the result of subtracting a negetive integer from a positive integer is a positve integer

Thanks Chris that is a really good answer to a really good question.  Actually it is an excellent answer.

I don't know why I wrote more - sometimes I just can't help myself.

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I am going to have another take on this.

Think about temperature.  In the freezer it would be a negative temperature and in a fire it would be a high positive temperature so you can think of positive numbers as being 'hot' numbers and negative numbers as being 'cold' numbers.

So  - - means take away cold.     If you take away cold then it must get HOTTER!   So - - = +

Lets think of the other possibilities 

- + means take away heats.  If you take away heat it must get colder So - + = -

+ - means add cold. If you add cold it must get colder So + - = -

+ + means add heat.  If you add heat it must get hotter. So + + = +

Now that you understand why this is true it is easy.  I'll say it in a different way.

If the + and - signs are SO close together that you can put a circle around them without anything else getting in the way then.  

If the signs are the same replace them with a +

If the signs are different replace them with a -

This is another post that you may find helpful.

 http://web2.0calc.com/questions/it-just-doesn-t-make-sense-to-me

You're probably asking why this is so...

Consider some helium-filled balloons that have a lead weight attched to them. The balloons want to "rise" in a "positive" direction,  and the lead weight wants to pull the balloons in a "negative" direction - "downward."

What happens when we "subtract" the "negative,"  i.e., get rid of the lead weight??"  The balloons rise !! Thus, "taking away" a negative from a positive gives us a "larger" positive !!!

Remember it like this.......

Cutting away the weight - subtracting a negative from a positive - makes the balloons rise higher - the balloons get more "positive."