Properties of Algebra

By: Will Bienkowski

Commutative Property

ExplanationThe commutative property

works for multiplication and addition. It states that switching the order of the numbers and variables will not change the sum or product.

Examples6+3=3+6 is for addition.

8·6=6·8 is for multiplication

Associative Property

Explanation

The associative property works for multiplication and addition. It states that that if you switch the grouping of numbers or variables the sum or product will stay the same.

Examples7+(6+2)=156+(7+2)=15

8(2·4)=642(8·4)=64

Identity Property

Explanation Example9+0=9

6·1=6

The identity property works for multiplication and addition. It states that anything added to zero or multiplied by one the result is that number.

Distributive Property

Explanation The distributive property

states that you can make hard and long problems easy and short.

Examples8·1048·100=8008·4=32800+32=832

Equality Property

ExplanationThe equality property states

that if you add or take away numbers from one side of the =,< or > you have to add or take the same number away from the other side.

Example3+b<9-3 -3b<6

Inverse Property

Explanation It states that addition and

subtraction can undo each other and multiplication and division can undo each other.

Examplea-a=0 and a+(-a)=0

a\a=1 and a·(-a)=1