NUMBERS

Basic math is basically numbers and operations on those numbers. We will therefore start this course by introduce ourselves to some group of numbers we will be using. Please note you do not need to memorize anything. Mastering "Introduction to Numbers" is your first step to mastering Pre-Algebra

To understand numbers, we have to know that there is nothing like the smallest number in the world or the largest number.

To illustrate this, we use the number line. The number line has two arrow edges that represent a continuation of the numbers and numbers arranged in order. As you move to your right the numbers get larger. As you move to your left the numbers get smaller

 

Natural Numbers

These are really the first set of numbers we get to know. These are the numbers we can actually count.

Natural Numbers are 1, 2, 3, 5, 6 ....

Let’s place them on the number line. Now we have a number line with Natural numbers

 

Whole Numbers

When we introduce the idea of not having anything. Example we can say, I have 1 orange, I have 3 oranges. If we want to say I have no oranges, we can rather say I have zero oranges.

This concept of zero and the natural numbers are what is known as whole numbers.

Whole Numbers are 0, 1, 2, 3, 4, 5, ...

 

Integers

We know that the smallest whole number is zero. But we said that there is really nothing like the smallest number, so there has to something smaller than zero. This is where negatives numbers are introduced.

It follows the same order as the counting numbers, but we are moving to the left.

So we have -1, -2, -3 and so on. With the same idea of the counting numbers we can continue these numbers indefinitely.

So when we have the negative numbers and the whole numbers, we have what is known as integers.

Integers are ..., -2, -1, 0, 1, 2, 3, ...

 

Rational Numbers

Now with the same idea of having one circle. We know we can divide the circle into smaller parts. So we can now have half of the circle or a quarter or just a small piece. These kind of numbers can still be represented on the number line.

We can divide any of these into smaller parts. So everything we have now is what is called rational numbers.

You will find rational numbers being defined as integer over an integer. We will visit that idea when we start working with rational numbers.

Examples of Rational numbers -1.5, 6, 0, -3

Please note that for rational numbers we cannot have a fixed list of numbers. Any number can be further reduced by dividing it by another number.

 

Fractions and Decimals

There are two ways of representing the numbers in between two integers. What we have been doing so far is representing them as fractions. So we used 1/2 and 1/4. We could have represented the 1/2 as 0.5 and the 1 ½ as 1.5 on the number line and so on. This is representing numbers in the decimal form. We will learn more in chapter 6