Distributive Property

Distributive Property

​

Multiple Choice

Do you feel like you can simplify this expression?

 $5\left(2x+3\right)$  

• Yes, I am confident I can simplify this.

• Sort of--I could do it, but I'm not sure if it would be correct.

• HELP! I am confused!

Open Ended

Simplify  $5\left(2x+3\right)$  to be written without parentheses.

Who put those letters in my math problem?!

Don't panic!

Interpreting Expressions with Parentheses

This can be read as

"four groups of 5 + 3y"

On a sheet of paper, write out

four groups of 5 + 37

It should look like this:

5 + 3y

5 + 3y

5 + 3y

5 + 3y

Let's see if we can write this a little bit simpler.

• 5 + 3y

  5 + 3y

  5 + 3y

  5 + 3y

• 20 + 12y

Multiple Choice

Use the repeated addition strategy to simplify  $5\left(2x-3\right)$  

•  $52x-53$  

•  $10x-15$  

•  $10x-3$  

•  $-5x$  

•  $10x+3$  

Thinking through the answer​

Why is there a subtraction sign in the answer?

If there is math left, shouldn't we solve it?

​

​

10x and 15 don't play nice with each other because one has a variable (x) and the other is a constant (plain number).

8 groups of 3 + 2x

• That's a lot of groups!

• What if you're feeling lazy and don't want to write out 8 groups?

• You have another option!

Invisible Multiplication

• Don't forget about the invisible multiplication between the 8 and the (

Dsitributive Multiplication

Multiple Choice

Which simplified expression is equivalent to  $$8\left(3+2x\right)$$  ?

• $$83+82x$$  

• $$24+2x$$  

• $$24+16x$$  

• $$40x$$  

• $$26x$$  

Poll

Which method do you prefer: repeated addition or distributive multiplication?

• Repeated Addition

• Distributive Multiplication

Practice Questions

• Pick one method that works best for you

• SHOW YOUR WORK in your notebook or on a sheet of paper

• Pay attention between questions when we go over them

• Ask questions if you aren't sure about something!

Multiple Choice

Simplify this expression

10(2a+1)

• 20a+10

• 12a+10

• 10a+101

• 20a+1

• 30a

Multiple Choice

Simplify this expression

6(7k+11)

• 7k+11

• 42k+66

• 13k+17

• 42k+11

• 108k

Multiple Choice

Simplify this expression

3(4 - 3r)

• 12 - 9r

• 7 - 6r

• 12 - 3r

• 34 - 33r

• 3r

Multiple Choice

Simplify this expression

8(x + 5)

• 8x + 13

• 8x + 5

• 8x + 40

• 13x

• 40x

Multiple Choice

Simplify this expression

• 35x+7

• 35x-1

• 35x-7

• 75x-71

• 28x

Multiple Choice

Fill in the blanks:

__(5x + 1) = 10x + 2

• 2

• 5

• 10

• x

Multiple Choice

Fill in the blank:

4(3x + __) = 12x + 16

• 4

• 16

• 4x

• 12

Multiple Choice

Fill in the blank:

2(x + 7) = 2x + __

• 7

• 14

• 7x

• 14x

Multiple Choice

Which of the following expressions is equivalent to 10x - 8?

• 2(5x - 8)

• 10(x - 8)

• 8(2x - 1)

• 2(5x - 4)