1)
(a) A Sa'ah of Terumah, Terumas Ma'aser (even) of Demai, Chalah and Bikurim becomes Batel - in a hundred and one Sa'ah.
(b) The source for all of these is the Pasuk in Korach (in connection with Terumas Ma'aser) "es Mikd'sho Mimenu" - implying that if the Terumas Ma'aser falls back into the Chulin that it was taken from it renders it Asur (and it was taken from ten Sa'ah of Ma'aser Rishon, which in turn was taken from a hundred Sa'ah of Tevel), but that if there is one Sa'ah more, it becomes Batel (see Tos. Yom-Tov).
(c) The Tana did not include Terumah of Demai - because there is no such thing, since the Amei ha'Aretz are not suspect on Terumah (see Tos. Yom-Tov).

2)
(a) If a mixture of all of the above falls into less than a hundred Sa'ah of Chulin - they render it Asur ...
(b) ... because they are all referred to by the Torah as Terumah.
(c) Despite the fact that one Sa'ah of the above is Batel in a hundred, the owner is nevertheless obligated to remove one Sa'ah from the hundred and one - because otherwise it is considered stealing from the Kohanim (see Tos. R. Akiva Eiger note 8 & 9, and Tiferes Yisrael).

3)
(a) One Sa'ah of Orlah and K'lai ha'Kerem only become Batel - in two hundred and one Sa'ah (see Tiferes Yisrael).
(b) We learn from the 'Gezeirah-Shavah' "Mele'ascha ve'Dim'acha Lo Se'acher" (Mishpatim, in connection with Terumah) "Pen Tikdash ha'Me'le'ah" (Ki Seitzei, in connection with K'lai ha'Kerem) - that just as Terumah can become Batel, so too can K'lai ha'Kerem.
(c) And we then learn that it becomes Batel only in two hundred and one - because unlike Terumah, K'lai ha'Kerem is Asur be'Hana'ah, too, and the Tana considers that double the Isur of Terumah. And he concludes that just as the Isur is double, so too, is the Bitul.
(d) If one Sa'ah of Orlah falls into two hundred of Heter and becomes Batel, the Tana does not add 've'Tzarich Leharim', like he did in the Reisha - because, due to the fact that he is not withholding anybody's dues, there is no reason why he should.

4)
(a) The Tana Kama forbids a combined (see Tos. Yom-Tov) Sa'ah of Orlah and K'lai ha'Kerem (that is dry) that fell into less than two hundred Sa'ah of Heter. If it was liquid - it would be Batel in sixty Sa'ah (provided the pot into which it fell was a different species).
(b) According to R. Shimon - they do not combine (seeing as, unlike the Isurim in the Reisha, they do not share the same name [see Tiferes Yisrael]).
(c) R. Eliezer says 'Mitztarfin be'Nosen Ta'am' (like the Tana Kama), by which he means - that they combine to render the pot Asur (if it contains less than sixty times the amount, but not if they are dry.
(d) The Halachah is like the Tana Kama.

5)
(a) When the Tana says that Terumah renders Orlah Batel, he means - that it combines with the Chulin into which it fell to Be Mevatel the Orlah.
(b) The case is for example - if one Sa'ah of Terumah fell into a hundred Sa'ah of Chulin (see next question), and then three Kabin (half a Sa'ah) of Orlah (or of K'lai ha'Kerem) fell into the mixture.
(c) When the Tana says that one Sa'ah of Terumah fell into a hundred Sa'ah of Chulin, he cannot mean this literally - because then the hundred Sa'ah of Chulin would not need the Sa'ah of Terumah to help be Mevatel the Orlah that fell in afterwards.
(d) What he must therefore mean is - that it fell into less than a hundred of Chulin (see Tos. Yom-Tov).

6)
(a) Similarly, Orlah or K'lai ha'Kerem render Terumah Batel - if one Sa'ah of Terumah fell into ninety-nine Sa'ah of Chulin, following which half a Sa'ah of Orlah (or K'lai ha'Kerem) fell into the mixture.
(b) The problem with this case is - that the Chulin is only a hundred and a bit as much as the Isur (like R. Yehoshua, who suffices with a hundred and a bit times the Isur, whereas we rule like R. Eliezer, who requires a hundred and one.
(c) To conform with R. Eliezer - we will have to establish our Mishnah where the Terumah fell into ninety-nine and a half Sa'ah of Chulin (see Tos. Yom-Tov).

