On p. 258, Vol. 1, of 'Ilal al-Sharai', and also on p. 92, Vol. 94, of Bihar al-Anwar, Imam Reza (A.S) was asked why an optional fast is recommended for the entire year, and he answered by saying that it served to complement obligatory fast. Then he was asked, "Why is there an optional fast for one day out of each ten days?" He (A.S) said, "It is so because Allah, the Praised and Exalted One, says, 'Whoever does a good deed will be rewarded ten-fold' (Surat al-An'am, verse 16); therefore, one who fasts one day in each ten days will be regarded (according to this verse) as though he had fasted the whole time.
" Salman al-Farsi, may Allah be pleased with him, used to say, "Fasting three [non-consecutive] days a month equals fasting the whole dahr, the whole time; so, if one can find anything beyond that, let him fast it!"
Imam Jafar Sadiq (A.S) was asked why a Thursday of the first tenth days is to be fasted, a Thursday of the last, and a Wednesday in-between are the designated days for such fast, and his answer was, "The deeds of each servant of Allah are displayed before Allah on each Thursday; therefore, He wished that it should be done while such servant is observing a fast. “Why another Thursday's fast at the end of the month, then?" the Imam (A.S) was asked. "It is so because if his deeds for eight days are displayed while he is fasting are more honorable for him and better than if he is not fasting. The reason for choosing a Wednesday in the second (middle) ten days of the month, according to Imam Sadiq (A.S), is due to the fact that Allah, the most Honored, the most Sublime, created hell on that day; it was on it that He annihilated the early generations; it is a day of continuous bad omen; so, He wished that His servants should shun such a bad omen by fasting that day."
Imam Jafer Sadiq (A.S) quotes his forefathers (A.S) saying that the Messenger of Allah (PBUH) once asked his companions, "Which one of you fasts the whole time?" Salman al-Farsi, may Allah have mercy on his soul, said, "I do, O Messenger of Allah!" The Messenger of Allah (PBUH) asked them, "Which one of you says prayers the whole night?" Salman al-Farsi, may Allah have mercy on his soul, again said, "I do, O Messenger of Allah!" The Messenger of Allah (PBUH) asked them, 'Which one of you recites the entire text of the Qur’an every day?"
Salman al-Farsi, may Allah have mercy on his soul, for the third time said, "I do, O Messenger of Allah!" One of the Prophet's companions became angry and said, "O Messenger of Allah! Salman is a Persian who wants to brag and demonstrate his superiority over us, we men of Quraysh. You asked us, 'Which one of you fasts the whole time?' and he said he does so, while he eats most of the time. And you asked us, 'Which one of you says prayers the entire night?' and he again said he did so, while he sleeps most of the night. And you asked us, 'Which one of you recites the entire text of the Qur’an every day?' and he for the third time said that he did so, while most of the time he is silent." The Messenger of Allah (PBUH) rebuked that man and said, "Keep your silence, so-and-so, for how far you are from Luqman the Wise! Ask him, and he will explain to you," whereupon that companion turned to Salman and asked him thus: "O father of Abdullah! You have claimed that you fast the whole time, haven't you?" Salman answered him in the affirmative, so the companion said, "But I have seen you eating most of the time!" Salman said, "It is not what you say! I fast three days in every month, and Allah, the most Exalted, the most Glorified One, says, 'Whoever does a good deed will be rewarded ten-fold' (Surat al-An'am, verse 16). And I join the month of Sha'ban with the month of Ramadhan in my fast, so it is regarded as though I fast the whole time." The man then asked him, "But you claim that you spend your entire night offering prayers, don't you?" Salman answered in the affirmative, whereupon that man said to him, "How so since most of your night you are in bed?" Salman said, "It is not as you say. I have heard my beloved Messenger of Allah (PBUH) say, 'Whoever remains in a state of tahara (purification) during his sleep will be regarded as though he spent the whole night offering prayers,' and I do remain tahir!" The man still asked him, "Have you not claimed that you recite the entire text of the Qur’an every day?" Salman said, "I have."
