Jesus taught that prayer should sometimes be with fasting (Mark 9:29). 

On one occasion, when Jesus cast out a demon from a boy, and His disciples earlier were not able to cast out the demon, they came to Him privately and said, “Why could we not cast him out?”  Jesus response was: “This kind can come out by nothing but prayer and fasting.”

So here Jesus was teaching that the most difficult things (in this case, casting out a demon) require both prayer and fasting.  Why?  Because when we fast we depend more on God, and so our prayers become stronger.  I suppose you could say that when we fast we receive an extra portion of the Holy Spirit, or perhaps we receive extra strength from the Holy Spirit.  However you want to put it, you will find that fasting will strengthen prayer.

Now we know that we should always pray about everything; or rather, we should always be in a spirit of prayer.  But here Jesus is teaching that there are some things that require a special time of prayer, or extra fervency of prayer, and that it should be accompanied with fasting.

I remember going to my pastor one time with a difficult problem.  His advice was to go on a fast.  He didn’t have the answer for me so He suggested fasting.  That was good advice.  Whenever you are stumped and can’t seem to find the answer, or you can’t seem to conquer a problem, you need extra strength in your prayers.  Fasting will do that for you.  It will deepen your spiritual roots so that you are more in tune to God and have more of the love of Christ in you.  Hence, fasting will aid you in receiving the faith of Christ so that nothing will be impossible for you.