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.
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) 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)
Find the area of the rectangle. Area = length x width
Find the area of the rectangle. Area = length x width
Find the area of the rectangle. Area = length x width 20 ft + 4 ft
Find the area of the rectangle. Area = length x width 20 ft + 4 ft
Find the area of the rectangle. Area = length x width 20 ft + 4 ft
Find the area of the rectangle. Area = length x width Find the area of each rectangle. 6 ft 6 ft 20 ft + 4 ft
Find the area of the rectangle. Area = length x width Find the area of each rectangle. 6 ft 6 ft 6 x 20 = 120 sq ft 20 ft + 4 ft
Find the area of the rectangle. Area = length x width Find the area of each rectangle. 6 ft 6 ft 6 x 20 = 120 sq ft 6 x 4 = 24 sq ft 20 ft + 4 ft
Find the area of the rectangle. Area = length x width Find the area of each rectangle. 6 ft 6 ft 120 sq ft 24 sq ft 20 ft + 4 ft
Find the area of the rectangle. Area = length x width Now put the two rectangles back together. 6 ft 6 ft 120 sq ft 24 sq ft 20 ft + 4 ft
Find the area of the rectangle. Area = length x width Now put the two rectangles back together. 6 ft 120 sq ft 24 sq ft 20 ft + 4 ft
Find the area of the rectangle. Area = length x width Now put the two rectangles back together. 6 ft 120 sq ft 24 sq ft 20 ft + 4 ft
Find the area of the rectangle. Area = length x width Now put the two rectangles back together. 6 ft 120 sq ft + 24 sq ft 24 ft
Find the area of the rectangle. Area = length x width Now put the two rectangles back together. 6 ft 144 sq ft 24 ft
A swimming pool has a shallow end and a deep end 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. 40 80 + 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
1) Which of the following expressions shows the distributive property for 5 x (3 + 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) ?
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) ?
5) Which of the following expressions is equivalent to: (5 x 9) + (5 x 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 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)?
11) Which expression is equivalent to 3(x + 7)? Correct! 3x + 21
12) Which expression is equivalent to 4(x + 5)?
12) Which expression is equivalent to 4(x + 5)? Correct!
13) Which expression is equivalent to 8(x + 2)?
13) Which expression is equivalent to 8(x + 2)? Correct!
14) Which expression is equivalent to 2(x + 3)?
14) Which expression is equivalent to 2(x + 3)? Correct!
The End.