# Chapter 2: Real Numbers

**At Grade**Created by: CK-12

## Introduction

Given a number like 5, 0.75, or \begin{align*}\sqrt{2}\end{align*}, how would you classify it beyond a real number? In this chapter you’ll learn three subsets of real numbers – rational numbers, irrational number, and integers – that you’ll find every day in your daily life. The number of students in your class – that’s an integer. The interest rate on your car loan – that’s a rational number. The ratio of a circle’s circumference to its diameter – that’s an irrational number. This chapter differentiates these various types of real numbers and explains important properties and rules that apply to them. It then shows you how to perform operations and solve problems involving rational numbers. Finally, it equips you with problem-solving strategies to solve problems involving rational numbers.

- 2.1.
## Properties of Rational Numbers

- 2.2.
## Additive Inverses and Absolute Values

- 2.3.
## Addition of Rational Numbers

- 2.4.
## Rational Numbers in Applications

- 2.5.
## Multiplication of Rational Numbers

- 2.6.
## Division of Rational Numbers

- 2.7.
## Mixed Numbers in Applications

- 2.8.
## Distributive Property

- 2.9.
## Square Roots and Irrational Numbers

- 2.10.
## Properties of Rational Numbers versus Irrational Numbers

- 2.11.
## Guess and Check, Work Backward

### Chapter Summary

## Summary

This chapter explains the difference between integers, rational numbers, and irrational numbers. It then focuses on adding, subtracting, multiplying, and dividing rational numbers. It also covers number opposites, absolute values, and the distributive property. Square roots are discussed as well. Finally, it introduces you to many real-world problems and provides the strategies of guess and check and working backward to solve them.