Properties of Operations For Addition and Multiplication

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

Commutative Property of Multiplication (think commute- to move)  

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

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

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

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.

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

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

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

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