What impact does negative rational numbers have on whether you add or subtract rational numbers?

Subtracting a rational number is the same as adding it's opposite. If you have a double negative , you add it like it is a positive , than keep the answer you get. Examples:  
                            1)   6 3/4 - (-8 4/8) is the same as saying 6 3/4 ÷ 8 4/8.
                             2)  -38 5/8  - 6 5/12  translates to -38 5/8 + (-6 5/12)