Math in short is a representatin of a pattern! in a continuation of our review section we are going to be discussing being able to recognize some of those patterns also known as Properties.There are 5 basic Properties that we are going to discuss, Associative, Commutative, Distributive, Identity , Inverse. Please see below for a breakdown.

Associative

Addition

Multiplication

Associative

This property simply means that rearranging the grouping in which the numbers or letters are placed has no affect on the sun, if additive, or the product, if multiplication.

Associative

Addition: b + ( x + n ) = n + ( x + b )

Multiplication: -n * ( b * x ) = ( b * – n ) * x

Commutative

Addition

Multiplication

Commutative

This property simply means that rearranging the order in which the numbers or letters are placed has no affect on the sun, if additive, or the product, if multiplication.

Commutative

Addition: x + n = n + x

Multiplication: nx = x*n

Distributive

Distributive

In this property it simply means that a real number will be distributed over the addition in the equation. This is also true for subtraction.

Distributive

Addition: x * ( b + n ) = x * b + x * n

Subtraction: x * ( b – n ) = x * b – x * n

Identity

Addition

Multiplication

Identity

In this property the deletion of zero makes no difference in the sum. this is the Additive Identity.

In this property the deletion of one makes no difference in the product. This is the Multiplication Identity.

Identity

Addition: 0 + b = b

Multiplication: bx * 1 = bx

Inverse

Addition

Multiplication

Inverse

In the Addition Inverse Property the sum of a real number and its inverse will equal zero.

In the Multiplication Inverse Property the product of a real number large than zero and it’s inverse will produce 1.

Inverse

Addition: x + -x = 0

Multiplication: x * (1/x) = 1

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