Commentary for Demai 5:2

נוטל אחד משלשים ושלש ושליש – which is one-third from one-hundred (i.e., thirty-three and one-third). And the Seah that he takes there has three thirds, two of them for the heave-offering which is two from one-hundred (i.e., 2/100 or 1/50) and one for the heave-offering of the tithe which is one out of one-hundred (i.e., 1/100). And he states regarding that Seah that he took one out of one-hundred that is here, whether all of it, which is a third of that Seah.

One who wishes to separate terumah and the terumat maaser together:
He should take one thirty third and say:
One hundredth part of what is here, on this side is non-sacred produce (, and the rest shall be terumah for the whole.
And the one hundred parts of non-sacred produce which is here on this side shall be tithe, and the rest that is next to it is tithe.
That which I made tithe shall become the terumat maaser for it.
The remainder will be hallah, and the second tithe tithe is to the north or to the south of it and that will be exchanged for money.”
In this mishnah a person wants to separate terumah and terumat maaser at the same time from his tevel, which is produce that we know has not been tithed. In other words, we are no longer discussing demai.
Terumah is supposed to be 1/50 of one’s produce. Together with terumat maaser, which is 1/100 of one’s produce, he must separate 3/100 or 1/33 of the produce.
I shall explain this procedure step by step.
1) The first thing he does is take 1/33, or 3/100 of the produce and separate it from the rest.
2) Then he says that 1/100 (meaning 1/3 of that which he separated) remains, for the meanwhile, non-sacred produce and the rest, meaning the other 2/100, is terumah. In this way he has fulfilled the requirement to separate teruamh. Note that he has to designate the terumah before he designates the tithe or the terumat maaser, the terumah taken from the tithe.
3) He now says that the other 1/100 that he separated is tithe, as well as the other 9/100 parts that are next to it, but still attached to the loaf. In this way he has separated 1/10 of the loaf to be tithe. Note that he must designate tithe before he declares that that which he separated should be terumat maaser.
4) Then he says that the 1/100 part that he separated is terumat maaser for the tithe that he has just designated. He has now successfully separated terumah and terumat maaser, all of which goes to the priest.
5) The final section about separating hallah and second tithe is missing in most manuscripts of the mishnah. It was probably accidentally brought here from the previous mishnah. It has nothing to do with our subject.

הרי הוא בצד זה חולין – its explanation: it should remain unconsecrated like it is now in is eatables that are forbidden pending the separation of sacred gifs at the side of the two-thirds that are with him, and the rest, which is two third-thirds will be heave-offering on everything.

מהחולין שיש כאן – that is the third that I spoke of that should remain unconsecrated, behold this is at the side of that tithe.

ושאר מעשר – that is another nine next to this one-third, those ten thirds will be a tithe on the one-hundred thirds. And not exactly ten, but rather a bit less according to the when we reach the [various] years of Terumah.

זה שעשיתי מעשר – that is the one-third that he designated by name to be Tithe first is made the heave-offering of the tithe on the nine thirds. But not a complete third, but rather missing a small amount. And for this it is stated from that unconsecrated that is here, which implies, but not all of the unconsecrated produce. But our Mishnah is like Abba Eleazar ben Gomel who stated at the end of the chapter כל הגט /”All bills of divorce” (Tractate Gittin 31a): just as the owner has the permission to separate the priestly gift of the Great Terumah (i.e., Terumah Gedolah – which is 1/50 which goes to a Kohen), so too he has the permission to separate the heave-offering of the tithe (i.e., the one-tenth of which the Levite ordinarily gives to the Kohen after receiving the First Tithe). And he is also permitted to separate the heave-offering of the tithe through a generous estimation in the chapter "כל המנחות באות מצה"/”All meal offerings are brought unleavened” (in the fifth chapter of Menahot 54b-55a), therefore, that one-third that he separates [to be donated] from the whole even though is was appropriate to be missing a little bit, with a generous portion/good will, he separates [these tithes] and it is permitted.