1. Properties of Operations For Addition and Multiplication

2. Commutative Property of Addition
The order numbers are added does not affect the sum.
+ = + y x

3. Commutative Property of Multiplication (think commute- to move)

4. Associative Property of Addition
The way you group (associate) numbers does not affect the sum.
+ ( ) = ( ) + 1

5. Associative Property of Multiplication Think: Who you associate with that day does not change your group of friends
The way you group (associate) factors does not change the product.
· ( · 1) = ( · ) · 1

6. Identity Property of Addition aka Additive Identity
The sum of any number and zero is that number.
Example: =
0 is the identifier for this property.

7. Identity Property of Multiplication aka Multiplicative Identity
The product of any number and 1 is that number.
Example: • 1 =
1 is the identifier for this property.

8. Multiplicative Property of Zero
The product of any number and 0 is 0.
Example: • 0 = 0

9. Inverse Operations Operations that cancel each other. Example: – = 0
List other inverse operations.

10. Reciprocal or Multiplicative Inverse Operations
When multiplied together multiplicative inverses (reciprocals) equal 1.
Example: 5 & 1/5 are reciprocals.
1 ½ & 2/3 are reciprocals.
** 1 is its own reciprocal, so is –1.
** 0 has no reciprocal

11. The Distributive Property
The distributive property lets you multiply a sum by multiplying each addend separately and then add the products.
EX: 3(x + 4) = 3(x) + 3(4)
OR 3x + 12