I. The duty of fasting is based on both the Old and New Testaments, and is closely connected with the duties of prayer and almsgiving
The teaching of the Law, dearly beloved, imparts great authority to the precepts of the Gospel, seeing that certain things are transferred from the old ordinances to the new, and by the very devotions of the Church it is shown that the Lord Jesus Christ “came not to destroy but to fulfil the Law.” For since the cessation of the signs by which our Saviour's coming was announced, and the abolition of the types in the presence of the Very Truth, those things which our religion instituted, whether for the regulation of customs or for the simple worship of God, continue with us in the same form in which they were at the beginning, and what was in harmony with both Testaments has been modified by no change.
Among these is also the solemn fast of the tenth month, which is now to be kept by us according to yearly custom, because it is altogether just and godly to give thanks to the Divine bounty for the crops which the earth has produced for the use of men under the guiding hand of supreme Providence. And to show that we do this with ready mind, we must exercise not only the self-restraint of fasting, but also diligence in almsgiving, that from the ground of our heart also may spring the germ of righteousness and the fruit of love, and that we may deserve God's mercy by showing mercy to His poor.
For the supplication, which is supported by works of piety, is most efficacious in prevailing with God, since he who turns not his heart away from the poor soon turns himself to hear the Lord, as the Lord says: “be ye merciful as your Father also is merciful....release and you shall be released.” What is kinder than this justice? What more merciful than this retribution, where the judge's sentence rests in the power of him that is to be judged? “Give,” he says, “and it shall be given to you.” How soon do the misgivings of distrust and the puttings off of avarice fall to the ground, when humanity may fearlessly spend what the Truth pledges Himself to repay.
Source: Sermons (New Advent)