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.

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 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

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

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!