Transcript EDI Lesson AF 1_3 - Pacoima Charter School

Today we use the distributive
property in equations and
expressions with variables.
distributive=to give out
When you see a number next to another
number in parentheses, this means to
multiply. For example: 8(8)= 64
What are other ways to arrange problems
that lets you know that you have to
multiply?
8(8 x y)
Term
When you have numbers in parentheses, you
call these numbers in parentheses, terms.
For example:
(9 + 6) is a term
(6 – y ) in a term
Distributive Property
states that the product of a number and
a sum is equal to the sum of the
individual products of the addends and
the number
An example is:
5(3 + t) = 5 × 3 + 5 × t
product=multiplication
Distributive Property
5(3 + t) =
5(3 + t) = 5 × 3
5×t
In summary, when you multiply the 5 and the 3
And the 5 and the t
you get 5 x 3 + 5 x t
Distributive Property
8(k - 2) =
8(k - 2) = 8 × k
8× 2
In summary, when you multiply the 8 and the k
And the 8 and the 2
you get 8 x k - 8 x 2
Distributive Property
5(3 + t) = 5 × 3 + 5 × t
Notice how the 5 is distributed by first
multiplying with the 3 and then the 1.
Distributive Property
5(3 + t) =
5(3 + t) = 5 × 3
When you multiply the 5 and the 3
you get 5 x 3
Distributive Property
5(3 + t) =
5(3 + t) = 5 × 3 +
5×t
When you multiply the 5 and the 1
you get 5 x t
Let’s look at Distributive Property in
a different way
states that the product of a number and a
sum is equal to the sum of the individual
products of the addends and the number
An example is:
(5 x 6) + (5 x t)=5(6 + t)
Why does this happen
(5 x 6) + (5 x t)=
1. What is the common factor in the above equation?
2. You factor it out
3. What remains in the 1st term?
4. What remains in the 2nd term?
5. What operation is being done?
5( 6
t)
Why does this happen
(8 x r) - (8 x 6)=
1. What is the common factor in the above equation?
2. You factor it out
3. What remains in the 1st term?
4. What remains in the 2nd term?
5. Once the numbers and variables are in the
parentheses, what do you do to the new term?
8( r
6)
 It is important to use the distributive
property to be able to solve complex
problems
 It will also prepare you for algebra which you
have to pass in order to graduate high school
Why else is it important to use the
distributive property in equations and
expressions with variables
We are going to use the distributive property in
equations and expressions with variables
When they look like this:
(5 + 6) + ( 5 + y)
•
You look at both terms and find the
common factor in both terms
5
• You place the number that you factored,
outside of the parentheses
5(
)
• You look at what remains in the first
term and you place it in the parentheses
5(6 )
• You look at what remains in the second
term and you place it in the parentheses
5(6 Y)
• Look at the operation sign between both
terms and place that in your new term
5(6 + y)
When they look like this:
6( 5 + y)=



You distribute (multiply) the factor
(6) with the first number in the term
and place them in a parentheses
( 6 x 5)
You distribute (multiply) the factor
(6) with the second number in the
term and place them in a
parentheses
( 6 x y)
You place both terms together and
include the operation sign found
inside the original term
(6 x 5) + (6 + y)
Let’s try one together
(8 + 6) + ( 8 + h)
• You look at both terms and find the common factor in both terms
8
• You place the number that you factored, outside of the parentheses
8(
)
. you place it in the
• You look at what remains in the first term and
parentheses
8(6
)
• You look at what remains in the second term and you place it in the
parentheses
8(6
h)
• Look at the operation sign between both terms and place that in your new
term
8(6 + h)
Let’s try one together
7( 6 + g)
• You distribute (multiply) the factor (7) with the first number in the term and
place it in parentheses
(7 x 6)
• You distribute (multiply) the factor (7) with the second number in the term
and place them in a parentheses
.
(7 x g)
• You place both terms together and include the operation sign found
inside the original
(7 x 6) + (7 x g)
Let’s do two steps at a time
(8 + 6) + ( 8 + h)
• You look at both terms and find the common factor in both terms
8
• You place the number that you factored, outside of the parentheses
8(
)
. you place it in the
• You look at what remains in the first term and
parentheses
8(6
)
• You look at what remains in the second term and you place it in the
parentheses
8(6
h)
• Look at the operation sign between both terms and place that in your new
term
8(6 + h)
Let’s try two steps at a time
7( 6 + g)
• You distribute (multiply) the factor (7) with the first number in the term and
place it in parentheses
(7 x 6)
• You distribute (multiply) the factor (7) with the second number in the term
and place them in a parentheses
.
(7 x g)
• You place both terms together and include the operation sign found
inside the original
(7 x 6) + (7 x g)
Let’s do them all on our own!
(8 + 6) + ( 8 + h)
• You look at both terms and find the common factor in both terms
8
• You place the number that you factored, outside of the parentheses
8(
)
. you place it in the
• You look at what remains in the first term and
parentheses
8(6
)
• You look at what remains in the second term and you place it in the
parentheses
8(6
h)
• Look at the operation sign between both terms and place that in your new
term
8(6 + h)
Let’s do all the steps together!
7( 6 + g)
• You distribute (multiply) the factor (7) with the first number in the term and
place it in parentheses
(7 x 6)
• You distribute (multiply) the factor (7) with the second number in the term
and place them in a parentheses
.
(7 x g)
• You place both terms together and include the operation sign found
inside the original
(7 x 6) + (7 x g)
Let’s review what we learned:
 What is distributive?
 Why is a term?
 What do you think is the most important reason to
know how use the distributive property in equations
and expressions with variables?
Do one last problem!
(3 + 5) – (3 + s)=