Gemara

52b (Chizkiyah): One may redeem Ma'aser Sheni worth less than a Perutah, and its Chomesh (he must add a quarter of the principal), on prior coins (on which Ma'aser was already redeemed), for surely he was not exact.

Question (Mishnah): The following apply to Terumah and Bikurim, but not to Ma'aser.... they can become Batel in 100 parts of Chulin.

Inference: Ma'aser is Batel in a majority of Chulin!

If one can redeem even less than a Perutah of Ma'aser, it is Yesh Lo Matirim (it can be permitted in some way). If so, it is never Batel!

Answer: The case is, he has no prior coins.

Question: He can redeem Ma'aser mixed with Chulin together with other Ma'aser worth a half-Perutah!

Answer: Mid'Oraisa, the Ma'aser is Batel in the mixture. It is considered Ma'aser only mid'Rabanan. It does not join with mid'Oraisa Ma'aser.

Question: He can redeem it together with a half-Perutah of Ma'aser of Demai (Peros bought from an Am ha'Aretz. Its Ma'aser is only mid'Rabanan!)

Answer: We decree not to, lest he redeem it with mid'Oraisa Ma'aser.

Question: He can redeem a Perutah and a half of mid'Oraisa Ma'aser on two Perutah coins, and redeem the mixed Ma'aser on the other half-Perutah!

Answer: If he does so, a Perutah of Ma'aser is redeemed on one coin, but the rest is not redeemed on the other coin (for it is less than a Perutah)!

Question: He can redeem mid'Oraisa Ma'aser on an Isar (worth eight Perutos), and redeem the mixed Ma'aser on Chulin that remains in the Isar!

Answer: We decree lest he redeem on Perutos.

53b (Beraisa): "If one will redeem mi'Ma'asero" excludes Ma'aser Sheni that there is not in it a Perutah.

(Rav Ami and R. Yochanan): The Ma'aser is less than a Perutah.

(Rav Asi and Reish Lakish): The Chomesh is less than a Perutah.

Question (Beraisa): If Ma'aser is worth less than a Perutah, it suffices to say that it and its Chomesh are redeemed on prior coins.

Granted, according to Rav Asi, even though the Ma'aser is more than a Perutah, since the Chomesh is not, it suffices to redeem on prior coins (he need not take it to Yerushalayim or redeem it with more Ma'aser so the Chomesh will be a Perutah).

According to Rav Ami the Ma'aser is less than a Perutah. Why does it say 'it suffices'? It should just say, he redeems it on prior coins!

This is left difficult.

54a (Beraisa - R. Eliezer): If one gave the principal (to redeem Ma'aser) but not the Chomesh, he may eat it;

R. Yehoshua says, he may not eat it.

Suggestion: They argue about whether the Chomesh is Me'akev!

Rejection (Rav Papa): All agree that it is not Me'akev (mid'Oraisa). They argue about whether Chachamim are stringent, lest he neglect to pay it.

Rishonim

Rambam (Hilchos Ma'aser Sheni 5:4): If the Chomesh of Ma'aser Sheni is worth less than a Perutah, one does not add a Chomesh to it.

Kesef Mishneh: The Rambam explains the Beraisa to teach that if the Chomesh is less than a Perutah, one does not add a Chomesh. Rashi explains that in such a case, one cannot redeem the Ma'aser.

Ri Korkus: The Yerushalmi is explicitly like the Rambam.

Tosfos (53b DH Ein): Granted, Rav Ami holds that the Ma'aser is less than a Perutah, so it is better to expound that it cannot be redeemed, than to say that it can be redeemed, and the exclusion exempts only from Chomesh. Rav Asi holds that the Chomesh is less than a Perutah. If so, it would be better to expound that the Ma'aser can be redeemed, but there is no Chomesh!

Toras Kohanim (Bechukosai 12:10): "Chamishiso" excludes less than a Perutah. "Yosif Alav" teaches that the Ma'aser and its Chomesh are five.

Ra'avad and R. Shimshon: Since Ma'aser less than a Perutah need not be redeemed, there is no Chomesh for it.

Ritva (52b DH Gufa): Chizkiyah holds that one redeems with intent that if later he will redeem more Ma'aser on the excess, it will become Kodesh then, and if not, it is Kodesh now. Rashi says that mid'Oraisa, less than a Perutah cannot be redeemed. This is wrong. If so, Chachamim would not enact that it becomes Chulin! Rather, mid'Oraisa one may redeem it on previous coins, or let it rot. Chizkiyah teaches that Chachamim obligate redeeming it on prior coins.

Question (Tosfos 53a DH Dilma (2)): When one redeems on Perutos, that exact number of Perutos of Ma'aser is redeemed, but no more. Why does the Mishnah (2:8) allow this? Whatever Ma'aser remains above a whole number of Perutos will be eaten without redemption!

