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Signed Numbers

Addition

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:


               


Example 1.

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.


+ =   


 

Exercise 1.

Now try a few yourself!



+ =   



How about these harder examples?



+ + + =   




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