MAT 105: College Algebra: 1.1 Real Numbers: Algebra Essentials

1.1 Real Numbers: Algebra Essentials

Learning Objectives

In this section, you will:

• Classify a real number as a natural, whole, integer, rational, or irrational number.
• Perform calculations using order of operations.
• Use the following properties of real numbers: commutative, associative, distributive, inverse, and identity.
• Evaluate algebraic expressions.
• Simplify algebraic expressions.

Vocabulary

Natural Numbers - the numbers that are used for counting and are a part of real numbers. The set of natural numbers includes only the positive integers, i.e., 1, 2, 3, 4, 5, 6, ……….∞.

Whole Numbers - a collection of all the basic counting numbers and 0. 

Integers - the collection of whole numbers and negative numbers that do not have fractional parts. 

Rational Numbers - a number that can be made as a fraction of two integers (an integer itself has no fractional part)

Examples:
• 1/2 is a rational number
• 0.75 is a rational number (3/4)
• 1 is a rational number (1/1)
• 2 is a rational number (2/1)
• 2.12 is a rational number (212/100)
• −6.6 is a rational number (−66/10)

Irrational Numbers - real numbers that cannot be written as a simple fraction

1.5 is rational, but π is irrational