Halacha

הלכה א
הַפֵּרוֹת שֶׁהוּרַם מֵהֶן תְּרוּמָה גְּדוֹלָה וּתְרוּמַת מַעֲשֵׂר הֵן הַנִּקְרָאִין חֻלִּין. וְאִם הִפְרִישׁ מֵהֶן שְׁאָר מַעַשְׂרוֹתֵיהֶן הֵן הַנִּקְרָאִין חֻלִּין מְתֻקָּנִין בְּכָל מָקוֹם:
כסף משנה
1.
Produce from which the great terumah and terumat ma'aser have been separated are referred to as "ordinary produce."1I.e., because the elements of the produce that are sacred have been removed from it [the Rambam's Commentary to the Mishnah (Demai 7:7)]. Terumat ma'aser should not be separated before the tithes themselves. Nevertheless, if one made such a separation, it is acceptable (Chapter 9, Halachah 5). When the other tithes have been separated from it, it is universally called "ordinary produce that has been made acceptable."

הלכה ב
טֶבֶל שֶׁנִּתְעָרֵב בְּחֻלִּין מְתֻקָּנִין מִין בְּמִינוֹ שֶׁאִי אֶפְשָׁר לְהַלֵּךְ אַחַר הַטַּעַם. אִם יֵשׁ לוֹ פֵּרוֹת אֲחֵרוֹת מוֹצִיא עַל אוֹתוֹ טֶבֶל תְּרוּמָה וּמַעַשְׂרוֹת לְפִי חֶשְׁבּוֹן. וְאִם אֵין לוֹ פֵּרוֹת אֲחֵרוֹת לְהוֹצִיא עַל אוֹתוֹ טֶבֶל הֲרֵי הַכּל אָסוּר עַד שֶׁיַּפְרִישׁ. וּכְשֶׁהוּא מַפְרִישׁ מַפְסִיד מִן הַחֻלִּין הַמְתֻקָּנִין כְּדֵי תְּרוּמַת מַעֲשֵׂר שֶׁבַּטֶּבֶל:
כסף משנה
2.
[The following laws apply when] tevel2In this instance, the term tevel refers to produce from which the tithes and terumat ma'aser have not been separated. Although the term has a more inclusive meaning, from the continuation of the Rambam's words, this appears to be the intent here. becomes mixed together with the same species of ordinary produce that has been made acceptable in which instance, [the tevel cannot be considered insignificant] because its flavor [cannot be detected].3I.e., were the tevel to be of another type of produce than the ordinary produce, the question of whether or not it is considered insignificant would depend on whether its flavor is detectable. In this situation, however, the two collections of produce are of the same species, so taste is not a factor and the tevel cannot be considered as insignificant.
When tevel is mixed with its own species, it is never nullified even if it is mixed with far more than its own size. The rationale is that it is a devar sheyeish lo matirin, i.e., the prohibition can be corrected by making the appropriate separations (Hilchot Issurei Ma'achalot 15:6).
If he has other produce, he should separate the terumat [ma'aser] and the tithes for the tevel according to the appropriate reckoning.4I.e., if he knows how much produce was mixed in, he can make the appropriate separations even if the produce itself is not distinct. If he does not have other produce from which to make the separations for that tevel, the entire mixture is forbidden until he makes separations from it. When he makes these separations, he forfeits a portion from the ordinary produce that has been made acceptable that is equivalent to the terumat ma'aser that must be separated from the tevel.5I.e., one hundredth of the tevel. The Rambam explains what he means by forfeiting this amount and why one must do so in the following halachah.

