#### What Are Negative Numbers?

Today I was watching the weather report on TV. It said the high for today will be 0 degrees Celsius. It also told me that the high yesterday was 6 degrees above zero or+6 and that tomorrow the high will only be 6 degrees below zero or -6. You are probably familiar with such reports and may even have a thermometer outside that you can read yourself.

But why did the weatherman on TV say plus 6 and minus 6 instead of just saying 6? The high yesterday was just as many degrees away from zero by 6 degrees as the high tomorrow will be away from zero by 6 degrees. We can’t just say the value of the distance from zero but we have also to say the direction away from zero, plus or minus, or with symbols, + or -. Numbers with a sign of + are called **positive numbers** and numbers with a sign of – are called **negative numbers**.

Until now, numbers for us have been adequately represented by their value. Now we have to add a new property of numbers and that is called **sign**. We also now want to be a bit more precise and qualify the value of a number as its **absolute value**. The idea of absolute value is important in computer programming and higher mathematics but not so much for us now.

#### A Few Things About Signs

When used to denote the sign of a number the symbols {+.-} are acting as operators. They have only one operand however, and are therefor called **unary operators**.

Further we have another unary operator,, the absolute value symbol, “**| **…**| **“, that operates on a number to give just its value without any sign. An example is the expression **| **-6**| **= 6.

You may have noticed that all the numbers we have used until now have shown no sign. Since most numbers we use are positive numbers, by **convention**, that means by agreement by most mathematicians, we don’t write the + sign for positive numbers. After all, we are mathematicians and don’t like extra writing. This causes a bit of possible confusion when we use the absolute value operator. We have to remember that the expression above is meant as it is written and does not stand for **| **-6**| **= +6.

**Updating the Number Line**

**Addition and Subtraction of Negative Integers**

#### Multiplication and Division of Negative Integers