# Properties Properties of Addition and Multiplication

Term Definition
The order of the addends doesn't change the sum. Commutative Property of Addition
The order of the factors doesn't change the product. Commutative Property of Multiplication
Any number plus 0 equals itself. Identity Property of Addition
Any number times 1 equals itself. Identity Property of Multiplication
The grouping of addends doesn't change the sum. Associative Property of Addition
The grouping of the factors doesn't change the product. Associative Property of Multiplication
The sum of two numbers times a third number is equal to the sum of each addend times the third number. Distributive Property
Any number multiplied by 0 equals 0. Multiplicative Property of Zero or Zero Property of Multicplication
A number plus its opposite equals 0. Inverse Property of Addition
A number multiplied by its reciprocal equals 1. Inverse Property of Multiplication
a + b = b + a Commutative Property of Addition
a x b = b x a Commutative Property of Multiplication
a + 0 = a Identity Property of Addition
a x 1 = a Identity Property of Multiplication
(a + b) + c = a + (b + c) Associative Property of Addition
(a x b) x c = a x (b x c) Associative Property of Multiplication
a(b + c) = (a x b) + (a x c) Distributive Property
a x 0 = 0 Multiplicative Property of Zero or Zero Property of Multiplication
a + -a = 0 Inverse Property of Addition
a x 1/a = 1 Inverse Property of Multiplication