math stuff

Introducing the…

Distributive Property

(Real World Connection, Lesson and Practice)

6.EE.3

� We are going to learn about the

“Distributive Property”.

� We’ll learn:

❑ The definition of the Distributive Property and how to

recognize it when you see it.

❑ How to apply the Distributive Property.

❑ How to use the Distributive Property to help you multiply

larger numbers.

❑ How to “undo” distribution by using common factors.

Today…

Part 1

Defining and Recognizing
the Distributive Property

Jeremy… Will you take the bowl of

lollipops and distribute them?

What is the Teacher Asking?

� Do you think that Jeremy’s teacher wants him to

hand a lollipop to one student… or … to pass them
out to every student in the classroom?

What does “Distribute”
mean?

Distribute means...

❑

To give or deliver something in shares.

❑

To deal out.

❑ To scatter or spread over an area.

So...

Jeremy’s teacher wants him to give every student in the

classroom a lollipop.

If he gave just one student a lollipop,
then he would not be “distributing” them as
he should.

You would see some pretty upset kids if

they were not given a lollipop!

Definition of: Distribute

Since we now have an understanding of
the word “distribute”…

Let’s look at the Distributive Property.

See if you can figure out
why it is called the
“Distributive Property”.

The Distributive Property involves the operations of…

multiplication and addition or multiplication and subtraction.

Example 1

Example 2

5(4 + 6)

2(8 – 3)

The multiplication must be located directly outside the parentheses.

The addition or subtraction must be on the inside of the parentheses.

Recognizing the Distributive
Property

Subtraction

Multiplicatio
n

Multiplicatio
n

Addition

Which of the following can the distributive property
be applied? Check all that apply.

❑ 2(4 + 6)

❑ 5(10 – 3)

❑ 7(2 ∙ 8)

❑ (9 + 4)∙2

❑ 7 + (8 ∙ 1)

How do you
recognize the
distributive
property?

1)Combination of multiplication with
either addition or subtraction.

2)Multiplication… outside of ( ).

3)Addition or subtraction… inside of ( ).

Think about this question.

Part 2

Applying/Distributive Property

How it Works

� Example 1

5(4 + 6)

= (5 ∙ 4) + (5 ∙ 6)

= 20 + 30

= 50

� Example 2

2(8 – 3)

= (2 ∙ 8) – (2 ∙ 3)

= 16 - 6

=10

When applying the Distributive Property…

You want to take the number on the outside of the parentheses

and

multiply it with every numberlocated inside the parentheses.

So…

Can anyone tell me now why this is referred to as

the… Distributive Property?

Think of Jeremy and to
whom he was to distribute
the lollipops!
Everyone, right?

5(4 + 6)

= (5∙4) + (5∙ 6)
= 20 + 30

=50

Apply the distributive property to evaluate the
following. Show all steps.

9(5 + 2)

=

(9∙ 5) + (9∙ 2)

=

45 + 18

= 63

You Try!

Example

6(n + 5)

=

(6 ∙ n) + (6 ∙ 5)

=

6n + 30

Dealing with Variables.

The distributive propertycan be applied even when variables are involved.

REMINDER

A variable is just
a letter that
stands for an
unknown
number.

n

x

Apply the distributive propertyto create an
equivalent expression. Show all steps.

11(a - 4)

=

(11 ∙ a) - (11 ∙ 4)

=

11a - 44

You Try!

Equivalent
means…

EQUAL

Equivalent
expression

Apply the distributive propertyto create an
equivalent expression. Show all steps.

6(7 + k)

=

(6 ∙ 7) + (6 ∙ k)

=

42 + 6k

or…

6k + 42 utilizing the commutative property!

You Try!

Apply the distributive propertyto create an equivalent
expression. Show all steps.

(x + 3)∙9

= (9 ∙ 3) + (9 ∙ x)

= 27 + 9x

or… 9x + 27

You Try!

Apply the distributive propertyto create an equivalent
expression. Show all steps.

3(x – y + 4)

=

(3 ∙ x ) - (3 ∙ y) + (3 ∙ 4)

=

3x - 3y + 12

You Try!

Use the distributive property to express the area
of the below garden.

4(x + 3)

= (4 ∙ x) + (4 ∙ 3)

= 4x + 12

You Try!

x

4

3

AREA of a
Rectangle

Length times
Width

Length = x + 3
Width = 4

Part 3

Using the Distributive

Property to Multiply

The distributive property can be useful when
multiplying larger numbers in your head.

6 ∙ 15 =

Multiplication made Easier!

Well…………

15 can be written as 10 + 5.

And…………

6(10 + 5) is the same as 6 ∙ 15

Now Distribute!

(6 ∙ 10) + (6 ∙ 5)

60 + 30 = 90

These are much easier
numbers to work with in
your head!

