Transcript Distributive Property

The Distributive Property
 Use the Distributive Property to evaluate
expressions.
 Use the Distributive Property to simplify
expressions.
1)
2)
3)
4)
5)
term
like terms
equivalent expressions
simplest form
coefficient
The Distributive Property
Eight customers each bought a
bargain game and a new release.
Calculate the total sales for
these customers.
The Distributive Property
Eight customers each bought a bargain
game and a new release.
Calculate the total sales for these
customers.
There are two methods you could use to calculate the video game sales.
sales of
bargain games



sales of
new releases

 

number of
customers

X
each customer' s
purchase price

The Distributive Property
Eight customers each bought a bargain
game and a new release.
Calculate the total sales for these
customers.
There are two methods you could use to calculate the video game sales.
sales of
bargain games



sales of
new releases

 

814.95

834.95
 119.60  279.60
 399.20
number of
customers

X
each customer' s
purchase price

The Distributive Property
Eight customers each bought a bargain
game and a new release.
Calculate the total sales for these
customers.
There are two methods you could use to calculate the video game sales.
sales of
bargain games



sales of
new releases

 

814.95

834.95
number of
customers

X
each customer' s
purchase price

 119.60  279.60
X 14.95  34.95
 849.90
 399.20
 399.20
8
The Distributive Property
Eight customers each bought a bargain
game and a new release.
Calculate the total sales for these
customers.
There are two methods you could use to calculate the video game sales.
sales of
bargain games



sales of
new releases

 

814.95

834.95
number of
customers

X
each customer' s
purchase price

 119.60  279.60
X 14.95  34.95
 849.90
 399.20
 399.20
8
This is an example of the ____________________.
The Distributive Property
Eight customers each bought a bargain
game and a new release.
Calculate the total sales for these
customers.
There are two methods you could use to calculate the video game sales.
sales of
bargain games



sales of
new releases

 

