You are fertile almost all the time. Every girl is different. But you can get pregnant if you are having sexual intercourse during your period. Nobody can really predict when your most fertile time is, because nobody really can answer. But the answer is yes, there is a possibility of getting pregnant if you have sex during your period.
It is possible to get pregnant when you are on your period because sperm can live in you for up to 5 days. If the sperm stays alive when your period ends it can then be fertilized.
If by fertile you mean chances of pregnancy and asking about these chances during periods then answer is no. It is not possible to get pregnant during periods. To get answer, you should know that why a woman get her periods?
Every month, reproductive system of women prepares uterus for pregnancy. These preparations include proliferation of endometrium, ovulation and transformation of endometrium. In common words, lining of uterus of a lady swell during her menstrual cycle. This process starts immediately after periods. If pregnancy does not take place then this preparation is wasted in the form of blood during periods. So, periods means, pregnancy was not there. So, as periods are destroying preparations for pregnancy that were made in the last cycle and laying foundations for the preparations of pregnancy for the next cycle, chances of pregnancy during periods are zero.