The man then asked him, "But you spend most of the day silent!" Salman said, "It is not as you say, but I have heard my beloved Messenger of Allah (PBUH) telling Ali (A.S): 'O father of al-Hassan (A.S)! Your similitude in my nation is like that of Surah al-Ikhlas: whoever recites it once is considered as having recited one third of the entire text of the Qur’an, and whoever recites it twice is considered as having recited two-thirds of the Qur’an, while whoever recites it thrice will be regarded as having recited the entire text of the Qur’an; whoever loves you with his tongue completes one third of his iman (conviction), and whoever loves you with both his tongue and heart completes two thirds of his iman, whereas whoever loves you with his tongue and heart and assists you with his hand (i.e. physically with his might and means) perfects his iman. I swear by the One Who sent me with the truth, O Ali! Had all people on earth loved you as those in the heavens do, nobody would have been tormented with the Fire,' and l do recite Surah al-Ikhlas thrice daily." The man then stood up and left as if someone had filled his mouth with a rock (as the Arabs put it). This incident is recorded on pp. 93-94, Vol. 94, of Bihar al- Anwar.
In the same reference cited above, Imam Sadiq (A.S) quotes his forefathers citing the Messenger of Allah (PBUH) saying, "I entered Paradise [during my ascension, mi'raj] and found most of its people to be those who are not evil, who are wise in spending their wealth, and who fast three days a month." Ibn Tareef quotes Ibn 'Alwan quoting Imam Sadiq (A.S) quoting his father Imam Baqir (A.S) saying that Imam Ali (A.S) used to imitate the fast observed by the Messenger of Allah (PBUH), saying, "The Messenger of Allah (PBUH) fasted siyam al-dahr as long as Allah willed, then he stopped doing so and observed the fast of his brother Dawood (A.S) (David): a day's fast for Allah, and a day for himself (to rest) as long as Allah willed. Then he stopped doing that, too, and started fasting each Monday and Thursday for as long as Allah willed. Then he stopped doing even that and upheld siyam al-beed [1]. Imam Ali (A.S) concludes his statement by saying that the Messenger of Allah (PBUH) continued to do so till he passed away. On p. 102, Vol. 94, of Bihar al-Anwar, the author states that Muhammad ibn Yahya has quoted Hammad ibn 'Uthman quoting Imam Abu Abdullah al-Sadiq (A.S) saying, 'The Messenger of Allah (PBUH) died while observing a fast of three days a month, saying, 'They equal fasting the whole time, and their fast removes ill intentions and feelings of hostility.' He (PBUH) was asked, 'Why were these specific days chosen for such fast?' He (PBUH) answered by saying, ' Retribution was inflicted upon nations before us during those days;' so, the Prophet (PBUH) observed the fast of those ominous days."
The Messenger of Allah (PBUH) is quoted on p. 108, Vol. 94, of Bihar al-Anwar as saying that one who observes the fast of the month of Ramadhan and follows it by fasting six days during the month of Shawwal will be rewarded as though he had fasted the entire year.
One may wonder whether offering sadaqa (charity) is more rewarding than fasting. It is. On p. 102, Vol. 94, of Bihar al-Anwar, it is stated that Imam Abu Abdullah al-Sadiq (A.S) was asked once by Ibrahim al-Muthanna, one of his followers, "I have found it very hard for me lately to fast three days a month; so, is there any way I can make it up by, say, giving one dirham by way of charity for each of these days?" The Imam (A.S) answered, "One dirham's charity is even better than fasting one day." In the same reference, on p. 106, Salih ibn 'Uqbah said to Imam Jafer Sadiq (A.S), "May my life be sacrificed for your sake! I have grown to be an old man, and I feel too feeble to observe the fast of these days." The Imam (A.S) responded by saying, 'Then offer sadaqa of one dirham (cash equivalent in value to 3.12 grams of silver) for each day." The Imam noticed that the man did not seem to be fully convinced, so he said to him, "Do you think one dirham for each of these days is too little?
Feeding one indigent person is better than the fast of a whole month."

Taken from: Fast of the Month of Ramadan Philosophy and Ahkam by Yasin T. al Jibouri International Islamic society of Virginia, Inc.

1. Ayaam Al Beed ”” The White Days are 3 days - 13th..14th..15th of each Islamic month.