1. Properties of Equality

2. A thing equals itself. A=A
Reflexive
A thing equals itself.
A=A

3. Equality is symmetric. If X = Y, then Y = X.

4. Transitive
The syllogism property. If X = Y AND Y = Z, then we can remove the middle man and X = Z.

5. Addition
The addition property states that you can add whatever to an equation without changing the equality as long as you add the same thing to both sides.

6. Multiplication
The multiplication property states that you can multiply an equation by whatever, as long as you multiply the same thing on both sides.

7. Substitution
If two things are equal, then they can be substituted for one another without harm.

8. Properties of Addition and Multiplication

9. CommutativE
Both addition and multiplication are commutative, in that order does not matter. A+B=B+A and AB=BA.

10. AssociativE
Both addition and multiplication are associative, in that grouping does not matter. A+(B+C)=(A+B)+C and A(BC)=(AB)C.

11. DistributivE
Multiplication can be distributed over addition in the following manner: A(B+C)=AB+AC.

12. Additive Identity
The identity value for addition is zero, in that adding it to any quantity does not change that quantity.

13. Additive Inverse
The additive inverse of any number A is the number that, when added to A, will result in the additive identity.

14. Multiplicative Identity
The identity value for multiplication is one, in that multiplying it by any quantity will not change that quantity.

15. Multiplicative Inverse
The multiplicative inverse of any number A is the number that, when multiplied by A, will result in the multiplicative identity.