Commutative, Associative, and Identity Properties of Addition and Multiplication

Associative Property

Changing the grouping of addends does not change the sum. (2 + 7) + 9=18

Associative Property

Changing the grouping of factors does not change the product. (5 × 2) × 3 = 30

Commutative Property

Changing the order of addends does not change the sum. 2 + 9 = 9 + 2

Commutative Property

Changing the order of factors does not change the product. 7 × 5 = 5 x 7

Inverse or Reciprocal Property

Division is the same as multiplying by a number's reciprocal

Inverse or Reciprocal Property

The product of any number and its reciprocal is 1

Identity Property

When a number is multiplied by 1, the value does not change. 40 x 1 = 40

Multiplication Property of -1

When any number is multiplied by -1, the product equals the opposite of the number. Ex. 25 × (-1) = -25

Property of Zero for Multiplication

When any number is multiplied by zero, the product equals zero. Ex. 25 × 0 = 0

Identity Property

When zero is added to any number, the value does not change. 12 + 0 = 12