Transcript Distributive Property PowerPoint

Distributive Property:
Advanced Problems
It may be necessary to review the
basic distributive property
problems in the number property
introduction PowerPoint
presentation
Recall the distributive property of
multiplication over addition . . .
symbolically:
a × (b + c) = a × b + a × c
and pictorially (rectangular array area model):
a
b
c
a×b
a×c
An example: 6 x 13
using your mental math skills . . .
symbolically:
6 × (10 + 3) = 6 × 10 + 6 × 3
and pictorially (rectangular array area model):
6
10
3
6 × 10
6×3
Use the Distributive Property to write
as an equivalent expression. Then evaluate
the expression.
Multiply.
Add.
Answer:
52
Use the Distributive Property to write
as an equivalent expression. Then evaluate
the expression. ***It doesn’t matter which side of the parenthesis the
number is on. The property works the same.
Multiply.
Add.
Answer:
30
Use the Distributive Property to write each expression as an equivalent
expression. Then evaluate the expression.
a.
b.
Answer:
Answer:
Real Life Example: Recreation North Country Rivers of York, Maine,
offers one-day white-water rafting trips on the Kennebec River. The trip
costs $69 per person, and wet suits are $15 each.
Write two equivalent expressions to find the total cost of one trip for a
family of four if each person uses a wet suit.
Method 1 Find the cost for 1 person, then multiply by 4.
cost for 1 person
Method 2
cost of 4 trips
Find the cost of 4 trips and 4 wet suits.
Then add.
cost of 4 wet suits
Evaluate either expression to find the total cost.
Distributive Property
Multiply.
Add.
Answer:
The total cost is $336.
Check
You can check your results by evaluating
4($84).
Movies The cost of a movie ticket is $7 and the cost
of a box of popcorn is $2.
a.
Write two equivalent expressions to find the total cost
for a family of five to go to the movies if each member
of the family gets a box of popcorn.
Answer:
b. Find the total cost.
Answer:
$45
Use the Distributive Property to write
as an equivalent algebraic expression.
Simplify.
Answer:
Use the Distributive Property to write
as an equivalent algebraic expression.
Simplify.
Answer:
Use the Distributive Property to write each expression as an equivalent
algebraic expression.
a.
Answer:
b.
Answer:
Use the Distributive Property to write
as an equivalent algebraic expression.
Rewrite
as
Distributive Property
Simplify.
Definition of subtraction
Answer:
Use the Distributive Property to write
as an equivalent algebraic expression.
Rewrite
as
Distributive Property
Simplify.
Answer:
Use the Distributive Property to write each expression as an equivalent
algebraic expression.
a.
Answer:
b.
Answer:
Real-Life Example 2
Mental Math
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
x5
+
3
x5
Then multiply each part by 5.
43 x 5 =?
40
x5
200
+
3
x5
15
Finally, sum your two products
43 x 5 =215
40
+
3
x5 x5
200 + 15
= 215
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
Sum the two products.
53 x 6 =
318
50
+
3
x6
x6
300 + 18 = 318
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
6 ft
24 ft
Find the area of the rectangle.
Area = length x width
6 ft
24 ft
Find the area of the rectangle.
Area = length x width
6 ft
20 ft
+
4 ft
Find the area of the rectangle.
Area = length x width
6 ft
20 ft
+
4 ft
Find the area of the rectangle.
Area = length x width
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
20 ft
+
4 ft
Find the area of the rectangle.
Area = length x width
Find the area of each rectangle.
6 ft
6 x 20 = 120 sq ft
20 ft
6 ft
+
4 ft
Find the area of the rectangle.
Area = length x width
Find the area of each rectangle.
6 ft
6 x 20 = 120 sq ft
6 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
120 sq ft
20 ft
6 ft
+
24 sq 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
20 ft
6 ft
+
24 sq 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
20 ft
24 sq 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
20 ft
24 sq ft
+
4 ft
Find the area of the rectangle.
Area = length x width
Now put the two rectangles back together.
6 ft
120 sq + 24 sq ft
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. Find the
surface area of the pool.
8
yds
deepw
ater
5 yds
shallow water
10 yds
Break the pool into a deep end and
a shallow end.
8
yds
deepw
ater
5 yds
8
yds
shallow water
10 yds
Find the area of the deep end.
8
yds
deepw
ater
5 yds
8
yds
shallow water
10 yds
Find the area of the deep end.
8
yds
8x
5=
40
5 yds
8
yds
shallow water
10 yds
Find the area of the shallow end.
8
yds
8x
5=
40
5 yds
8
yds
shallow water
10 yds
Find the area of the shallow end.
8
yds
8x
5=
40
5 yds
8
yds
8 x 10 =
80
10 yds
Now sum the two areas together.
8
yds
8x
5=
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
5 yds
80
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)
5 yds
+
(9 x 20)
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 + 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!
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
yd
s
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
yd
s
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
yd
s
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
yd
s
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.
5x2 +
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!
Click below to see video
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