Transcript The Distributive Property The distributive property is mental math strategy that can be used when multiplying. 24 x 6 =?

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
20
+
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
x6
+
4
x6
Then multiply each part by 5.
24 x 6 =?
20
x6
120
+
4
x6
24
Finally, add your two products
24 x 6 =144
20
+
4
x6 x6
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
x6
+
3
x6
Multiply each part by 6.
53 x 6 = ?
50
x6
300
+
3
x6
18
Add the two products.
53 x 6 = 318
50
+
3
x6 x6
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
and 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 and 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
8x5
= 40
5 yds
8
yds
shallow water
10 yds
Find the area of the shallow end.
8
yds
8x5
= 40
5 yds
8
yds
shallow water
10 yds
Find the area of the shallow end.
8
yds
8x5
= 40
5 yds
8
yds
8 x 10 = 80
10 yds
Now sum the two areas together.
8
yds
8x5
= 40
5 yds
8
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
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
4x3
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
4x3
3 yds
4
yds
4x9
9 yds
6) Write an expression that shows how to find
the area of the rectangle and uses the
distributive property.
4x3
4
yds
4x9
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.
4x3
4x9
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.
4x3
4x9
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.
4x3 + 4x9
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
6x4
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
6x4
4 yds
6
yds
6x8
8 yds
7) Write an expression that shows how to find
the area of the rectangle and uses the
distributive property.
6x4
6
yds
6x8
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.
6x4
6x8
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.
6x4
6x8
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.
6x4 + 6x8
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
5x2
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
8x3
3 yds
8x5
5 yds
9) Write an expression that shows how to find
the area of the rectangle and uses the
distributive property.
8x3
+
8x5
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
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.
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)?
3x + 21
Correct!
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 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!