הלכה ג
כֵּיצַד. מֵאָה סְאָה שֶׁל טֶבֶל שֶׁנִּתְעָרֵב בְּמֵאָה סְאָה שֶׁל חֻלִּין מְתֻקָּנִין מַפְרִישׁ מִן הַכּל אֶחָד וּמֵאָה. וְכָל שֶׁהִפְרִישׁ טֶבֶל וְיִשָּׁאֵר צ''ט חֻלִּין מְתֻקָּנִין נִמְצָא מַפְסִיד סְאָה אַחַת. וְכֵן אִם הָיָה אוֹתוֹ טֶבֶל טָבוּל לִתְרוּמָה מַפְסִיד מִן הַחֻלִּין הַמְתֻקָּנִין כְּדֵי תְּרוּמָה וּתְרוּמַת מַעֲשֵׂר. וְלָמָּה מַפְסִיד סְאָה זוֹ כְּדֵי שֶׁלֹּא יֹאמַר מֵאָה שֶׁהִפְרִישׁ הֵן מֵאָה שֶׁל חֻלִּין וְהַמֵּאָה שֶׁנִּשְׁאֲרוּ הוּא הַטֶּבֶל. וְכֵן אִם הָיָה הַטֶּבֶל פָּחוֹת מִן הַחֻלִּין אוֹ מְרֻבֶּה עַל הַחֻלִּין מַגְבִּיהַּ הַטֶּבֶל וּכְדֵי תְּרוּמַת מַעֲשֵׂר שֶׁבַּטֶּבֶל מִן הַחֻלִּין אוֹ כְּדֵי תְּרוּמָה וּתְרוּמַת מַעֲשֵׂר אִם הָיָה הַטֶּבֶל טָבוּל לִתְרוּמָה:
כסף משנה
3.
What is implied? If 100 se'ah of tevel is mixed with 100 se'ah of ordinary produce that has been made acceptable, he should separate 101 [se'ah] from the entire mixture. Everything that he sets aside is considered as tevel. Thus 99 se'ah of ordinary produce that has been made acceptable remain. He has thus lost a se'ah [of the ordinary produce].6I.e., it is considered as if the se'ah of terumat ma'aser fell into the ordinary produce in which instance, it would be necessary to remove one se'ah from the mixture [the Rambam's Commentary to the Mishnah (Demai 7:7)]. Similarly, if terumah had also not been separated from the tevel, he must forfeit an amount from the ordinary produce that has been made acceptable that is equivalent to the terumah and terumat ma'aser [to be separated from the tevel].7I.e., three se'ah, two se'ah for the great terumah and one se'ah for the terumat ma'aser.
Why must he forfeit this se'ah?8For the se'ah that will ultimately be separated from the tevel can be considered as the se'ah that must be removed from the ordinary produce (ibid.). So that he will not say: "The 100 se'ah that I set aside are ordinary produce and the 100 that remain are tevel."9For the opposite is true, the produce that remains is the ordinary produce (ibid.). Similarly, if the amount of the tevel exceeded or was less than ordinary produce, one should separate [an amount equivalent] to the tevel and [an amount] from the ordinary produce [equivalent] to the terumat ma'aser [to be separated from the tevel] or equivalent to the terumah and terumat ma'aser [to be separated] if it was tevel from which terumah was not separated.

הלכה ד
וְכֵן אִם נִתְעָרֵב מַעֲשֵׂר טָבוּל בְּחֻלִּין מְתֻקָּנִין אוֹסֵר בְּכָל שֶׁהוּא. אִם יֵשׁ לוֹ מַעֲשֵׂר אַחֵר מוֹצִיא אוֹתוֹ עַל מַעֲשֵׂר הַטָּבוּל תְּרוּמַת מַעֲשֵׂר לְפִי חֶשְׁבּוֹן. וְאִם אֵין לוֹ מַעֲשֵׂר מַגְבִּיהַּ הַמַּעֲשֵׂר שֶׁנִּתְעָרֵב וּמַפְסִיד מִן הַחֻלִּין הַמְתֻקָּנִין כְּדֵי תְּרוּמַת מַעֲשֵׂר שֶׁבַּמַעֲשֵׂר הַטָּבוּל:
כסף משנה
4.
Similarly, if tithes10I.e., produce that had been separated as the tithes. Beforehand, terumah had been separated. that were tevel11I.e., a person separated tithes and gave them to a Levite who did not separate terumat ma'aser from them as of yet. became mixed with ordinary produce that has been made acceptable, even the slightest amount causes the mixture to be prohibited. If the person has other tithes, he should make a separation for the terumat ma'aser for the tithes that require this according to the appropriate proportion.12Setting aside one tenth of the quantity of the tithes. This is the desired approach, because then the necessary separations are being made without losing anything. If he does not have other tithes,13And thus cannot exercise the above option. he should remove the tithes and forfeit from the ordinary produce that has been made acceptable an amount equal to the terumat ma'aser in the tithes.14I.e., one tenth of the tithes.

