Before us is Mishnah 2 in Chapter 4 - a cryptic Mishnah whose meaning cannot be understood from its wording alone. Several explanations have been offered for it, and we will focus on the two explanations brought by the Bartenura. The proper way to learn this Mishnah is to first read its wording and translate it word by word, without getting into the substance, in order to appreciate the difficulties in understanding it; only afterwards should we turn to the Bartenura's two approaches.
The text of the Mishnah:
"Mi shehayu peirosav bimgurah" - someone who has produce, let us say grain, in the storage bin where the grain is kept.
"V'nasan se'ah l'Levi" - a se'ah is a measure, let us say twelve liters, which he gave to a Levi.
"U'se'ah l'ani" - a second se'ah, another twelve liters, which he gave to a poor man.
"Mafrish ad shemonah se'in v'ochlan" - he separates another eight se'in, and eats them.
"Divrei Rabbi Meir" - this is the opinion of Rabbi Meir.
"Va'chachamim omrim, eino mafrish ela lefi cheshbon" - in the opinion of the Sages, he separates and eats only according to the calculation.
As you can see, the meaning of the Mishnah is quite obscure. The Bartenura offers two explanations for it, entirely independent of one another.
The Bartenura's first explanation:
The case is set up with the owner, the farmer who owns the produce, being an am ha'aretz - meaning he cannot necessarily be relied upon to have tithed his produce properly, as we learned in Maseches Demai. The worker he hired, on the other hand, is a chaver, who is careful and precise in separating tithes properly. The halachah is that a chaver may not rely on an am ha'aretz to have tithed properly, and this is the foundation of all of Maseches Demai.
In the time of the Mishnah it was extremely common for workers to receive food from their employer as a matter of course, since most people made a subsistence living from farming or from labor, and providing food for a worker was an inseparable part of his terms of employment. From here arises the problem of the worker in our case: he cannot eat the food that his farmer employer supplies him without first verifying that the proper tithes were separated from it.
The case in the Mishnah, then, is this: the worker, who is a chaver and is careful about tithes, saw his farmer employer give a vessel containing a se'ah of grain to a Levi, and afterwards a second vessel containing a se'ah to a poor man. It was not specified whether these gifts were given as maaser rishon to the Levi and maaser ani to the poor man, or whether they were simply given as a present. The Mishnah says in the name of Rabbi Meir that the worker who is a chaver may safely assume that these were indeed maaser rishon and maaser ani.
This means that at the starting point there were about ten se'in of grain requiring tithing: ten percent goes to maaser rishon, and another ten percent to maaser ani. The numbers are admittedly not entirely precise, but the Mishnah is often not exacting about this, and it is not its concern here. Based on these assumptions, the worker may assume that the gifts were maaser rishon and maaser ani, and that eight se'in of properly tithed food now remain that he is permitted to eat.
As for Terumah gedolah - there is no concern here at all. The rule, as we learned in Maseches Demai, is that an am ha'aretz can be relied upon to have separated Terumah gedolah properly. Beyond that, the worker could not have seen it separated in the storage bin, since the time for Terumah gedolah is immediately upon the completion of the processing, and it was therefore separated back at the threshing floor. It emerges that there is no concern of Terumah gedolah, and maaser rishon and maaser ani have already been given, and therefore the worker may assume that the grain is properly tithed and eat from it up to a total of eight se'in. These are the words of Rabbi Meir.
The Sages say that he cannot necessarily assume this. Perhaps the gift given to the Levi was merely a present, and only the amount needed to permit the current meal was given as maaser rishon; and the same regarding the gift given to the poor man - perhaps it was given as a general gift and not as maaser ani, and only the minimum was separated as maaser ani. For the employer knows that the worker must eat, and so he presumably saw to it that at least the meal in front of him was properly tithed. After the worker saw the gifts being given, he may therefore assume that the grain is properly tithed only up to the amount of the current meal - and this is the meaning of "lefi cheshbon": the calculated amount of food for that meal. But at the next meal he once again cannot assume that the food is properly tithed, and the usual demai problems return, which he will have to separate and deal with, and that is not the concern of this Mishnah.
