Math
Properties

The __Commutative
Property__ deals with an order change. For
example 3 + 5 = 5 + 3. The 3 and the 5 switched order, yet the two expressions are
equal. Also, 4(6) = 6(4). The commutative property holds for both addition
and multiplication, but not for subtraction or division.

The __Associative Property__ deals with a grouping change. For example 6 +(3+4) = (6+3)+4. Notice that order did not change, but rather how
the numbers were grouped. The associative property holds for both
addition and multiplication.

The __Identity
Property__ states that zero may be added to any number, or one multiplied to any number
and the original number keeps its *identity* … 5+0=5 and 5_{}(1)=5.

The __Inverse Property__ states that every
number has an additive inverse and a multiplicative inverse, which when applied will
result in the identity elements of respectively 0 and 1 … 5+(-5)=0 and 5_{}(1/5)=1. -5 is called the additive inverse and 1/5 is
called the multiplicative inverse (sometimes referred to as the reciprocal.)

The __Distributive Property__ uses the number
in front of the parenthesis (including the sign of the number) to multiply all numbers
(and their signs) within the parenthesis. For
example, 5(3+4) = 5(3)+5(4).