Properties of Equality

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

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

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

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.

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

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

Properties of Addition and Multiplication

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

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

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

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

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

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

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