7)
(a) The Tana rules - that Orlah is Mevatel Kil'ayim, and vice-versa (in the same way as it is Mevatel Terumah, as we learned in the previous Mishnah).
(b) When the Tana adds that Orlah is Mevatel Orlah, he means - that it is Mevatel Orlah that turned into Neta Revai (in the fourth year) or vice-versa (since it is not possible for an Isur to be Mevatel the same Isur [see also Tiferes Yisrael]).
(c) The case of Orlah or Kil'ayim being Mevatel Orlah is - where a Sa'ah of Orlah fell into a bit less than two hundred Sa'ah of Chulin, and then a Sa'ah plus (see Tos. Yom-Tov) of Neta Revai (see Tiferes Yisrael [or vice-versa]) or of K'lai ha'Kerem fell into the mixture (see b. and c. in the previous answer).
(d) The Mishnah presents a case of Orlah Mevatel Orlah (because Orlah incorporates Neta Revai, as we explained), but not of Kil'ayim Mevatel Kil'ayim - since there are no two cases of K'lai ha'Kerem.

8)
(a) The Mishnah now discusses 'Kol ha'Mechametz, ha'Metavel ve'ha'Medamei', which mean - adding (yeast [Tiferes Yisrael]), crushed apples (see Tos. Yom-Tov) or dregs to a dough to make it rise, adding spices to a pot and mixing liquid with liquid (see Tiferes Yisrael).
(b) The Tana concludes 'bi'Terumah, u've'Orlah u'vi'Kelai ha'Kerem' - Mechametz and Metavel Chulin with Orlah or K'lei ha'Kerem, and Medamei Chulin with Terumah (see Tos. Yom-Tov).
(c) When Beis Shamai says 'Af Metamei', he means - that if he adds a Tamei yeast or Tamei spices (even if they comprise less than a k'Beitzah) to a Tahor dough or to a Tahor pot, it renders it Asur.
(d) Beis Hillel - permit it unless the Tamei dough comprises a k'Beitzah.

9)
(a) Dustai from the village of K'far Yasma was - a Talmid of Beis Shamai ...
(b) ... in whose name he testified that Tum'ah applies only to a Tamei dough that comprises a k'Beitzah.

10)
(a) The Chachamim go le'Chumra exclusively with regard to Mechametz, Metavel and Medamei - in a case of Min be'Mino ...
(b) ... whereas about Min be'she'Eino Mino - they are sometimes lenient and sometimes strict (as we shall now see).
(c) In a case where a yeast of wheat falls into a dough of wheat, assuming ...
1. ... the former is sufficient to affect the latter - it renders it Asur even if the latter comprises a hundred times more than it.
2. ... the latter does not comprise a hundred times than the former - it nevertheless becomes Asur even if the former contains insufficient to affect it.

11)
(a) In a case where beans of Terumah (see Tiferes Yisrael) are cooked together with lentils, assuming the latter ...
1. ... give taste to the former - they will render it Asur even if it comprises a hundred times than what fell into it.
2. ... do not give taste to the former - then it will not become Asur, even if it comprises less than a hundred times of that what fell into it.
(b) The reason for this leniency is - because the Pasuk ("es Mikdesho Mimenu"), which serves as the source of Bitul in a hundred and one by Terumah refers specifically to Min be'Mino.
(c) If this Mishnah was discussing yeast of Terumah that fell into a dough - the Din would be exactly the same, says the Tos. Yom-Tov ...
(d) ... and the reason that the Tana switched to beans and lentils is - because it is not common to find yeast that is not the same species as the dough (see also Tiferes Yisrael).

12)
(a) The Tana Kama rules that if a yeast of Terumah or K'lai ha'Kerem falls into a dough after a yeast of Chulin (comprising sufficient to cause it to rise) fell into it ...
1. ... but before the dough actually rose - it renders the dough Asur (to Zarim or to everyone (respectively), and so it is if it fell into it ...
2. ... after the dough had already risen.
(b) R. Shimon disagrees with second ruling - because since the dough had already risen when the Asur yeast fell into it, all it achieved was to spoil the dough, and we have a principle 'Nosen Ta'am le'Fegam, Mutar'.
(c) The Tana Kama forbids it nonetheless - because even though it spoils the taste of the dough, it does give it more power to cause additional doughs to rise.
(d) The Halachah is - like the Chachamim.

