The Basic Concept of Negative Numbers
When people first find out about subtraction, they often hear that you can't take away more than you have. For example, if you have four pencils, you can take away one, two, three, or even all four of them, but you can't take away more than that.
It isn't long, though, before you find out what any credit card holder knows only too well: You can, indeed, take away more than you have — the result is a negative number.
For example, if you have $4 and you owe your friend $7, you're $3 in debt. That is, 4 – 7 = –3. The minus sign in front of the 3 means that the number of dollars you have is three less than 0.
Here's how you place negative whole numbers on the number line.
Adding and subtracting on the number line works pretty much the same with negative numbers as with positive numbers. For example, here's how to subtract 4 – 7 on the number line.
Placing 0 and the negative counting numbers on the number line expands the set of counting numbers to the set of integers.