The Shulhan Aruch (Orah Haim 319:1) delineates three conditions that must be met for Borer – separating mixed substances from one another – to be permissible on Shabbat:
1) One must separate the Ochel (edible food) from the Pesolet (inedible food), and not the other way around.
2) One must separate "Be’yad" – by hand, and not with a utensil.
3) One must separate "Mi’yad" – for immediate purposes, and not for a later time.
The first condition, that the edible food must be separated from the inedible food, is based on the premise that the normal process eating entails taking food and placing it in one’s mouth. Removing the Ochel from the Pesolet is thus considered eating, and not an act of separating, and is therefore permissible on Shabbat.
Tosafot (Talmud commentaries by Medieval French and German scholars), however, in Masechet Shabbat (74), impose an important restriction on this Halacha. They claim that this condition applies only if there is more edible food than inedible food. In such a case, the normal way of separating would be to remove the inedible food, which would be far simpler given that it is the minority. In order to avoid the Torah prohibition against separating on Shabbat, therefore, Halacha requires separating the Ochel from the Pesolet, which is the abnormal manner of separating in such a case. If, however, there is more Pesolet than Ochel, then the normal method of separating would be to separate the edible food from the inedible substance. In order to avoid the prohibition of Borer, one would have to separate in the opposite manner, removing the Pesolet from the Ochel. According to Tosafot, then, before separating two substances that are mixed together, one must first determine which substance constitutes the majority and which constitutes the minority, as this will determine the Halachically permissible method of separation.
The Be’ur Halacha (Rav Yisrael Meir Kagan of Radin, 1839-1933) cites Halachic authorities who note than the Shulhan Aruch did not accept Tosafot’s position, or even take it into account at all. According to the Shulhan Aruch, the respective proportions of the Ochel and Pesolet are of no Halachic consequence with regard to the laws of Borer, and in all situations, one must remove the edible food from the inedible food, and not the other way around. This is the ruling of Sephardic Chief Rabbi Shelomo Amar, in his work of responsa Shema Shelomo (Orah Haim 10:1), and this is, indeed, the accepted Halacha.
Summary: If edible food is mixed with an inedible substance, one may remove the edible food from the inedible substance, but it is forbidden to remove the inedible substance from the edible food. This applies regardless of which of the two substances constitutes the majority in the mixture.