הלכה ה
כֵּיצַד. מֵאָה מַעֲשֵׂר שֶׁנִּתְעָרֵב בְּמֵאָה חֻלִּין מְתֻקָּנִין מַפְרִישׁ מִן הַכּל מֵאָה וְעֶשֶׂר וְכָל שֶׁהִפְרִישׁ מַעֲשֵׂר וְהַתִּשְׁעִים הַנִּשְׁאָרוֹת הֵן חֻלִּין כְּשֶׁהָיוּ. וְכֵן אִם הָיוּ הַחֻלִּין מְרֻבִּין עַל הַמַּעֲשֵׂר הַטָּבוּל אוֹ פְּחוּתִים מִמֶּנּוּ מַפְרִישׁ הַמַּעֲשֵׂר וּכְדֵי תְּרוּמַת מַעֲשֵׂר שֶׁבַּמַעֲשֵׂר הַטָּבוּל מִן הַחֻלִּין:
כסף משנה
5.
What is implied? 100 [se'ah of] tithes become mixed with 100 [se'ah of] ordinary produce that has been made acceptable. He should separate 110 se'ah from the entire mixture. Everything that he separates is considered as the tithes. The 90 [se'ah] that remain are ordinary produce as before. Similarly, if the amount of the ordinary produce exceeds or is less than that of these tithes, he should separate the tithes and from the ordinary produce, an amount equivalent to the terumat ma'aser in the tithes.15In his Commentary to the Mishnah (op. cit.), the Rambam explains that this ruling is given because the situation at hand is an intermediate level between an instance where terumat ma'aser becomes mixed with ordinary produce (in which instance 101 times the amount of terumat ma'aser would be necessary) and a situation where the terumat ma'aser need not be considered at all. There is a basis for such leniency, since ultimately, no separation had been made and terumat ma'aser was never mixed with the produce. On the other hand, since a tenth of the tithes is fit to be separated as terumat ma'aser, some recognition should be made. Hence our Sages arrived at the above compromise.

