4.

6

6

20 4

What is the total of each array?

6

6

20 4

6 x 20 is 6 x 2 tens or 12 tens which is 120.

6

6

6 x 20 120

20 4

6 x 4 is 24.

6

6

6 x 20 120

6 x 4 24

20 4

Now, put the two arrays back together.

6

120

24

20 4

Here they are together again.

6

120

24

20 4

Add the two arrays together. 120 24 144.

6

120

24

24

So the answer to 6 x 24 is 144.

6

144

24

Lets look at it in an equation.

Break apart the double-digit number.

24 x 6 ?

20 4

Then multiply each part by 5.

24 x 6 ?

20 4

x 6 x 6

Then multiply each part by 5.

24 x 6 ?

20 4

x 6 x 6

120 24

Finally, add your two products

24 x 6 144

20 4

x 6 x 6

120 24

144

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

Add 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)

- 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 32

- 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 32 112

- Break 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)

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

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

deepwater

8 yds

8 yds

shallow water

10 yds

5 yds

Find the area of the deep end.

deepwater

8 yds

8 yds

shallow water

10 yds

5 yds

Find the area of the deep end.

8 x 5 40

8 yds

8 yds

shallow water

10 yds

5 yds

Find the area of the shallow end.

8 x 5 40

8 yds

8 yds

shallow water

10 yds

5 yds

Find the area of the shallow end.

8 x 5 40

8 yds

8 yds

8 x 10 80

10 yds

5 yds

Now sum the two areas together.

8 x 5 40

8 yds

8 yds

8 x 10 80

10 yds

5 yds

Now sum the two areas together.

80

40

8 yds

10 yds

5 yds

40 80 120 square yards

40

80

8 yds

5 yds

10 yds

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

(9 x 5)

5 yds

20 yds

Find the areas for each individual rectangle.

9 yds

(9 x 5)

(9 x 20)

5 yds

20 yds

Sum the two areas.

9 yds

(9 x 5)

(9 x 20)

5 yds

20 yds

(9 x 5) (9 x 20) area

9 yds

(9 x 5)

(9 x 20)

5 yds

20 yds

Practice Time

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

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

4 yds

4 x 3

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

4 yds

4 x 3

4 x 9

3 yds

9 yds

6) Write an expression that shows how to find the

area of the rectangle and uses the distributive

property.

4 x 3

4 x 9

4 yds

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 x 3

4 x 9

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 x 3

4 x 9

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 x 3

4 x 9

4 yds

3 yds

9 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

7) Write an expression that shows how to find the

area of the rectangle and uses the distributive

property.

6 yds

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

6 yds

6 x 4

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

6 yds

6 x 4

6 x 8

4 yds

8 yds

7) Write an expression that shows how to find the

area of the rectangle and uses the distributive

property.

6 x 4

6 x 8

6 yds

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 x 4

6 x 8

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 x 4

6 x 8

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 x 4

6 x 8

6 yds

4 yds

8 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

8) Write an expression that shows how to find the

area of the rectangle and uses the distributive

property.

5 yds

5 x 2

5 x 10

2 yds

10 yds

8) Write an expression that shows how to find the

area of the rectangle and uses the distributive

property.

5 x 2

5 x 10

5 yds

2 yds

10 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

9) Write an expression that shows how to find the

area of the rectangle and uses the distributive

property.

8 yds

8 x 3

8 x 5

3 yds

5 yds

9) Write an expression that shows how to find the

area of the rectangle and uses the distributive

property.

8 x 3

8 x 5

8 yds

3 yds

5 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

10) Write an expression that shows how to find

the area of the rectangle and uses the

distributive property.

5 yds

5x

5 10

x yds

10 yds

10) Write an expression that shows how to find

the area of the rectangle and uses the

distributive property.

5x

5 10

5 yds

x yds

10 yds

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

x 10

x 21

3x 7

3x 21

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

Correct!

3x 21

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

x 9

4x 20

4x 5

9x

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

4x 20

Correct!

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

10x

8x 2

8x 16

8x 10

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

8x 16

Correct!

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

2x 6

2x 5

2x 3

2x 2

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

2x 6

Correct!

The End.

1) Which of the following expressions shows the

distributive property for 5 x (3 7)?

(5 3) x (5 7)

(5 x 3) x (5 x 7)

(5 x 3) (5 x 7)

1) Which of the following expressions shows the

distributive property for 5 x (3 7)?

Correct!

(5 x 3) (5 x 7)

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 to2 3 2 3 and shows the

distributive property.

2 2 3 3

2 x (2 3)

3 x (2 3)

3) Which of the following expressions is

equivalent to2 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) ?

3 x (4 8)

8 x (3 4)

4 x (3 8)

4) Which of the following expressions is

equivalent to(4 x 3) (4 x 8) ?

Correct!

4 x (3 8)

5) Which of the following expressions is

equivalent to(5 x 9) (5 x 3) ?

3 x (9 5)

5 x (9 3)

9 x (3 5)

5) Which of the following expressions is

equivalent to(5 x 9) (5 x 3) ?

5 x (9 3)

Correct!

3) Which of the following expressions is

equivalent to2 3 2 3 and uses the

distributive property.

2 2 3 3 This shows the commutative property.

Try again.

Sorry!

- Try again.