13)
(a) The Mishnah rules in a case where three ...
1. ... of the same spice (peppers say [see Tos. Yom-Tov]), but of three different Isurim (one of Orlah, one of Asheirah and one of Terumah) fall into a pot of Heter Chulin, they combine to render the contents of the pot Asur (either to everyone or to a Zar), and the same applied to ...
2. ... different spices of the same Isur fall into a pot of Heter Chulin.
(b) The Tana say 'Asur' - refers to Lach (when the Isur us wet and gives taste) and 'Mitztarfin' - to Yavesh (when it is dry) see also Tos. Yom-Tov and Tiferes Yisrael).
(c) According to R. Shimon - two or three different Isurim of the same species, or two different species of the same Isur do not combine.

14)
(a) In a case where two yeasts, one of Chulin and one of Terumah (neither of which is able to cause the dough to rise on its own) fall into a dough and cause it to rise, R. Eliezer goes after the one that fell last. Assuming that the yeast of Chulin fell in last, he permit the dough - provided the Terumah yeast was removed before the dough actually rose.
(b) This latter ruling is based on the principle 'Zeh ve'Zeh Gorem, Asur'.
(c) The Chachamim - who hold 'Zeh ve'Zeh Gorem, Mutar', permit the dough (as long as the Isur could not have caused it to rise without the Heter), irrespective of the order in which the two yeasts fell into it.
(d) The Halachah is like - the Chachamim.

15)
(a) Yo'ezer Ish ha'Birah - a Talmid of Beis Shamai, asked Raban Gamliel ha'Zaken what the Din will be in the previous case.
(b) Raban Gamliel, at the time, was standing beside the east gate of the Azarah.
(c) What is remarkable about the fact that he asked Raban Gamliel, says the Tos. Yom-Tov, is - the fact that a Talmid of Beis Shamai should consult the grandson of Hillel.
(d) The latter replied - that as long as the Isur could not have caused the dough to rise without the Heter, the dough is permitted, irrespective of the order in which the two yeasts fell into it.

16)
(a) The Mishnah now discusses a leather vessel that was anointed with Tamei oil - and then left to dry and Toveled (see Tos. Yom-Tov and Tiferes Yisrael), before being anointed with Tahor oil , or vice-versa.
(b) When R. Eliezer says that he goes after the first one, he means - that the vessel will exude the oil that was anointed first as well as the oil that was anointed last (Tiferes Yisrael) that the, in which case it remains perpetually Tamei.
(c) According to the Chachamim - the last oil alone is exuded, in which case, if that oil was the Tahor oil, the vessel is Tahor.

17)
(a) In a case where a yeast comprising Terumah and K'lai ha'Kerem (neither of which would have affected the dough) fell into a Chulin dough and caused it to rise, the Chachamim, who forbids the dough to Zarim - follow their reasoning, that spices of two or three different Isurim combine to forbid the Heter food into which they fell (as we learned earlier).
(b) On the other hand, they permit Kohanim to eat it - since the K'lai ha'Kerem yeast was not able to affect the Chulin dough on its own.
(c) R. Shimon - who permits the dough to Zarim as well, follows his own reasoning too, in that two or three different Isurim do not combine ... .
(d) In a case where a mixture of spices of Terumah and K'lai ha'Kerem fell into a pot containing Chulin and gave taste to the food - the Chachamim permit Kohanim exclusively, to eat the dough, whereas - R. Shimon permits Zarim to eat it too (see Tos. Yom-Tov and Tiferes Yisrael).

18)
(a) According to the Tana Kama, a piece of Kodshei Kodshim, and one of Pigul or Nosar (or Tamei [see Tos. Yom-Tov]) fell into pieces of Chulin or of Kodshim Kalim (see Tiferes Yisrael), assuming that the latter contained sufficient to render one of them Batel (but not both) - they are Asur to Zarim, but Kohanim may eat them (The Rambam explains the Mishnah quite differently [see Tos. Yom-Tov]).
(b) R. Shimon - permits them to Zarim as well.

19)
(a) If a piece of Kodshei Kodshim and a piece of Kodshim Kalim are cooked together with a piece of Basar Ta'avah (see Tos. Yom-Tov), which contains sufficient to render either of the Kodshim pieces Batel - the mixture is permitted Tehorim (even Zarim) even according to the Rabbanan, and forbidden to Teme'im (even Kohanim) ...
(b) ... even according to R. Shimon.