What are the rules for adding and subtracting positive and negative fractions with different denominators?

first must find Least Common Denominator

http://www.loisterms.com/lois21.htm

First of all, if you want to know about adding fractions, check out "How to Add Fractions". Be sure to follow the math examples carefully. To subtract fractions, follow the same steps as for adding, except subtract where you would add. Now about those positive and negative signs. The rules are the same whether you are working with integers or fractions. I will give you a method of learning the rules for the signs that has worked for many other students. Copy off this "Rules for Integers" chart and paste it on a large index card. Put the card in your math book or folder and refer to it often while you are doing your homework. If you keep using the card, you will get better with the signs.