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While fasting IS good for the individual who is doing the fasting, it is also beneficial to others.
28 And when he was come into the house, his disciples asked him privately, Why could not we cast him out?
29 And he said unto them, This kind can come forth by nothing, but by prayer and fasting. Mark 9
It appears that our prayers have more substance when we fast and pray, versus just praying. In the above example, Christ's disciples were apparently not able to rid the individual from the demonic possession. However, when Christ succeeded in doing so and they inquired why they had failed in their own efforts, Christ informed them that these things can only be accomplished with fasting and prayer.
This leads us to believe that if we not only pray, but fast, our prayers - for ourselves and others, "hold more water." You sacrifice a bit on behalf of your neighbor.
Furthermore, sometimes if one fasts, the simple act encourages others to do so, as well. Of course we should never boast of our own "fasting", however, if someone notices you reaching for the vegetable versus the steak and realizes why, it might help them to do the same.