Properties of Addition and Multiplication

Commutative Property In the sum you can add the numbers in any order. a+b = b+a In the product you can multiply the numbers in any order ab= ba

Associative Property Changing the grouping of numbers in a sum does not change the sum (a+b)+c = (b+c)+a Changing the grouping of the numbers in a product does not change the product (ab)c= a(bc)

Identity Properties The sum of a number and the additive identity (0) is the number a+0=a The product of a number and the multiplicative inverse (1) is the number a·1 = a

Distributive Property The Distributive Law says that multiplying a number by a group of numbers added together is the same as doing each multiplication separately a(b+c)= ab+ac (b+c)a= ba+ca a(b-c)= ab - bc (b-c)a= ba - ca