הלכה ו
טֶבֶל שֶׁנִּתְעָרֵב בְּמַעֲשֵׂר טָבוּל אִם הָיָה הַטֶּבֶל כַּמַעֲשֵׂר מַפְסִיד מִן הַטֶּבֶל כְּדֵי תְּרוּמַת מַעֲשֵׂר שֶׁבּוֹ. כֵּיצַד. מֵאָה סְאָה טֶבֶל שֶׁנִּתְעָרֵב בְּמֵאָה סְאָה מַעֲשֵׂר מַפְרִישׁ אֶחָד וּמֵאָה וְזֶה שֶׁהִפְרִישׁ מַעֲשֵׂר וְתִשְׁעִים וְתֵשַׁע הַנִּשְׁאָרוֹת טֶבֶל. הָיָה הַטֶּבֶל מְרֻבֶּה עַל הַמַּעֲשֵׂר מַפְרִישׁ הַמַּעֲשֵׂר בִּלְבַד. וְלֹא יַפְסִיד מִן הַטֶּבֶל כְּלוּם שֶׁאִם יִקְרָא שֵׁם לִתְרוּמַת מַעֲשֵׂר שֶׁנִּטְבַּל נִמְצָא הַמַּעֲשֵׂר מְדֻמָּע בִּתְרוּמַת מַעֲשֵׂר שֶׁל טֶבֶל שֶׁעָלְתָה עִמּוֹ. הָיָה הַמַּעֲשֵׂר מְרֻבֶּה עַל הַטֶּבֶל קוֹרֵא שֵׁם לִתְרוּמַת מַעֲשֵׂר [שֶׁבַּטֶּבֶל] וּמַפְרִישׁ הַטֶּבֶל וּכְדֵי תְּרוּמַת מַעֲשֵׂר שֶׁל טִבְלוֹ אֶחָד מִמֵּאָה מִן הַמַּעֲשֵׂר וְיִהְיֶה הַטֶּבֶל כֻּלּוֹ מְדֻמָּע וְיִמְכְּרֶנָּה לְכֹהֵן חוּץ מִדְּמֵי שְׁתֵּי תְּרוּמוֹת שֶׁבּוֹ וְנִמְצָא מַפְסִיד מִן הַמַּעֲשֵׂר אֶחָד מִמֵּאָה שֶׁבּוֹ שֶׁהוּא כְּמוֹ תְּרוּמַת מַעֲשֵׂר שֶׁבַּטֶּבֶל. כֵּיצַד. מֵאָה טֶבֶל עִם מָאתַיִם מַעֲשֵׂר מַפְרִישׁ מֵאָה וְשָׁלֹשׁ וְהַשָּׁלֹשׁ הֵן תְּרוּמַת מַעֲשֵׂר שֶׁל מֵאָה טֶבֶל וְשִׁעוּר תְּרוּמַת מַעֲשֵׂר מִמָּאתַיִם כְּדֵי שֶׁלֹּא יָבוֹא לִטְעוֹת אִם נִתְעָרְבוּ בִּכְמוֹתוֹ וְיִשָּׁאֵר קצ''ז וְהֵם מַעֲשֵׂר כְּשֶׁהָיוּ:
כסף משנה
6.
[The following laws apply when] tevel becomes mixed together with tithes16I.e., produce that had been separated as the tithes. Beforehand, terumah had been separated. that were tevel.17I.e., a person separated tithes and gave them to a Levite who did not separate terumat ma'aser from them as of yet. If the amount of tevel was equivalent to the amount of the tithes, he must forfeit from the tevel an amount equivalent to the terumat ma'aser it contains.18I.e., 1/100th of the tevel.
What is implied? There were 100 se'ah of tevel that became mixed with 100 se'ah of tithes. He should separate 101 [se'ah]; they are considered as tithes.19The se'ah of terumat ma'aser from the tevel that is added is considered as mixed in with the tithes (ordinary) produce and therefore betal, subsumed, in it. Hence the person can make use of the produce in the ordinary manner. The 99 remaining are considered as tevel.20The Ra'avad differs with the Rambam. The commentaries justify the Rambam's view.
If there was more tevel than tithes, he should separate the tithes alone and he does not forfeit anything from the tevel. For if he would designate the terumat ma'aser of the tevel,21And thus separate an additional amount. the tithes would be meduma,22A mixture of terumah and ordinary produce. An ordinary person cannot benefit from such a mixture. Instead, it must be sold to a priest at the price of terumah with the exception of the price of the portion that is terumat ma'aser, as the Rambam continues to explain. The tithes would be meduma, because there would not be enough ordinary produce for the terumat ma'aser to be subsumed within them. a mixture of [the tithes]23Which are ordinary produce. and the terumat ma'aser from the tithes which are separated together.
If there were more tithes than tevel, he should designate the terumat ma'aser in the tevel, setting aside the tevel and an amount equivalent to the terumat ma'aser for the tevel, i.e., one one-hundredth of the tithe. The tevel should be considered as if it is all meduma and sold to a priest with the exception of the worth of the two [portions of] terumah in it. Thus he will forfeit one hundredth of the tithes which is equivalent to the terumat ma'aser in the tevel.
What is implied? If there were 100 [se'ah] tevel with 200 [se'ah] of the tithes, he should set aside 103. The three [se'ah] are the terumat ma'aser of the 100 [se'ah] of tevel and the measure of terumat ma'aser for the 200 [se'ah of the tithes]. [This separation is necessary] so that people will not come to err if [the tithes] became mixed with an equivalent amount [of tevel]. Therefore he should leave 197 [se'ah] which will remain tithes as they were.24In this way, he is forfeiting from the tithes the amount of terumat ma'aser in the tithes and the amount of terumat ma'aser in the tevel. The Ra'avad differs with the Rambam and the commentaries support the Rambam's decision.