The text of the Mishnah according to the first explanation:
"Mi shehayu peirosav bimgurah" - a farmer who has produce stored in a granary.
"Venasan se'ah leLevi use'ah le'ani" - the worker saw that the owner of the produce gave one se'ah to a Levite and a second se'ah to a poor man, and he may assume that they were given as Maaser Rishon and Maaser Ani respectively.
"Mafrish ad shemonah se'in ve'ochlan, divrei Rabbi Meir" - from here he may separate another eight se'in from the granary, making ten in all, and everything is properly tithed and there is no problem.
"Vachachamim omrim, eino mafrish ela lefi cheshbon" - he may not make that assumption; rather he separates only for the meal in front of him, and beyond that he must be concerned that what is served to him at the next meal may not have been properly tithed.
The second explanation of the Bartenura:
Here we are dealing with an entirely different case, and one must erase the whole previous picture and paint a new one, even though the words are the very same words. There are no workers and employers here at all, but a single person: the owner of the field and of the produce, who has grain in his storehouse that requires tithing. He has not yet decided which produce he wishes to tithe, and it is possible that for some reason he will prefer one batch over another. A Levite comes and knocks at his door, and he gives him a se'ah of grain; afterwards a poor man comes and asks him for food, and he gives him too a se'ah of grain.
Afterwards the householder goes to the barn and says: I hereby tithe ten se'in of grain. He now chooses the produce retroactively, and declares: the grain in the hands of the Levite shall be Maaser Rishon, and the grain in the hands of that poor man, wherever he has gone, shall be Maaser Ani; and with that the ten se'in are properly tithed, and eight se'in remain in my possession which I may eat. In other words, according to Rabbi Meir he may assume that the Levite still holds his se'ah of grain intact, and so too the poor man, and these gifts will serve as the source for separating the tithes required from those eight se'in that remain in the barn.
And the Sages say: absolutely not. Who says the Levite did not eat the grain, and who says the poor man did not eat his? And if the poor man ate part of the grain or all of it, it can no longer serve as the gift of Maaser Ani and be designated as tithe for the eight se'in in the barn. Therefore the owner of the produce does nothing until he clarifies how much is left of the Maaser Rishon and of the Maaser Ani, and only on the basis of that updated information does he separate: if it turns out that only half of each remains, he cannot eat eight se'in but only four, for that is all that is available to him. He does not rely on the assumption that the grain is still in their possession; rather he clarifies the matter anew and separates according to that reckoning.
The wording of the Mishnah according to the second explanation:
"Mi shehayu peirosav bimgurah" - the householder has a large amount of grain in his storehouse.
"Venasan se'ah leLevi use'ah le'ani" - he gave one vessel holding a se'ah to a Levite, and a second vessel holding a se'ah to a poor man, without declaring them at that time to be Maaser Rishon and Maaser Ani.
"Mafrish aleihen shemonah se'in ve'ochlan, divrei Rabbi Meir" - at a later time he takes another eight se'in from the storehouse and says: the Maaser Rishon is lying in the hand of the Levite, and the Maaser Ani in the hand of the poor man who went on his way, and these shall serve as the tithes for a total of ten se'in; eight remain in my possession, and those I eat. Rabbi Meir permits this, since the householder may confidently assume that the grain he gave to the Levite and to the poor man is still intact.
"Vachachamim omrim, eino mafrish ela lefi cheshbon" - he does not separate tithes until he first clarifies what actually remains of the Maaser Rishon and of the Maaser Ani, and only then does he tithe what is left in the granary according to the updated reckoning of what remains of those gifts.
In summary: we have learned two explanations in the Bartenura for this cryptic Mishnah. According to the first explanation the Mishnah deals with a chaver working for an am ha'aretz employer and eating from his food, and with the question of whether he may assume that the gifts he saw were given as Maaser Rishon and Maaser Ani. According to the second explanation the Mishnah deals with the householder himself, and with the question of whether he may determine retroactively that the gifts he gave will serve as tithes for the grain in his storehouse. And whatever the plain meaning may be, the halachah is certainly like the Sages.