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Study Guides > Intermediate Algebra

Introduction: Classify and Define Properties of Real Numbers

The real numbers can be divided into three subsets: negative real numbers, zero, and positive real numbers. Each subset includes fractions, decimals, and irrational numbers according to their algebraic sign (+ or –). In this section we will further define real numbers and use their properties to solve linear equations and inequalities. The classes of numbers we will explore include:

Natural numbers

The most familiar numbers are the natural numbers (sometimes called whole numbers or counting numbers): 1,2,31, 2, 3, and so on. The mathematical symbol for the set of all natural numbers is written as N\mathbb{N}, and sometimes  N0\mathbb{N_0}  or  N1\mathbb{N_1} when it is necessary to indicate whether the set should start with 00 or 11, respectively.

Integers

When the set of negative numbers is combined with the set of natural numbers (including 0), the result is defined as the set of integers, Z\mathbb{Z}

Rational numbers

A rational number is a number that can be expressed as a fraction with an integer numerator and a positive integer denominator.

Real numbers

The real numbers include all the measuring numbers. The symbol for the real numbers is  R\mathbb{R}. Real numbers are usually represented by using decimal numerals.
  The specific things you’ll learn in this section include:
  • Classify a real number as a natural, whole, integer, rational, or irrational number
  • Define and use the commutative property of addition and multiplication
  • Define and use the associative property of addition and multiplication
  • Define and use the distributive property
  • Define and use the identity property of addition and multiplication
  • Define and use the inverse property of addition and multiplication
  • Define and identify constants in an algebraic expression
  • Evaluate algebraic expressions for different values

The learning activities for this outcome include

  • Read: Classify real numbers
  • Self-Check: Classify real numbers
  • Read: Use properties of real numbers
  • Self-Check: Use properties of real numbers
  • Read: Evaluate algebraic expressions
  • Self-Check: Evaluate algebraic expressions
 

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