We can visualise positive numbers as the distances to points on a line, measured to the right of some chosen "zero point" called the origin.
Negative numbers can then be thought of as
corresponding to distances measured to the left of the origin:
We call this a number line.
For any number x, the number -x (called the negative of x) is the number which is the same distance from the origin as x, but on the opposite side. Note that this is also true when x itself is a negative number, for example -(-2) = 2.
Since the effect of placing a minus sign before a number is to "reflect" the number about the origin, it follows that for any number x (positive or negative):
-(-x) = x
That is, two successive "reflections" take you back to where you started.
Adding a positive number x to another number can be thought of as moving a distance x to the right of the other number, for example -2 + 5 = 3:
Adding a negative number will then correspond to moving the equivalent distance to the left, for example 4 + (-7) = -3:
Hit the "New Example" button below to view some examples of adding positive and negative numbers. Each time you hit the button a new example will appear.
Now try a few yourself!
How about these harder examples?