1. Introducing the… Distributive Property
(Real World Connection, Lesson and Practice)
7.EE.A.1

2. Today… 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 “undo” distribution by using common factors.

3. Part 1
Defining and Recognizing
the Distributive Property

4. What is the Teacher Asking?
Jeremy… Will you take the bowl of lollipops and distribute them?
Proceed to next slide to ask the more specific question.

5. What does “Distribute” mean?
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?
Allow students a moment to think about the question and then have a volunteer to answer.
See if someone can define the word distribute.
Proceed to next slide for the definition of the word “distribute”.

6. Definition of: Distribute
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!

7. 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”.

8. Recognizing 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.
Subtraction
Multiplication
Addition
Remind students that when a number is pressed up against parenthesis without a symbol, it is assumed to be multiplication.

9. Think about this question.
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?
Combination of multiplication with
either addition or subtraction.
Multiplication… outside of ( ).
Addition or subtraction… inside of ( ).
Give students a few moments to make their choices… then click mouse for answer.
Go through each problem and explain why or why not.
2(4+6) Yes… multiply on outside, add on inside
5(10-3) Yes… multiply on outside, subtract on inside
7(2 x 8) No… has to be add or subtract inside the parentheses.
(9+4) x Yes… multiply on outside, add on inside
7+(8 x 1) No… the multiply must be on the outside and the add should be on the inside.

10. Part 2
Applying/Distributive Property

11. How it Works Example 1 5(4 + 6) = (5 ∙ 4) + (5 ∙ 6) = 20 + 30 = 50
When applying the Distributive Property…
You want to take the number on the outside of the parentheses and multiply it with every number located inside the parentheses.
Example 1
5(4 + 6)
= (5 ∙ 4) + (5 ∙ 6) = =
Example 2
2(8 – 3)
= (2 ∙ 8) – (2 ∙ 3) = =
As you are reviewing the problems on this slide…
- Draw the traditional arrows from the outside number to the numbers located inside the parentheses (as a visual).
Stress again….Why multiply? Because the number on the outside is pressed up to the parentheses which indicates that we are to multiply.
Just to prevent confusion… Remind students that these two particular problems can also be solved using Order of Operations. However… many of our problems, as you’ll see, involve a variable (unknown number) which forces you to use the Distributive Property.

12. So…. Can anyone tell me now why this is referred to as
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) = =
It is called the distributive property because the number on the outside is to be distributed (or multiplied) with ALL of the numbers on the inside of the parentheses. You distribute the 5 to the 4. Then distribute the 5 to the 6.
Relate it to Jeremy distributing lollipops to ALL the members in the class.

13. You Try!
Apply the distributive property to evaluate the following. Show all steps. 9(5 + 2) = (9 ∙ 5) + (9 ∙ 2) = = 63
Allow students to try this one as practice.
Then click the mouse to review the answer.

14. Dealing with Variables.
The distributive property can be applied even when variables are involved.
Example 6(n + 5) = (6 ∙ n) + (6 ∙ 5) = 6n + 30
REMINDER
A variable is just a letter that stands for an unknown number. n x

15. You Try!
Apply the distributive property to create an equivalent expression. Show all steps. 11(a - 4) = (11 ∙ a) - (11 ∙ 4) = 11a - 44
Equivalent means…
EQUAL
Equivalent expression

16. You Try!
Apply the distributive property to create an equivalent expression. Show all steps. 6(7 + k) = (6 ∙ 7) + (6 ∙ k) = k or… 6k + 42 utilizing the commutative property!
Commutative Property of Addition says that the order in which you are adding the terms does not change the value of the expression.

17. You Try!
Apply the distributive property to create an equivalent expression. Show all steps. (x + 3)∙9 = (9 ∙ 3) + (9 ∙ x) = x or… 9x + 27
Explain that the distributive property can be applied to this problem as well.
It is still multiplication which is located directly outside of the parentheses and add or subtract on the inside. It doesn’t matter that the 9 is behind the ( ).

18. You Try!
Apply the distributive property to create an equivalent expression. Show all steps.
3(x – y + 4)
= (3 ∙ x ) - (3 ∙ y) + (3 ∙ 4)
= 3x y
There can be more than just two terms inside the parentheses.
Again… multiplication on the outside and add or subtract on the inside.

19. You Try! x 3 Use the distributive property to express the area
of the below garden.
4(x + 3)
= (4 ∙ x) + (4 ∙ 3)
= x x 4 3
Length = x + 3
Width = 4
To find the area of a rectangle you want to multiply the length x width.
The length would be x + 3
The width would be 4
For the entire length to be multiplied by 4 then the x+3 must be inside ( ).
Answer: 4(x+3)
AREA of a Rectangle
Length times Width

20. Try this tricky one!
Apply the distributive property to create an equivalent expression. Show all steps. -3(-10 - x) = (-3 ∙ -10) - (-3 ∙ x) = 30 - (-3x) = x

21. Part 3
Undoing the Distributive Property by Factoring

22. “Undoing” the distribution.
What if…
You have an expression that has already been distributed and you wish to put it back in its original form?
Given
36x (9x + 2)
Well, you have to undo the distribution.
Some call this process of “undoing”…
reverse distribution
(Because basically you are going backwards.)

23. How do you reverse distribute?
Given
36x (9x + 2)
You use a common factor to reverse distribute.
A common factor is just a number that divides evenly into both terms.
Notice… 4 goes into both 36 and 8 evenly.

24. Greatest Common Factor (GCF)
Given
36x (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.

25. Use factoring to rewrite the following distributed expression:
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
4( )
4(? + ? )
4(9x + 2 )
Because… 4 times 9x… gives you the 36x
4 times 2….. gives you the 8

26. You Try! Factor the following expression. Use the GCF. 12 + 144x
12(? + ?)
12(1 + 12x)  Answer
Allow students to try this one as practice.
Then click mouse to walk through answer.

27. You Try! Factor the following expression. Use the GCF. 56x - 24
8(? + ?)
8(7x - 3)  Answer
Allow students to try this one as practice.
Then click mouse to walk through answer.

28. You Try! Factor the following expression. Use the GCF. 9x + 18x + 27
9(? + ? + ?)
9(x + 2x + 3)  Answer
Allow students to try this one as practice.
Then click mouse to walk through answer.

29. You Try! Factor the following expression. Use the GCF. 6x – 33x
3x(2 - 11)  Answer
Allow students to try this one as practice.
Then click mouse to walk through answer.

30. You Try! Factor the following expression. 17x + 7
Just leave the answer as 17x + 7 since the GCF = 1.
Allow students to try this one as practice.
Then click mouse to walk through answer.

31. Last One! Factor the following expression. Use the GCF. – 25b - 5
-5(? - ?)
-5(5b + 1)  Answer
Allow students to try this one as practice.
Then click mouse to walk through answer.

32. What have we learned? 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 number located 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 __________?
I like to finish up the lesson by having a student “distribute” dum-dums to “every” person in the class.
This can be done after asking these closure questions.
Give or deliver in shares; to deal out; to scatter or spread over an area.
multiplication and addition or multiplication and subtraction
multiply it
(5 x 10) + (5 x 4) = 70
Any of these answers would be correct: factoring, factors, GCF