Ah. I think I understand now. Thanks for catching my error. I have no idea why I didn't consider that initially. Back to the drawing board.

Edit: What do you think the best way of representing the degree:min:sec is? I am leaning to simply converting everything to seconds, doing the arithmetic, and then converting to deg:min:sec format as Anomalous Monk did. I planned on extending the calculator to accept decimals anyway. But if I wanted to accept integer input, what would be the best way of representing this situation of small negatives?