814.95

834.95
number of
customers

X
each customer' s
purchase price

 119.60  279.60
X 14.95  34.95
 849.90
 399.20
 399.20
8
Distributive Property
This is an example of the ____________________.
The Distributive Property
For any numbers, a, b, and c,
The Distributive Property
For any numbers, a, b, and c,
a(b+c) =
The Distributive Property
For any numbers, a, b, and c,
a ( b + c ) = ab + ac
The Distributive Property
For any numbers, a, b, and c,
a ( b + c ) = ab + ac
and
(b+c)a =
The Distributive Property
For any numbers, a, b, and c,
a ( b + c ) = ab + ac
and
( b + c ) a = ba + ca
The Distributive Property
For any numbers, a, b, and c,
a ( b + c ) = ab + ac
a(b–c) =
and
( b + c ) a = ba + ca
The Distributive Property
For any numbers, a, b, and c,
a ( b + c ) = ab + ac
a ( b – c ) = ab – ac
and
( b + c ) a = ba + ca
The Distributive Property
For any numbers, a, b, and c,
a ( b + c ) = ab + ac
and
( b + c ) a = ba + ca
a ( b – c ) = ab – ac
and
(b–c)a =
The Distributive Property
For any numbers, a, b, and c,
a ( b + c ) = ab + ac
and
( b + c ) a = ba + ca
a ( b – c ) = ab – ac
and
( b – c ) a = ba – ca
The Distributive Property
Rewrite 8(10 + 4) using the Distributive Property.
Then evaluate.
The Distributive Property
Rewrite 8(10 + 4) using the Distributive Property.
 810  84
Then evaluate.
The Distributive Property
Rewrite 8(10 + 4) using the Distributive Property.
 810  84
 80  32
Then evaluate.
The Distributive Property
Rewrite 8(10 + 4) using the Distributive Property.
 810  84
 80  32
 112
Then evaluate.
The Distributive Property
Rewrite 8(10 + 4) using the Distributive Property.
Then evaluate.
 810  84
 80  32
 112
Rewrite (12 – 4)6 using the Distributive Property.
Then evaluate.
The Distributive Property
Rewrite 8(10 + 4) using the Distributive Property.
Then evaluate.
 810  84
 80  32
 112
Rewrite (12 – 4)6 using the Distributive Property.
 612   64
Then evaluate.
The Distributive Property
Rewrite 8(10 + 4) using the Distributive Property.
Then evaluate.
 810  84
 80  32
 112
Rewrite (12 – 4)6 using the Distributive Property.
 612   64
 72  24
Then evaluate.
The Distributive Property
Rewrite 8(10 + 4) using the Distributive Property.
Then evaluate.
 810  84
 80  32
 112
Rewrite (12 – 4)6 using the Distributive Property.
 612   64
 72  24
 48
Then evaluate.
The Distributive Property
A family owns two cars.
In 1998, they drove the first car
18,000 miles and the second car
16,000 miles.
Use the graph to find the total cost of
operating both cars.
The Distributive Property
A family owns two cars.
In 1998, they drove the first car 18,000 miles
and the second car 16,000 miles.
Use the graph to find the total cost of
operating both cars.
0.4618,000  16,000 
The Distributive Property
A family owns two cars.
In 1995, they drove the first car 18,000 miles
and the second car 16,000 miles.
Use the graph to find the total cost of
operating both cars.
0.4618,000  16,000 
 8280  7360
The Distributive Property
A family owns two cars.
In 1995, they drove the first car 18,000 miles
and the second car 16,000 miles.
Use the graph to find the total cost of
operating both cars.
0.4618,000  16,000 
 8280  7360
 15,640
The Distributive Property
A family owns two cars.
In 1995, they drove the first car 18,000 miles
and the second car 16,000 miles.
Use the graph to find the total cost of
operating both cars.
0.4618,000  16,000 
 8280  7360
 15,640
It cost the family $15,640 to operate their two cars.
The Distributive Property
Rewrite 4(r – 6) using the Distributive Property.
Then simplify.
The Distributive Property
Rewrite 4(r – 6) using the Distributive Property.
4r  6
Then simplify.
The Distributive Property
Rewrite 4(r – 6) using the Distributive Property.
4r  6
 4r   46
Then simplify.
The Distributive Property
Rewrite 4(r – 6) using the Distributive Property.
4r  6
 4r   46
 4r  24
Then simplify.
The Distributive Property
A term is a ________, a _________, or a ________ or _________
of numbers and variables.
The Distributive Property
A term is a ________,
number a _________, or a ________ or _________
of numbers and variables.
The Distributive Property
A term is a ________,
number a _________,
variable or a ________ or _________
of numbers and variables.
The Distributive Property
A term is a ________,
product or _________
number a _________,
variable or a ________
of numbers and variables.
The Distributive Property
A term is a ________,
product or _________
number a _________,
variable or a ________
quotient
of numbers and variables.
The Distributive Property
A term is a ________,
product or _________
number a _________,
variable or a ________
quotient
of numbers and variables.
Example:
y, 4a, p3 , and
8g2h
are all terms.
The Distributive Property
A term is a ________,
product or _________
number a _________,
variable or a ________
quotient
of numbers and variables.
Example:
y, 4a, p3 , and
8g2h
are all terms.
Like terms are terms that contain the same _______, with corresponding variables
having the same ______.
The Distributive Property
A term is a ________,
product or _________
number a _________,
variable or a ________
quotient
of numbers and variables.
Example:
y, 4a, p3 , and
8g2h
are all terms.
variable with corresponding variables
Like terms are terms that contain the same _______,
having the same ______.
The Distributive Property
A term is a ________,
product or _________
number a _________,
variable or a ________
quotient
of numbers and variables.
Example:
y, 4a, p3 , and
8g2h
are all terms.
variable with corresponding variables
Like terms are terms that contain the same _______,
power
having the same ______.
The Distributive Property
A term is a ________,
product or _________
number a _________,
variable or a ________
quotient
of numbers and variables.
Example:
y, 4a, p3 , and
8g2h
are all terms.
variable with corresponding variables
Like terms are terms that contain the same _______,
power
having the same ______.
2x2  6x  5
The Distributive Property
A term is a ________,
product or _________
number a _________,
variable or a ________
quotient
of numbers and variables.
Example:
y, 4a, p3 , and
8g2h
are all terms.
variable with corresponding variables
Like terms are terms that contain the same _______,
power
having the same ______.
2x2  6x  5
three terms
The Distributive Property
A term is a ________,
product or _________
number a _________,
variable or a ________
quotient
of numbers and variables.
Example:
y, 4a, p3 , and
8g2h
are all terms.
