# Recognizing Patterns in Real Numbers (Properties)​

## Recognizing Patterns in Real Numbers (Properties)​  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

• 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

• 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

• 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

• 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

• 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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