**What Are Integers?**

The numbers that we made in Introduction to Numbers are called **integers** or **whole numbers**. In that section we counted our cats. The numbers we made counted whole cats since we don’t have any partial cats – say a half of a cat – walking around. We also have pies in our house, but someone keeps eating pieces of the pies. We can’t count our pies because we do have half pies in the cupboard. We therefore need some way to count parts of pies and we will explore these ways later in Fractions and

**The Integers (Whole Numbers) and the Number Line**

- counting cats and pies.
- The numbers we have talked about are the numbers {0,1,2,…,10,11,12,…,20,21,22,…} these are called integers or whole numbers. Supposing you had half a pie left from supper. What kind of a number would a mathematician use to represent half a pie? We will find out later, but if our integers represent pies, the number to represent half a pie isn’t among them. Hence the integers represent the numbers of whole pies or whole numbers.
- Take a ruler marked in centimeters, draw a line from one end of the ruler on the leftÂ to the other and mark on it the integers shown up to 10.
- The first thing you may notice is that there is no number at the beginning of the ruler which is the first mark on the ruler. This is actually the number 0.
- The next thing you may notice is that between any two numbers on the ruler there are 9 marks in between. We will talk about their meaning later.
- Depending on the length of the ruler, the line you draw may allow up t0 30 marks that are numbered and evenly spaced. Longer rulers would allow us to mark more numbers on a longer number line. To be able to mark 1,000 on the number line, we would need a ruler possibly longer than the room you are in. Another characteristic of mathematicians I forgot to tell you is that big numbers don’t scare them. In fact some get excited over the size of really, really big numbers that they invent.

**Addition and Subtraction of Integers**

#### Multiplication and Division of Integers

#### Comparison of Integers

#### Key Points

A number has the following properties:

- It has a representation consisting of the ten digits.
- It represents a quantity or value.
- The position of each digit in the number is a place value with a distinct name.