# Chapter 1: Welcome to the Real World

**Advanced**Created by: CK-12

**Introduction**

The real number system is made up of rational and irrational numbers. The rational numbers include the natural numbers, whole numbers, integers and rational numbers. The natural numbers are the counting numbers and consist of all positive, whole numbers. The natural numbers are numbers in the list 1, 2, 3... and are often referred to as positive integers. The whole numbers are the natural numbers and zero. They are the numbers in the list 0, 1, 2, 3... Integers are the numbers in the list..., -3, -2, -1, 0, 1, 2, 3... . These numbers are the natural numbers, their opposites and zero. The rational numbers are numbers that can be written as the ratio of two numbers \begin{align*}\frac{a}{b}\end{align*} and \begin{align*}b \neq 0\end{align*}. The rational numbers include all terminating decimals as well as those decimals that are non-terminating but have a repeating pattern of digits. Included in the rational numbers are the natural numbers, whole numbers and the integers. The irrational numbers are those that cannot be expressed as the ratio of two numbers. The irrational numbers include decimal numbers that are non-terminating decimals as well as those with digits that do not repeat with a pattern. The rational numbers along with the irrational numbers make up the real number system.

The chapter will continue with lessons on how to perform the basic operations of addition, subtraction, multiplication and division with real numbers. All of these operations will then be applied to order of operations.

Students will also learn how to express a fraction as a decimal and a decimal number as a fraction. The final section of the chapter will deal with representing real numbers on a number line.

**Lessons**

In this chapter you will do the following lessons:

- Addition of Real Numbers
- Subtraction of Real Numbers
- Multiplication of Real Numbers
- Division of Real Numbers
- Properties of Addition
- Properties of Multiplication
- Order of operations with Real Numbers
- Decimal Notation
- Graphing real Numbers on a Number Line

- 1.1.
## Addition of Real Numbers

- 1.2.
## Subtraction of Real Numbers

- 1.3.
## Multiplication of Real Numbers

- 1.4.
## Division of Real Numbers

- 1.5.
## Quiz

- 1.6.
## Properties of Addition

- 1.7.
## Properties of Multiplication

- 1.8.
## Quiz

- 1.9.
## Decimal Notation

- 1.10.
## The Real Number Line

- 1.11.
## Chapter Test