Fasting and Prayer Isaiah 58:1-11.

58 Cry aloud, spare not, lift up thy voice like a trumpet, and shew my people their transgression, and the house of Jacob their sins.

2 Yet they seek me daily, and delight to know my ways, as a nation that did righteousness, and forsook not the ordinance of their God: they ask of me the ordinances of justice; they take delight in approaching to God.

3 Wherefore have we fasted, say they, and thou seest not? wherefore have we afflicted our soul, and thou takest no knowledge? Behold, in the day of your fast ye find pleasure, and exact all your labours.

4 Behold, ye fast for strife and debate, and to smite with the fist of wickedness: ye shall not fast as ye do this day, to make your voice to be heard on high.

5 Is it such a fast that I have chosen? a day for a man to afflict his soul? is it to bow down his head as a bulrush, and to spread sackcloth and ashes under him? wilt thou call this a fast, and an acceptable day to the Lord?

6 Is not this the fast that I have chosen? to loose the bands of wickedness, to undo the heavy burdens, and to let the oppressed go free, and that ye break every yoke?

7 Is it not to deal thy bread to the hungry, and that thou bring the poor that are cast out to thy house? when thou seest the naked, that thou cover him; and that thou hide not thyself from thine own flesh?

8 Then shall thy light break forth as the morning, and thine health shall spring forth speedily: and thy righteousness shall go before thee; the glory of the Lord shall be thy reward.

9 Then shalt thou call, and the Lord shall answer; thou shalt cry, and he shall say, Here I am. If thou take away from the midst of thee the yoke, the putting forth of the finger, and speaking vanity;

10 And if thou draw out thy soul to the hungry, and satisfy the afflicted soul; then shall thy light rise in obscurity, and thy darkness be as the noon day:

11 And the Lord shall guide thee continually, and satisfy thy soul in drought, and make fat thy bones: and thou shalt be like a watered garden, and like a spring of water, whose waters fail not.

verses 7. see also Matthew 25:31-45.

7 Is it not to deal thy bread to the hungry, and that thou bring the poor that are cast out to thy house? when thou seest the naked, that thou cover him; and that thou hide not thyself from thine own flesh?

Matthew 25:31-40  King James Version (KJV)

31 When the Son of man shall come in his glory, and all the holy angels with him, then shall he sit upon the throne of his glory:

32 And before him shall be gathered all nations: and he shall separate them one from another, as a shepherd divideth his sheep from the goats:

33 And he shall set the sheep on his right hand, but the goats on the left.

34 Then shall the King say unto them on his right hand, Come, ye blessed of my Father, inherit the kingdom prepared for you from the foundation of the world:

35 For I was an hungred, and ye gave me meat: I was thirsty, and ye gave me drink: I was a stranger, and ye took me in:

36 Naked, and ye clothed me: I was sick, and ye visited me: I was in prison, and ye came unto me.

37 Then shall the righteous answer him, saying, Lord, when saw we thee an hungred, and fed thee? or thirsty, and gave thee drink?

38 When saw we thee a stranger, and took thee in? or naked, and clothed thee?

39 Or when saw we thee sick, or in prison, and came unto thee?

40 And the King shall answer and say unto them, Verily I say unto you, Inasmuch as ye have done it unto one of the least of these my brethren, ye have done it unto me.

See also Isaiah 61:1-3.

Isaiah 61:1-3  King James Version (KJV)

61 The Spirit of the Lord God is upon me; because the Lord hath anointed me to preach good tidings unto the meek; he hath sent me to bind up the brokenhearted, to proclaim liberty to the captives, and the opening of the prison to them that are bound;

2 To proclaim the acceptable year of the Lord, and the day of vengeance of our God; to comfort all that mourn;

3 To appoint unto them that mourn in Zion, to give unto them beauty for ashes, the oil of joy for mourning, the garment of praise for the spirit of heaviness; that they might be called trees of righteousness, the planting of the Lord, that he might be glorified.

