Fractions:

To add or subtract fractions with the same bottom number:

Simple addtion where the bottom numbers already match:
2     3      5  <- Only add the top numbers
-  +  -   =  -
4     4      4  <- The bottom numbers MUST stay the same

Simple subtraction where the bottom numbers match:

3     2     1  <- Only subtract the top numbers
-  -  -  =  -
4     4     4  <- The bottom numbers MUST stay the same


Addition if the bottom numbers do not match:

3     1
-  +  -
4     2

The first step is to determine what the multiples of the bottom numbers are
Multiples means which numbers multiply into both bottom numbers or which 
numbers both bottom numbers can multiply into.

Multiples of 4 are: 1,2, and 4
Multiples of 2 are: 1 and 2

A common multiple is 2. Since 3/4 cannot be reduced, we must increase 1/2 to
a fraction in the terms of #/4.

1     #   <- The top number must be multiplied by the same as the bottom, 
-  =  -  =   which, in this case was 2.
2     4   <- In order to obtain the 4, 2 had to be multiplied by 2.

1 x2  2
-  =  -
2 x2  4

Now this makes the addition problem:
3     2     5
-  +  -  =  -
4     4     4

Subtraction with different bottom numbers:

 1     3
3-  -  -  = Again you must find the common multiples and convert the first
 2     4    fraction to the terms of #/4.

 2     3
3-  -  -  = Notice the first fraction is smaller than the 2nd, this would
 4     4    be a problem if there was not a 3 in front of the 1st fraction.
            Since there is a 3, we can "borrow" from it.

Borrowing 1 from three will give you a 2, now you must add that 1 to the 2/4
fraction.
    2
1 + - = We must convert the 1 into a fraction. Remeber, any number over 
    4   itself will equal 1.

1   2
- + - = Now you have to find common multiples to add the fractions.
1   4

1 x4   4                     4     2     6
-    = -  Now the problem is -  +  -  =  -
1 x4   4                     4     4     4

      2     3      6     3     3
Now (3-  -  - ) = 2-  -  - =  2-
      4     4      4     4     4