today we use the distributive property in equations and expressions with variables. distributive=to...

distributive=to give out

When you see a number next to another number in parentheses, this means to multiply. For

example: 8(8)= 64What are other ways to arrange

problems that lets you know that you have to multiply?

8(8 x y)

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

5(3 t) =

5(3 + t) = 5 × 3 5 × t

+

8(k 2) =

8(k - 2) = 8 × k 8× 2

-

5(3 + t) = 5 × 3 + 5 × t

5(3 + t) =

5(3 + t) = 5 × 3

5(3 + t) =

5(3 + t) = 5 × 3 + 5 × t

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)

(5 x 6) + (5 x t)=

5(

1. What is the common factor in the above equation?2. You factor it out3. What remains in the 1st term?4. What remains in the 2nd term?5. What operation is being done?

6 t )

+

(8 x r) - (8 x 6)=

8(

1. What is the common factor in the above equation?2. You factor it out3. 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?

r 6)

-

Why else is it important to use the distributive property in equations and

expressions with variables

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

We are going to use the distributive property in equations and expressions with variables

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)

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 term5(6 + y)

.

(8 + 6) + ( 8 + h)• You look at both terms and find the common factor in both terms

• You place the number that you factored, outside of the parentheses

• You look at what remains in the first term and you place it in the parentheses

• You look at what remains in the second term and you place it in the parentheses

• Look at the operation sign between both terms and place that in your new term

8

8( )

8(6 h)

8(6 + h)

8(6 )

.

7( 6 + g)• You distribute (multiply) the factor (7) with the first number in the term and

place it in parentheses

• You distribute (multiply) the factor (7) with the second number in the term and place them in a parentheses

• You place both terms together and include the operation sign found inside the original

(7 x 6)

(7 x g)

(7 x 6) + (7 x g)

.

(8 + 6) + ( 8 + h)• You look at both terms and find the common factor in both terms

• You place the number that you factored, outside of the parentheses

• You look at what remains in the first term and you place it in the parentheses

• You look at what remains in the second term and you place it in the parentheses

• Look at the operation sign between both terms and place that in your new term

8

8( )

8(6 h)

8(6 + h)

8(6 )

.

7( 6 + g)• You distribute (multiply) the factor (7) with the first number in the term and

place it in parentheses

• You distribute (multiply) the factor (7) with the second number in the term and place them in a parentheses

• You place both terms together and include the operation sign found inside the original

(7 x 6)

(7 x g)

(7 x 6) + (7 x g)

.

(8 + 6) + ( 8 + h)• You look at both terms and find the common factor in both terms

• You place the number that you factored, outside of the parentheses

• You look at what remains in the first term and you place it in the parentheses

• You look at what remains in the second term and you place it in the parentheses

• Look at the operation sign between both terms and place that in your new term

8

8( )

8(6 h)

8(6 + h)

8(6 )

.

7( 6 + g)• You distribute (multiply) the factor (7) with the first number in the term and

place it in parentheses

• You distribute (multiply) the factor (7) with the second number in the term and place them in a parentheses

• You place both terms together and include the operation sign found inside the original

(7 x 6)

(7 x g)

(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)=