1. Properties of Algebra
By: Will Bienkowski

2. Commutative Property Explanation Examples
The 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.
6+3=3+6 is for addition. 8·6=6·8 is for multiplication

3. Associative Property Explanation Examples
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.
7+(6+2)=15 6+(7+2)=15 8(2·4)=64 2(8·4)=64

4. Identity Property Explanation Example
The identity property works for multiplication and addition. It states that anything added to zero or multiplied by one the result is that number.
9+0=9 6·1=6

5. Distributive Property
Explanation
Examples
The distributive property states that you can make hard and long problems easy and short.
8·104 8·100=800 8·4= =832

6. Equality Property Explanation Example
The 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.
3+b< b<6

7. Inverse Property Explanation Example
It states that addition and subtraction can undo each other and multiplication and division can undo each other.
a-a=0 and a+(-a)=0 a\a=1 and a·(-a)=1