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