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Negative Numbers

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

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