# The Distributive Property The distributive property is mental

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 x 20 = 120 20 + 6 6 x 4 = 24 4

Now, put the two arrays back together. 6 120 20 24 + 4

Here they are together again. 6 120 20 24 + 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 x 6 + 4 x 6

Then multiply each part by 5. 24 x 6 =? 20 x 6 120 + 4 x 6 24

Finally, add your two products 24 x 6 =144 20 + 4 x 6 120 + 24 = 144

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 x 6 + 3 x 6

Multiply each part by 6. 53 x 6 = ? 50 x 6 300 + 3 x 6 18

Add the two products. 53 x 6 = 318 50 + 3 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)

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

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

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

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

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

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

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

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

40 + 80 = 120 square yards 8 yds 40 80 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) 5 yds (9 x 20) 20 yds

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

(9 x 5) + (9 x 20) = area 9 yds (9 x 5) 5 yds (9 x 20) 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 x 3 3 yds 4 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 x 3 3 yds 4 x 9 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 yds 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

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 x 4 4 yds 6 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 x 4 4 yds 6 x 8 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 yds 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

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 2 yds 5 x 10 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 3 yds 8 x 5 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 5 x x yds 5 ∙ 10 10 yds

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

11) Which expression is equivalent to 3(x + 7)? x + 10 x + 21 3 x + 7 3 x + 21

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

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

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

13) Which expression is equivalent to 8(x + 2)? 10 x 8 x + 2 8 x + 16 8 x + 10

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

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

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

- Slides: 107