Basic Rules of Algebra

There are basic properties in math that apply to all real numbers. When working
with variables in algebra,
these properties still apply. We will apply most of the following properties to
solve various Algebraic problems.

Algebraic Properties

Let a, b, and c be real numbers, variables, or algebraic expressions.

Commutative Property of Addition

We can add numbers in any order.

Commmutative Property of Multiplication

We can also multiply numbers in any order.

Associative Property of Addition

We can group numbers in a sum any way we want and get the same answer.

Associative Property of Multiplication

We can group numbers in a product any way we want and get the same answer.

Distributive Property

When we are adding and multiplying with a parenthesis, we can distribute the multiplication
through the addition.

For an in depth discussion, see Distributive Property

Additive Identity Property

If we add 0 to any number, we will end up with the same number.

Multiplicative Identity Property

If we multiply 1 to any number, we will end up with the same number.

Additive Inverse Property

If we adda number by the opposite of itself, we will end up with 0.

Multiplicative Inverse Property

If we multiply a number by its reciprocal, we will end up with 1.

Keep in mind that subtraction is also considered addition, but with a negative number.
Similarly, divison can be thought of as inverse multiplication, but with a restriction
that the denominator cannot be equal to 0.