Can someone please help a freshman noob with integer mathematics?

I found a website that explains all the things you need to know better than I could explain myself. The link is in my sources, but the key points are:

Add a positive integer by moving to the right on the number line

Add a negative integer by moving to the left on the number line

Subtract an integer by adding its opposite

Negative + Negative = Negative

Ex:

-3 + (-3) = -6

Negative + Positive = + or - depending what is bigger

Ex:

-23 + 3 = -20

23 - 3 = 20

Negative - Negative = - or +

Ex:

-9 - (-3) = -6

-9 - (-19) = 10

Here is some tips.

If two negative signs are next each other then it becomes positive

Ex: -9 -(-9)

-9+9= 0

If you are adding two negative numbers the answer will ALWAYS be negative

(you don't subtract negative numbers unless it's negative - positive number)

Ex: -9 -9 =-18

If you are adding a positive number and a negative number then depending on which is bigger (positive or negative) will be the answer's sign

Ex:

Bigger Positive Number

25-5= 20

Bigger Negative Number

-25+5= -20

Studying the number line and keeping one handy while you work out problems will be a big help. In fact, learning the number line is the key to understanding how to work with negative numbers:

http://www.mathsisfun.com/number-line.html