הלכה ז
מִי שֶׁהָיוּ לוֹ עֶשֶׂר שׁוּרוֹת שֶׁל עֶשֶׂר עֶשֶׂר כַּדֵּי יַיִן וְקָבַע כַּד אֶחָד מִשּׁוּרָה הַחִיצוֹנָה מַעֲשֵׂר עַל מָקוֹם אַחֵר וְאֵין יָדוּעַ אֵי זוֹ שׁוּרָה הַחִיצוֹנָה הִיא. נוֹטֵל שְׁתֵּי חָבִיּוֹת בַּאֲלַכְסוֹן וּמְעָרֵב שְׁתֵּיהֶן וּמַפְרִישׁ מֵהֶן:
כסף משנה
7.
[The following laws apply when a person] has [a stack with] ten lines, each containing ten barrels of wine and [the owner] allocated25The commentaries explain that we are not speaking about an instance where he actually set aside the barrel as tithes, for the Rambam concludes the halachah by saying that he should set aside the tithes. Instead, he merely pledged to separate a barrel from that surface for ten barrels of other wine. one barrel of the outer line26I.e., one of the external surfaces of the cube that is the pile [the Rambam's Commentary to the Mishnah (Demai 7:8)]. as tithes for other wine,27The Rambam mentions this point, because otherwise, one could rightly ask: Why does the Mishnah (ibid.) speak about only one barrel of wine as tithes for 100 barrels (Radbaz)? but he does not know which outer line [he intended]. He should take two barrels from [the corners] on a diagonal,28Our translation is taken from the Rambam's Commentary to the Mishnah (ibid.). The intent is that each of the barrels on the corners is part of two surfaces. Since he is taking a barrel from opposite corners, he will have certainly taken a barrel from the surface he intended. Nevertheless, since he does not know which one of the two is appropriate, he should mix them together. mix them, and separate [the tithes] from them.29Preferably, he should also use the remaining amount as tithes for other produce. Thus the barrel separated will be used entirely as tithes (Kin'at Eliyahu).

הלכה ח
קְבָעָהּ בַּחֲצִי שׁוּרָה הַחִיצוֹנָה וְאֵין יָדוּעַ אֵי זוֹ חֲצִי שׁוּרָה הִיא נוֹטֵל אַרְבַּע חָבִיּוֹת מֵאַרְבַּע זָוִיּוֹת. קְבָעָהּ בְּשׁוּרָה אַחַת מֵהֶן וְאֵין יָדוּעַ אֵי זוֹ שׁוּרָה הִיא נוֹטֵל שׁוּרָה אַחַת בַּאֲלַכְסוֹן. קְבָעָהּ בַּחֲצִי שׁוּרָה וְאֵין יָדוּעַ אֵי זוֹ חֲצִי שׁוּרָה הִיא נוֹטֵל שְׁתֵּי שׁוּרוֹת בַּאֲלַכְסוֹן שֶׁהֲרֵי נָטַל חָבִית מִכָּל חֲצִי שׁוּרָה וּמְעָרֵב וּמַפְרִישׁ:
כסף משנה
8.
If he allocated [one barrel from] the half30These and the following bracketed additions are made on the basis of the Rambam's Commentary to the Mishnah (loc. cit.). of an outer row [as tithes], but does not know from which [outer] half a row, he should take four barrels, [one] from each of the corners.31Each of the barrels is part of two outer half rows, so that the barrel he intended to allocate is certainly among these four barrels. If he allocated [a barrel from] one row, but does not know which row, he should take [a barrel] from a diagonal row.32By doing so, he will have taken a barrel from every row. If he allocated [a barrel from] half a row, but does not know which half a row, he should take [a barrel] from two diagonal rows.33In a criss-cross as depicted in the accompanying diagram. Thus he will be taking a barrel from each half row. He should then mix them together and separate [the tithes].

הלכה ט
קָבַע הַמַּעֲשֵׂר בְּכַד אַחַת מֵהֶן וְאֵין יָדוּעַ אֵי זוֹ הִיא נוֹטֵל מִכָּל כַּד וְכַד מִן הַמֵּאָה וּמְעָרֵב וּמַפְרִישׁ כְּדֵי כַּד אַחַת וּמְעַשֵּׂר:
כסף משנה
9.
If he allocated one barrel as tithes but does not know which barrel it is, he should take [some wine] from each of the 100 barrels, mix it together, and separate enough for one barrel as tithes.

זרעים הלכות מעשרות פרק ח
Zeraim Maaser Chapter 8