Answer #1 (Tosfos): One may redeem onto an Isar and Perutos together. (One can redeem on an Isar any amount between a Perutah and the entire value of the Isar.) There, we do not decree lest he redeem on Perutos alone, for people know that a half-Perutah cannot put Kedushah on a coin.

Answer #1B (Tosfos ha'Rosh DH Chetzi, citing R. Shlomo of Travyash): Chachamim are lenient and are not concerned he redeem on Perutos alone, to enable a solution. Regarding a mixture we are concerned lest he bring Vadai Tevel, lest it (be Yesh Lo Matirim) and it can be Batel. Tevel is never Batel. Avodah Zarah 73b explains that any amount forbids, just like the Heter (any amount of Terumah permits the entire stack). It didn't say that Tevel is Yesh Lo Matirim (one could buy Demai and separate from it on the mixture), for we similarly decree lest one buy Vadai Tevel.

Gra (YD 122:22): Why did the Gemara need to say that oe buys Demai to tithe on the mixture? Ma'aser of anything bought is only mid'Rabanan! See Tosfos 88a DH Tevu'as. (R. Tam says that what one buys after Miru'ach (final processing) is exempt mid'Oraisa. Rivam exempts mid'Oraisa what one buys before Miru'ach.)

Answer #2 (Tosfos ha'Rosh DH Chetzi): We said that one cannot calculate the exact value of Ma'aser Sheni, i.e. without exertion, and one would not do so for a whole stack. When one wants to be exact, he can, and this suffices, for the Torah was given to mortals.

Lechem Mishneh (Erchin 5:1): The Rambam rules like one may not redeem Hekdesh for less than four Perutos, for the Chomesh must be at least a Perutah. Why is this different than Ma'aser Sheni?

Rambam (5): If one redeemed Ma'aser Sheni and has other Ma'aser, if the Chomesh of the latter is not worth a Perutah, it suffices to say 'it and its Chomesh are redeemed on the first coins', for one cannot be exact with coins.

Ri Korkus: Rava did not count this among places where we rule like Reish Lakish against R. Yochanan, for other Amora'im also argued. One cannot be exact with coins, so he redeems onto more than the value of the Ma'aser, lest he eat without redemption. He redeems now on the excess.

Rambam (ibid): If one redeems Ma'aser for more than its value, the excess does not get Kedushas Ma'aser.

Kesef Mishneh: The Yerushalmi says so.

Ri Korkus: The Yerushalmi says that if one redeems Hekdesh for more than its value, the excess gets Kedushas Ma'aser, for people are prone to be Makdish more.

Chidushei R. Meir Simchah (53b DH v'Da): The Chomesh can join with the Ma'aser to the Shi'ur of a Perutah only if the Chomesh is Me'akev.

Poskim

Minchas Shlomo (1:63 DH v'Hach): Nowadays, we may redeem any amount of Ma'aser onto a Perutah. The Gemara says that one cannot redeem a half Perutah of Ma'aser mid'Rabanan with a half Perutah of Ma'aser mid'Oraisa. One can investigate whether one can redeem, onto one Perutah, a Perutah of Ma'aser mid'Rabanan with a Perutah of Ma'aser mid'Oraisa. If we consider each Ma'aser to be redeemed on a half Perutah, it is not a Pidyon, for the two Ma'aseros do not join. Or, perhaps the Ma'aser mid'Oraisa is Tofes (puts Kedushah onto) the entire Perutah, and the Ma'aser mid'Rabanan is redeemed along with it, The Gemara means only that a half Perutah of each cannot join. The same applies if the Ma'aser mid'Rabanan is a Perutah, but if the Ma'aser mid'Oraisa is a Perutah, it is Tofes an entire Perutah, and Ma'aser mid'Rabanan less than a Perutah can be redeemed along with it, as if it had no Pidyon. However Hekdesh does not become Chulin for free (without Pidyon). This is why we say that what is bought with Kesef Ma'aser cannot be redeemed when it is Tahor, for its Kedushah is too weak to put Kedushah onto Chulin used to redeem it (Pesachim 38a). This is why R. Shimshon (Ma'aser 2:2) says that Chulin that absorbed taste from Ma'aser cannot be redeemed. Alternatively, Pidyon does not apply to taste, for taste has no value. If Ma'aser mid'Rabanan could be redeemed along with Ma'aser mid'Oraisa for free, we should similarly be able to redeem Ma'aser that is too weak to put Kedushah on Chulin! Rather, we must say that Kedushas Ma'aser never vanishes for free. Therefore, one who wants to redeem mid'Oraisa and mid'Rabanan Ma'aser at once cannot do so on one Perutah.