You Try!

Fill in the missing number to make the
statement true.

4 ∙ 24 = (4 ∙ _ ) + ( 4 ∙ 4 )

20

You Try!

Fill in the missing number to make the
statement true.

16 ∙ 5 = (10 ∙ 5) + ( _ ∙ 5) 6

You Try!

Fill in the missing number to make the
statement true.

9 ∙ 6 = (9 ∙ 10) - (9 ∙ _ )

4

You Try!

Fill in the missing numbers to make the
statement true.

8 ∙ 7 = ( _ ∙ 5) + ( _ ∙ 2)

8

8

You Try!

Fill in the missing sign to make the statement
true.

3 ∙ 7 = ( 3 ∙ 10) _ (3 ∙ 3)

-

Part 4

Undoing the Distributive Property

by Factoring

� What if…

You have an expression that has already been distributed and
you wish to put it back in its original form?

Given

36x + 8

4(9x + 2)

� Well, you have to undo the distribution.

� Some call this process of “undoing”…

reverse distribution

“Undoing” the distribution.

(Because basically you are going backwards.)

Given

36x + 8

4(9x + 2)

� You use a common factorto reverse distribute.

� A common factoris just a number that divides

evenly into both terms.

Notice… 4 goes into both 36 and 8 evenly.

How do you reverse distribute?

Given

36x + 8

4(9x + 2)

� Even though you can use any common factor to reverse

distribute…

This lesson will focus on using the
Greatest Common Factor.

� The Greatest Common Factor(GCF) is the largest number

that divides evenly into both terms.

Greatest Common Factor (GCF)

Use factoring to rewrite the following distributed expression:

36x + 8

Step 1

Find the GCF
of the terms.

Step 2

Pull out the GCF and
write it on the
outside of the ( ).

Step 3

Think…
What number times the
GCF will give me the
original distributed
terms?

4

Because… 4 times 9x… gives you the 36x

4 times 2….. gives you the 8

4( ? + ? )

4( + )

4(9x + 2)

Use factoring to rewrite the following distributed expression:

25x - 5y

Step 1

Find the GCF
of the terms.

Step 2

Pull out the GCF and
write it on the
outside of the ( ).

Step 3

Think…
What number times the
GCF will give me the
original distributed
terms?

Factor the following expression. Use the GCF.

12 + 144x

GCF = 12

12(? + ?)

12(1 + 12x) 🡨Answer

You Try!

Factor the following expression. Use the GCF.

56x - 24

GCF = 8

8(? + ?)

8(7x - 3) 🡨Answer

You Try!

Factor the following expression. Use the GCF.

6x – 33x

GCF = 3x

3x(? - ?)

3x(2 - 11) 🡨Answer

You Try!

Factor the following expression.

17x + 7

Just leave the answer as 17x + 7 since the GCF = 1.

You Try!

1)

What does “distribute” mean?

2)

The distributive property always involves a combination of which operations?

3)

When applying the distributive property… you want to take the number on the
outside of the parentheses and ___________ with every numberlocated inside
the parentheses.

4)

How can you use the distributive property to make multiplying larger numbers
easier? Example: 5 x 14

5)

To “undo” something that has been distributed you use __________?

What have we learned?

Sales Tax

And
Tip

Sales Tax is determined

by finding a certain

percentage of a purchase
price. It is added to your
total bill when you make

a purchase.

A TIP is money given to

someone to show

appreciation for a

service.

Calculating Sales Tax and Tip – Method

One

Multiply the price and the
decimal.

$15.50 x 5% = .775 round to
.78

Figure out your total bill, if you buy a
CD for $15.50 with a sales tax of 5%.

Add the tax or tip to the price.

$15.50 + .78 = $16.28

Lindsey went to Best Buy and bought an MP3 Player. If
the MP3 Player costs $78.99 and the sales tax was 6.5%,

what was her total bill?

First: $78.99 x 6.5% = $5.13

Then: $78.99 + $5.13 = $84.12

Shayna and Samantha went to Patrick Henry Mall.

Shayna bought some earrings for $9.95. If the tax was

5.5%, what was her total bill?

First: $9.95 x 5.5% = .55

Then: $9.95 + .55 = $10.50

Lee went to Smart Clips to get a haircut before his job
interview. The haircut costs $51.49 and he left a tip that
was 6% of the cost. What was his total bill for the haircut
with tip?

First: $51.49 x 5.5% = $2.83

Then: $51.49 + $2.83 = $54.32

Karlie is at lunch with her friends at Salsa. They had a
delicious meal that cost $21.23. If they tip their waitress

18%, what was their total bill?

First: $21.23 x 18% = $3.82

Then: $21.23 + $3.82 = $25.05

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