# 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 just identifying it as a real number? In this chapter you’ll learn three subsets of real numbers – rational numbers, irrational numbers, and integers – that you’ll find in 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. You will learn how to perform operations on, and solve problems involving, rational numbers. The Concepts in this chapter will equip 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. There are Concepts exploring number opposites, absolute values, the distributive property, and square roots. There are many real-world problems to encourage practice of *guess and check* and *working backward* strategies to solve them.

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