Math A

 Properties
of Real Numbers 


Hints for working with the properties of real numbers: 

 Commutative - interchange or switch the elements

Think of the elements as "commuting" from one location to another.  "They get in their cars and drive to their new locations."  This explanation will help you to remember that the elements are "moving" (physically changing places).

  =

 

 Associative - regroup the elements 

The associative property can be thought of as illustrating "friendships"  (associations).  The parentheses show the grouping of two friends.  In the example below, the red girl (y) decides to change from the blue boyfriend (x) to the green boyfriend (z).   "I don't want to associate with you any longer!"  Notice that the elements do not physically move, they simply change the person with whom they are "holding hands." 

 

 Identity - What returns the input unchanged?

Try to remember the "I" in the word identity.  Variables can often times have an "attitude".  "I am the most important thing in the world and I do not want to change!"  The identity element allows the variable to maintain this attitude.


Additive Identity is 0.


Multiplicative Identity is 1.

 

 Inverse - What brings you back to the identity element using that operation?

Think of the inverse as "inventing" an identity element. What would you need to add (multiply) to this element to turn it into an identity element? 


The Additive Inverse is the negation of the element.


The Multiplicative Inverse is one divided by the element.

 

 Distributive - multiply across the parentheses.  Each element inside the parentheses is multiplied by the element outside the parentheses.

Let's consider the problem 3(x + 6).  The number in front of the parentheses is "looking" to distribute (multiply) its value with all of the terms inside the parentheses.   

= 3x + 18

 

 


Roberts