Demai, Chapter Seven, Mishnah Seven
In this mishnah we learn how one remedies a situation in which produce of varying status (untithed, tithed, etc.) becomes mixed up with produce of a different status.
This mishnah is quite difficult, so be forewarned.
1) One hundred [parts of] tevel which [were mixed with] a hundred [parts of] common produce, one must take out a hundred and one [parts].
2) One hundred [parts of] tevel which [were mixed with] a hundred [parts of first] tithe, one must take out a hundred and one [parts].
3) One hundred [parts of] common produce from which tithes had been separated [were mixed with] a hundred [parts of] tithe, one must take out a hundred and ten [parts].
4) One hundred [parts of] tevel [were mixed with] ninety [parts of] tithe, or ninety [parts of] tevel [were mixed with] eighty [parts of] tithe, he has not lost anything.
5) This is the general rule: whenever the tevel is the greater [portion of the mixture] he has not lost anything.
Section one: The tevel mentioned throughout this mishnah is not regular tevel, from which no terumah or tithes have been removed, but tevel similar to demai, from which terumah has already been taken. Terumat maaser (the terumah taken from the tithe) and maaser have not been removed. One hundred parts of this tevel produce then becomes mixed up with one hundred parts of common produce, produce from which all tithes and terumah have already been separated. The owner wants to take out the terumat maaser from this mixture, because if he doesnt he wont be able to eat any of the mixture. So first, from this mixture he takes out 101 parts, one of which is certainly the untithed produce. He can then make one of these into terumat maaser for the 100 parts of tevel which had not had terumat maaser removed. What he says is that nine parts of the 101, along with the one that he has in his hand are tithe, and that the one in his hand is terumat maaser for this tithe. He still cant eat any of these 101 parts, because he is not sure that the one in his hand is the one part that came from the untithed produce. But he can sell the 100 of the 101 parts to a priest because only one of them is actually owed to the priest. The priest will buy them at a lower price; terumah is cheaper than common produce, because there is a much smaller market for terumah. The value of the one part he must give for free, because he owes one part as terumat maaser. The other 99 parts are his to do as he wishes. If they were originally the common produce, then there is no problem. And if they were tevel, then he has taken out the terumat maaser. In this way, he takes out 99 parts that become totally his, and 100 parts that he can sell, albeit at a reduced price.
Section two: In this case, 100 parts of tevel are mixed in with 100 parts tithe from which terumat maaser has not been removed. In this mixture there are now 11 parts terumat maaser (one from the tevel, and ten from the tithe). Again, he takes out 101 parts, and sells them all to a priest, subtracting the value of 11 parts, which he owes the priest as terumat maaser. The 99 that remain are his, for whether they were originally from the tevel or from the tithe, he has taken out terumat maaser for them. What he cannot do is simply take out 11 parts from the original mixture, because some of these parts may have been from the tevel and from 100 parts of tevel, one cant give eleven parts terumat maaser, because terumat maaser has to be separated from tithe, and there are only ten parts tithe in one hundred parts of produce.
Section three: In this case, 100 parts tithed produce get mixed up with one hundred parts of tithe. There are now 10 parts terumat maaser in this mixture. He must take 110 parts of the mixture, since in 110 parts there are certainly ten parts that come from the tithe and these ten parts become the terumat maaser. He can sell the 110 parts to a priest, subtracting the value of ten parts which he has to give to the priest. The other 90 parts are his to keep.
Section four: In the final example, 100 parts of tevel become mixed in with a lower amount of tithe. In these cases he doesnt lose out at all. For instance in the case of 100 parts tevel mixed in with 90 parts tithe, he takes out ten parts (this is the actual amount of terumat maaser in the mixture, ten from the tithe and one from the tevel) and stipulates: If these are from the tevel, then they are tithe for the 100 parts of tevel. Now I also have 100 parts tithe left, and I am going to use these 10 parts as terumat maaser for the tithe. If these ten parts were from the tithe, then I am separating out from the mixture the tevel, wherever it may be, leaving one hundred tithe in the mixture (10 from the tevel and the 90 of the tithe). The ten that I have in my hand are now terumat maaser for the one hundred part tithe. The same method can be applied to other mixtures, although the numbers will have to be slightly adjusted. As long as there is more tevel in the mixture then the tithe, he doesnt lose out at all.