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

  • 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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