Here we have a wonderful Mishnah - Mishnah 13 in the fourth chapter of Maseches Terumos - which deals with the question of whether a meduma mixture can become nullified within a larger mixture.
Presenting the case:
A bundle of vegetables that is half Terumah and half chullin has a well known status: the chullin is not one hundred times the amount of the Terumah, and therefore the entire mixture is forbidden and is treated as Terumah. Such a mixture is called meduma. Now let us add another layer: before us are fifty identical bundles of pure chullin, and into them fell that meduma bundle, which we relate to as Terumah. How do we calculate the ratio between the permitted and the forbidden?
There are two possible approaches:
Counting whole bundles: There are fifty bundles of chullin against one meduma bundle. That is not one hundred times as much, and therefore the entire mixture is forbidden.
Counting halves: In the fifty bundles of chullin there are one hundred half bundles of chullin, and against them only a single half bundle of Terumah - and this is without even including the half bundle of chullin found within the meduma bundle itself. It turns out that there are one hundred against one, the Terumah is nullified, and the entire mixture is permitted.
The words of the Mishnah:
"Amar Rabbi Yosei: ma'aseh ba lifnei Rabbi Akiva b'chamishim agudos shel yarak, shenaflah achas mehen l'sochan" - Rabbi Yosei said: a case came before Rabbi Akiva involving fifty bundles of chullin vegetables, into which fell a fifty first bundle that was half Terumah, that is, a meduma bundle. The question is as described above: do we count fifty bundles of chullin against one meduma bundle, in which case everything is forbidden, or do we count one hundred and two halves, only one of which is Terumah, in which case everything is nullified and permitted.
"V'amarti lefanav: ta'aleh" - Rabbi Yosei ruled in Rabbi Akiva's presence that the Terumah is nullified and the entire mixture is permitted. "Lo shehaTerumah ta'aleh b'echad v'chamishim, ela shehayu sham me'ah ushnei chatza'im" - the reason is not that fifty one bundles are enough to nullify Terumah. Rather, there are not fifty one bundles here with one of them being meduma, but one hundred and two half bundles, only one of which is Terumah - and that ratio is sufficient to nullify it.
Rabbi Akiva did not respond with any objection, which indicates that he agreed with him, and the halachah follows Rabbi Yosei.
In summary: We have learned that when a meduma bundle falls into bundles of chullin, we do not count whole bundles. Instead, we break the calculation down into halves, and once we find a ratio of one hundred against one, the Terumah is nullified and the mixture is permitted.
In the next section, in Mishnah 6 of chapter 5, we will return to this topic and ask what our Mishnah is teaching us that is new. A small hint: here all the components of the prohibition are mixed in together, whereas there only some of them become mixed in.