We appreciate your concern for your religious responsibilities and your interest in not falling in committing sins. We wish to clarify that hearing the backbiting does not invalidate the fast nor does it invalidate the prayers. It is not even prohibited. What is prohibited is reacting to the backbiting and becoming a part of it and supporting it. You are encouraged to be busy with reciting and studying the Holy Quran and supplications, offering prayers and giving in charity, and maintaining your relations to your kin during this month. If you are forced to be in a situation that necessitates you to listen to the backbiting, you can suggest to them to stop this in a calm and nice way. May Allah guide them to stop committing such sins.