Introduction to Whole Numbers

Introduction to Whole Numbers

Even though counting is first taught at a young age, mastering mathematics, which is the study of numbers, requires constant attention. If it has been a while since you have studied math, it can be helpful to review basic topics. In this tutorial, we will focus on numbers used for counting as well as the four arithmetic operations—addition, subtraction, multiplication, and division. This tutorial is not so necessary for those that already have a solid foundation in mathematics. We will simply discuss some vocabulary that are useful throughout our study of mathematics.

Purchasing fruits at a fruit market requires a basic understanding of numbers. Image credit: Dr. Karl-Heinz Hochhaus, Wikimedia Commons

By the end of this lesson and the next few, you should be able to:

• Identify counting numbers and whole numbers
• Model whole numbers
• Identify the place value of a digit
• Use place value to name whole numbers
• Use place value to write whole numbers
• Round whole numbers

Identify Counting Numbers and Whole Numbers

You may have heard of the mathematical term that terrifies many, algebra. Algebra is the part of mathematics in which letters and other general symbols are used to represent numbers and quantities in formulae and equations.

Learning algebra is similar to learning a language. You start with a basic vocabulary and then add to it as you go along. You need to practice often until the vocabulary becomes easy to you. The more you use the vocabulary, the more familiar it becomes.

Algebra uses numbers and symbols to represent words and ideas. Let’s look at the numbers first. The most basic numbers used in algebra are those we use to count objects: \(1, 2, 3, 4, 5,...\) and so on. These are called the counting numbers. The notation “…” is called an ellipsis, which is another way to show “and so on”, or that the pattern continues endlessly. Counting numbers are also called natural numbers.

Counting numbers and whole numbers can be visualized on a number line as shown in the figure below.

The numbers on the number line increase from left to right, and decrease from right to left. Image credit: OpenStax Prealgebra

The point labeled \(0\) is called the origin. The points are equally spaced to the right of \(0\) and labeled with the counting numbers. When a number is paired with a point, it is called the coordinate of the point.

The discovery of the number zero was a big step in the history of mathematics. Many early number systems originally lacked a zero after they had mastered counting. This was because the concept of zero in counting was not always clearly needed. Including zero with the counting numbers gives a new set of numbers called the whole numbers.

We stopped at \(5\) when listing the first few counting numbers and whole numbers. We could have written more numbers if they were needed to make the patterns clear.