variable with corresponding variables
Like terms are terms that contain the same _______,
power
having the same ______.
2x2  6x  5
three terms
3y2  6 y2  5 y
The Distributive Property
A term is a ________,
product or _________
number a _________,
variable or a ________
quotient
of numbers and variables.
Example:
y, 4a, p3 , and
8g2h
are all terms.
variable with corresponding variables
Like terms are terms that contain the same _______,
power
having the same ______.
2x2  6x  5
three terms
3y2  6 y2  5 y
like terms
The Distributive Property
A term is a ________,
product or _________
number a _________,
variable or a ________
quotient
of numbers and variables.
Example:
y, 4a, p3 , and
8g2h
are all terms.
variable with corresponding variables
Like terms are terms that contain the same _______,
power
having the same ______.
2x2  6x  5
three terms
3y2  6 y2  5 y
like terms
unlike terms
The Distributive Property
The Distributive Property and the properties of equality can be used to show that
5n + 7n = 12n
5n
and
7n
are __________.
The Distributive Property
The Distributive Property and the properties of equality can be used to show that
5n + 7n = 12n
5n
and
7n
like terms
are __________.
The Distributive Property
The Distributive Property and the properties of equality can be used to show that
5n + 7n = 12n
5n
and
7n
like terms
are __________.
5n  7 n  (5  7)n
The Distributive Property
The Distributive Property and the properties of equality can be used to show that
5n + 7n = 12n
5n
and
7n
like terms
are __________.
5n  7 n  (5  7)n
The expressions 5n + 7n and
they denote the same number.
12n
are called ______________________ because
The Distributive Property
The Distributive Property and the properties of equality can be used to show that
5n + 7n = 12n
5n
and
7n
like terms
are __________.
5n  7 n  (5  7)n
The expressions 5n + 7n and
they denote the same number.
12n
equivalent expressions because
are called ______________________
The Distributive Property
The Distributive Property and the properties of equality can be used to show that
5n + 7n = 12n
5n
and
7n
like terms
are __________.
5n  7 n  (5  7)n
The expressions 5n + 7n and
they denote the same number.
12n
equivalent expressions because
are called ______________________
An expression is in simplest form when it is replaced by an equivalent expression
having no __________ or ____________.
The Distributive Property
The Distributive Property and the properties of equality can be used to show that
5n + 7n = 12n
5n
and
7n
like terms
are __________.
5n  7 n  (5  7)n
The expressions 5n + 7n and
they denote the same number.
12n
equivalent expressions because
are called ______________________
An expression is in simplest form when it is replaced by an equivalent expression
having no __________
like terms or ____________.
The Distributive Property
The Distributive Property and the properties of equality can be used to show that
5n + 7n = 12n
5n
and
7n
like terms
are __________.
5n  7 n  (5  7)n
The expressions 5n + 7n and
they denote the same number.
12n
equivalent expressions because
are called ______________________
An expression is in simplest form when it is replaced by an equivalent expression
parentheses
having no __________
like terms or ____________.
The Distributive Property
Simplify each expression.
a)
7 x  11x
The Distributive Property
Simplify each expression.
a)
7 x  11x
 18 x
The Distributive Property
Simplify each expression.
a)
b)
7 x  11x
 18 x
9n  13n2  4n2
The Distributive Property
Simplify each expression.
a)
b)
7 x  11x
 18 x
9n  13n2  4n2
 9n  17 n 2
The Distributive Property
Simplify each expression.
a)
b)
7 x  11x
 18 x
9n  13n2  4n2
 9n  17 n 2
c)
1
1
y y
6
3
The Distributive Property
Simplify each expression.
a)
7 x  11x
 18 x
c)
1
1
y y
6
3
1
2
 y y
6
6
b)
9n  13n2  4n2
 9n  17 n 2
The Distributive Property
Simplify each expression.
a)
7 x  11x
 18 x
c)
1
1
y y
6
3
1
2
 y y
6
6
b)
9n  13n2  4n2
 9n  17 n 2
3
 y
6
The Distributive Property
Simplify each expression.
a)
7 x  11x
 18 x
c)
1
1
y y
6
3
1
2
 y y
6
6
b)
9n  13n2  4n2
 9n  17 n 2
3
 y
6
1
 y
2
The Distributive Property
Study Tip!
Like terms may be defined as terms that are the same or vary only by the coefficient.
The Distributive Property
Study Tip!
Like terms may be defined as terms that are the same or vary only by the coefficient.
The coefficient of a term is the _______________.
The Distributive Property
Study Tip!
Like terms may be defined as terms that are the same or vary only by the coefficient.
numerical factor
The coefficient of a term is the _______________.
The Distributive Property
Study Tip!
Like terms may be defined as terms that are the same or vary only by the coefficient.
numerical factor
The coefficient of a term is the _______________.
Example: in the term
17xy,
the coefficient is ____.
The Distributive Property
Study Tip!
Like terms may be defined as terms that are the same or vary only by the coefficient.
numerical factor
The coefficient of a term is the _______________.
Example: in the term
17xy,
the coefficient is ____.
17
The Distributive Property
Study Tip!
Like terms may be defined as terms that are the same or vary only by the coefficient.
numerical factor
The coefficient of a term is the _______________.
Example: in the term
17xy,
the coefficient is ____.
17
3x 2
in the term
the coefficien t is
4
The Distributive Property
Study Tip!
Like terms may be defined as terms that are the same or vary only by the coefficient.
numerical factor
The coefficient of a term is the _______________.
Example: in the term
17xy,
the coefficient is ____.
17
3
3x 2
in the term
the coefficien t is
4
4
The Distributive Property
Find the perimeter of the rectangle.
The Distributive Property
Find the perimeter of the rectangle.
P  25in  9in 
The Distributive Property
Find the perimeter of the rectangle.
P  25in  9in 
 214in 
The Distributive Property
Find the perimeter of the rectangle.
P  25in  9in 
 214in 
 28in
The Distributive Property
Find the perimeter of the rectangle.
P  25in  9in 
 214in 
 28in
P  25in   29in 
The Distributive Property
Find the perimeter of the rectangle.
P  25in  9in 
 214in 
 28in
P  25in   29in 
 10in   18in 
The Distributive Property
Find the perimeter of the rectangle.
P  25in  9in 
P  25in   29in 
 214in 
 10in   18in 
 28in
 28in
The Distributive Property
Find the perimeter of the rectangle.
P  25in  9in 
P  25in   29in 
 214in 
 10in   18in 
 28in
 28in
The perimeter of the rectangle is 28 inches.