Combining like terms and Properties

Properties Definitions

100

This property says the order of the numbers does not matter and can be switched in a multiplication or addition problem.

Commutative Property

200

This property says the value inside the parenthesis may change. 

Associative Property

300

Any number multiplied by 1 or adding by zero 

Identity Property

400

Numbers multiplied into the parenthesis

Distributive Property

500

Number multiplied by zero 

Multiple of Zero 

Property Examples

100

Name the Property 

3 + (5 +2) = 2 + (3 +5)

Associative Property

200

3(4x + 7) = 12x +28

Distributive Property 

300

7 x 3 x 5 = 3 x 7 x 5

Commutative Property 

400

6 x 1 = 6

Identity Property 

500

320 x 0 = 0

Multiple of Zero 

Combine Like Terms

100

13x + 42 - 9x + 21

4x + 63

200

-27x + 21 - 34x - 32

-61x - 11

300

21y + 45x - 20 + 5y - 20x

26y + 25x -20

400

12x + 15y - 31 + 30y + 31

12x + 45y

500

61x + 31y - 48 + 53 - 12y + 32x

93x + 19y + 5 

Distributive Property

100

4(2x + 9)

8x + 36

200

5(7 + 8y) 

35 + 40y

300

8(3x + 9)

24x + 72

400

-3(7 - 12x)

-21 + 36x

500

-15(4y + 2x -10)

-60y -30x + 150

Distributive and Combining

100

12x + 15y -4(2x + 8y)

4x -17y

200

12 + 4x -9(2x - 7y) + 81

-14x -63y + 93

300

5y + 21x - 6(4x + 9y - 5)

49y - 3x + 30

400

30x + 52 - 3(7x + 10)

7x + 22

500

72y + 24x - 8(5x - 4y) 

-16x + 104y