Distributive Property Notes

Before we start, let's review some vocabulary!

Remember... If you take notes along the way you can use them on your quiz and test!

Multiple Select

An expression is a mathematical phrase that contains...

(there are 3 correct answers)

• numbers

• variables

• operations

• pizza

Multiple Choice

A variable is symbol acting as a place holder for a number we don't know yet.

• True

• False

Multiple Choice

Like terms have to have the same ________ and exponent.

• variable

• positive

• negative

• coefficient

Read over the problem

Multiple Choice

How does Taylor's approach differ from Tash's?

• They are solving the problem the same way.

• Taylor set up multiplication first, Tash added first.

• Taylor added inside the () first, Tash set up multiplication first.

Drag and Drop

Complete Taylor's Work

5(11) =​

Placeholder

Drag these tiles and drop them in the correct blank above

55

5/11

5.11

16

6

Drag and Drop

Complete Tash's Work

5(9 + 2)

5(9) + 5(2)

​

Placeholder

​ +

Placeholder

​

Placeholder

Drag these tiles and drop them in the correct blank above

45

10

55

14

7

21

22

​Using Tash's approach we get
7(x) + 7(2) We can multiply 7 and x because the 7 is telling us how many x's we have.
7x + 14 We can not combine x's and 14 so stop here

​The distributive property allows the NUMBER outside the parentheses to be DISTRIBUTED to the terms inside the parentheses.

What does distributed mean?

It means to give out or pass out, think "we distributed the notes to everyone" or "I distributed my birthday invitations"

We distribute to ALL terms in the ( )

Dropdown

4(d + 2p + c)

​ ​

Select answer

(d) + 4(​

Select answer

) + 4(c)

​

Select answer

+ ​

Select answer

+ ​

Select answer

​Area models can be helpful when distributing.

When making the model you need one row, that is where the number outside the ( ) will go.
The numbers inside the ( ) will tell you how many columns you need. In this case we had 3x and 2, that is 2 terms so we need 2 columns.

​Now using the model find the area of each section. (Area = length X width)

Left Box has the terms 5 and 3x, lets set it up:

5(3x) now multiply the constant 5 and the coefficient 3

15x you have the first term for our expression! Write it in the left box.

​Now using the model find the area of each section. (Area = length X width)

Right Box has the terms 5 and 2, lets set it up:

5(2) now multiply the constant 5 and the constant 2

10 you have the second term for our expression! Write it in the right box.

​15x

And that is it, you are done!

The answer for #2 is

15x+10

**The + came from the 10 being positive

​15x

​10

​We will again multiply the outside number by both terms in the expression, this way we get 2 terms in our answer.
7(x) + 7(-9)
7x + (-63) or 7x - 63

4. The cost (in dollars) of a custom-made sweatshirt is represented by 3n+30, where n is the number of different colors in the design. Write and interpret a simplified expression that represents the cost of 15 sweatshirts.

We need to find the cost of 15 sweaters.

Since n = 15 we can use the expression they gave us. We will replace the variable with 15 then do the math.

3n + 30
3(15) + 30
45 + 30
75

Labelling

Use the distributive property to simplify the expression.

Drag labels to their correct position on the image

5

6x

45

30x

9

Labelling

Use the distributive property to simplify the expression.

Drag labels to their correct position on the image

4

+

-

12k

-2

2

8

3k

Labelling

Use the distributive property to simplify the expression.

Drag labels to their correct position on the image

3

7.5t

6t

1.5

2

3.5

9t

Labelling

Use the distributive property to simplify the expression.

Drag labels to their correct position on the image

-

6j

+

4

1/2

3j

3

-6j

8

Labelling

Use the distributive property to simplify the expression.

Drag labels to their correct position on the image

16q

-2q

8

8p

-16q

7

p

-56

-7

2q

Labelling

Use the distributive property to simplify the expression.

Drag labels to their correct position on the image

-2

10

-12

24c

4c

Labelling

Use the distributive property to simplify the expression.

Drag labels to their correct position on the image

23b

42

18b

5b

3b

7

Labelling

Use the distributive property to simplify the expression.

Drag labels to their correct position on the image

2

7

8x

3x

6x

2x

11x

15x

4x

15

Error Alert!

Some addition and subtraction problems look very similar to distributive property problems.

Make sure to read the problems carefully!!

Match

Match each expression with the correct explanation.

Your notes will be helpful for this :)

• This expression requires the distributive property. -3 is multiplied with the expression inside the parenthesis, there is addition inside the parenthesis.

• This expression requires the distributive property. -2 is multiplied with the expression inside the parenthesis, there is subtraction inside the parenthesis.

• This expression has no number touching the outside of the parenthesis. 

  It does not need the distributive property.

• This expression does not have addition or subtraction inside the parenthesis. 

  It does not need the distributive property.

-3(x + 7)

(5 – x)(-2)

(5 – x) – 8

2(n • 4)

• -3(x + 7)

• (5 – x)(-2)

• (5 – x) – 8

• 2(n • 4)

Categorize

Options (8)

4(2 • n)

-a(3 + b)

(-a)(3) + (b)

(3 – g)(-5)

(3 + b) - a

(-4)(6) + n

(8 + h) - 2

(3 + b)(-a)

Sort the expressions into which ones need the distributive property and which ones do not.

On your notes you will circle the ones that do, and cross out the ones that don't.

Needs the Distributive Property

Doesn't Need the Distributive Property