Integers and Rationals

Introduction and Summary

Table of Contents


This chapter will explore many different types of numbers and how they are classified. There will be a special focus on negative numbers and how to use them in calculations.

The first section will explain how to arrange numbers on a number line. It will also introduce the concept of negative numbers, which have corresponding opposites in the set of positive numbers. In addition, it will show the reader how to place fractions and decimals on the number line.

The second section will explain how mathematicians classify numbers--natural numbers, whole numbers, integers, rational numbers, irrational numbers, and real numbers. These classifications are important to pre- algebra, to algebra, and even to much higher mathematics like set theory and number theory.

The third section will further explore negative numbers, first looking at how to subtract a larger number from a smaller number. Next, we will learn how to use operations-- addition, subtraction, multiplication, and division--with negative numbers.

The final section will discuss absolute value--the positive distance between a number and zero on the number line. This section will show how to perform computations when absolute values are involved.

This chapter is important for two reasons. First of all, it is crucial to understand negative numbers and how to perform computations with them. Second, it is important to understand the terminology that mathematicians use when talking about numbers. Knowing the terminology may not affect a numerical answer to a problem, but it will influence how well you understand some of the concepts underlying the numerical answers.