Luke 4:16-21  King James Version (KJV)

16 And he came to Nazareth, where he had been brought up: and, as his custom was, he went into the synagogue on the sabbath day, and stood up for to read.

17 And there was delivered unto him the book of the prophet Esaias. And when he had opened the book, he found the place where it was written,

18 The Spirit of the Lord is upon me, because he hath anointed me to preach the gospel to the poor; he hath sent me to heal the brokenhearted, to preach deliverance to the captives, and recovering of sight to the blind, to set at liberty them that are bruised,

19 To preach the acceptable year of the Lord.

20 And he closed the book, and he gave it again to the minister, and sat down. And the eyes of all them that were in the synagogue were fastened on him.

21 And he began to say unto them, This day is this scripture fulfilled in your ears.

see also Isaiah 58:12; and Isaiah 61:4. 

Isaiah 58:12.

12 And they that shall be of thee shall build the old waste places: thou shalt raise up the foundations of many generations; and thou shalt be called, The repairer of the breach, The restorer of paths to dwell in.

 Isaiah 6:4.

4 And they shall build the old wastes, they shall raise up the former desolations, and they shall repair the waste cities, the desolations of many generations.

Isaiah 58 is an excellent example on Fasting and its desired results and though it doesnt mention prayer and fasting hand in hand though Jesus does when confronte with a boy and his Father  after Jesus comes down from gthe mountain after having been transfigured  for a moment and witnessed by his closest descibles and the those left behind  were un able tohelp the boy and his Father, (see Matthew 17:14-21)

Matthew17:14-21.

Matthew 17:14-21 King James Version (KJV)

14 And when they were come to the multitude, there came to him a certain man, kneeling down to him, and saying,

15 Lord, have mercy on my son: for he is lunatick, and sore vexed: for ofttimes he falleth into the fire, and oft into the water.

16 And I brought him to thy disciples, and they could not cure him.

17 Then Jesus answered and said, O faithless and perverse generation, how long shall I be with you? how long shall I suffer you? bring him hither to me.

18 And Jesus rebuked the devil; and he departed out of him: and the child was cured from that very hour.

19 Then came the disciples to Jesus apart, and said, Why could not we cast him out?

20 And Jesus said unto them, Because of your unbelief: for verily I say unto you, If ye have faith as a grain of mustard seed, ye shall say unto this mountain, Remove hence to yonder place; and it shall remove; and nothing shall be impossible unto you.

21 Howbeit this kind goeth not out but by prayer and fasting.

 Which to some degree takes one back to Isaiah 58:7

Is not this the fast i have chosen? to loose the bands of wickedness, to undo the heavy burdens, and let the oppressed go free and break every yoke.

There is another element to fasting and prayer that is mentioned above and that is that some forms of fasting and prayer is as of the prompting of Father God Himself in such fasting and prayer He Father God draws onself closer to Himself on behalf of others (and in rare occasions on behalf of oneself too), during which time one is interceding on behalf of those others.

Though I hasten to add, for some it is  not necessaryly wise for some to completely fast say for a day or in some instances a number of days often  up to 3days perhaps even more as Father God directs etc. in accordance with a burden He Father God may have laid upon someone on behalf of others, due to various considerations known only to themselves and Father God and His son Jesus and those to whom it is relevant, in such instances as Father God knows ones heart etc. would quite understand in such circumstances if one missed a meal or two during in a day as prompted by Father God and during that time one could or would be drawn to Father God  in prayer etc. as father God prompts on behalf of others perhaps. 

 If one is prompted to fast it is best to have a fluids forf example drinks of water or sips of water unless one is absolutley sure one is otherwise prompted of Father God as a consequence of the serious of the burden or is interceding on behalf of others etc. 

Also if one has just come of a fast it is best to have something to eat whhich is light rather than a heavy meal especially if one has fasted for a number of days. 

as mentioend earlier  there is an excellent book on Fasting by Arthur Wallis :-

Gods Chosen Fast by Arthur Wallis.

and anther Boook on Fasting by David R Smith :-

Fasting a neglected Discipline by David R Smith.