The fifth perek continues the topic of mixtures of terumah. The second Mishnah discusses a case where tameh terumah mixed into one hundred parts chulin (regular produce). We have learnt that terumah is annulled if it is mixed into chulin that is one hundred times it. In that case, part of the mixture equal to the volume of terumah that was mixed in, is removed, and given to the kohen. In this case however the original terumah was tameh, which a kohen is not allowed to eat and would have been burnt. The Mishnah therefore records a debate regarding how the matter is resolved.
R' Eliezer maintains that the portion removed is burnt. R' Eliezer rules stringently that one must be concerned that that which was removed was the original tameh terumah. Interestingly, the Gemara (Bechorot 22b) reads that R' Eliezer maintains that that which is removed must be left to rot. The Bartenura explains that that is also the intention in our Mishnah as well. In other words, one is not allowed to derive any benefit from that portion as it is being burnt, out of concern that one would also eat that portion, assuming it is permitted due to bitul. Importantly, the Gemara adds that according to R' Eliezer, the remaining chulin must be eaten in a manner ensuring that it will not become tameh.
The Chachamim however disagree. They maintain that the removed terumah must be eaten in a way that it cannot become tameh -- either ensuring that the mixture does not become susceptible to tumah or making small portions such that there is not enough tumah in one place to make it tameh. How do we understand the Chachamim? If the terumah is batel, and the replacement, which is treated as terumah can be eaten, it would seem that the tumah is also batel.
The Gemara explains that the Chachamim were concerned that the separated part would get mixed with other, slightly less chulin that was tameh. One would assume that the tameh chulin would be annulled in the majority of the mixture. However, since the original portion contained some tameh terumah, it would be "reawakened" such that the tumah parts are not in the minority and not annulled.
Importantly, Rashi understands that this explanation is important for both the opinions of R' Eliezer and the Chachamim. It explains why, according to R' Eliezer the remainder must be eaten in a way it will not become tameh. Since he treats the separated terumah like the one that fell in, one could assume that none of the original tameh terumah remained. Similarly, it explains why the separated terumah according to the Chachamim is also treated in this way. Rashi explains that the Chachamim would maintain that even the remainder should also be consumed in this fashion. In summary, since that which is removed, according to R' Eliezer, is treated like the original terumah, and according to the Chachamim is given to the kohen to be consumed, one might mistakenly think that the issue with the original tumah terumah is resolved, and not realise that if further tumah was added, it could combine with the original terumah temeah that was mixed in. The careful treatment of the remainder according to R' Eliezer and the entire amount according to the Chachamim ensures that that mistake is not made.
The Rambam however rules that only the removed portion must be treated in the way. Furthermore, R' Chaim Kanievsky ztzl (Beur Halacha 14:13) notes that the Rambam teaches the case of tahor terumah that is mixed with tameh terumah in the same halacha to which the gezeira described in Bechorot would not apply. R' Chaim asserts that the Rambam understood that the Gemara only provided an explanation for R' Eliezer as to why the remainder must be eaten in a way that ensure it remains tahor. The concern is only really for R' Eliezer who treats the replacement like the original, that one might thing that no tumah remains. How then do we understand the position of the Chachamim?
R' Chaim cites the Shita Mekubetzet, that the Chachamim did not completely dismiss the terumah tameah. R' Chaim notes that the Chachamim treated that which is removed as terumah. Granted that they did not treat it like the terumah that fell in, nevertheless a hint of the original tameh terumah remained. Indeed, the kohen is allowed to eat that separated terumah since one can assume that they are eating tahor food. Nevertheless, one needs to be concerned that the small tumah amount should not make the separated part tameh. This logic only applies to the part that is removed because it is treated as terumah. For the remained however, once it is annulled, it is completely annulled and there is no concern.
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