Chapter 2.0: Real Numbers and Their Properties

In algebra several different sets of numbers are used. Natural numbers are sometimes called counting numbers. The set of whole numbers includes zero.

 Natural Numbers = {1, 2, 3 ...} Whole Numbers = {0, 1, 2, 3 ...}

The set of rational numbers includes numbers which can be expressed as a ratio.
 a - where b is not equal to 0. b

 The set of rational numbers includes whole numbers and counting numbers.

Grouping Symbols and the Order of Operations
Symbols are used in algebra to show the order in which operations are to be performed.
 Any operation inside the parenteses should be done first. The fraction bar is a grouping symbol. Computations above and below the bar should be done before dividing.

 Practice using grouping symbols with these exercises

 Here are the solutions to the mental math problems:

The Commutative Properties
 The expressions x+3 and 3+x have the same value for all values of x. Other similar expressions have the same values.

The commutative property is a special rule that is frequently used in algebra. It states that for addition and mupltiplication these relationships will always be true:
 Commutative Properties For Addition: for any numbers a and b, it is true that a+b=b+a. For Multiplication: for any numbers a and b, it is true that ab=ba.

 In other words, when adding, we can change the order of the numbers without affect the sum.

 Similarly, for multiplication, the order in which two numbers are multiplied does not affect the product.