As we have learned, the laws of ĥametz are uniquely strict: even a miniscule amount of ĥametz mixed with a permitted food renders the entire mixture forbidden for consumption or benefit. However, most poskim maintain that if the ĥametz is less than one sixtieth of the mixture, one may salvage its monetary value by selling it to a gentile. For example, if a kilogram of ĥametz falls into a metric ton of another food, it is permitted to sell the mixture to a gentile as long as one first throws away a kilogram of the mixture in order to avoid benefiting from the added ĥametz. This is because when the Sages forbade benefiting from such mixtures, their intention was to forbid benefiting from the ĥametz as well. Thus, if one disposes of a quantity of the mixture equaling the amount of ĥametz that was added, he does not benefit from the ĥametz, and he can then sell the mixture to a gentile. If a single wheat grain of ĥametz fell into a large amount of cooked food, it all becomes forbidden to eat and benefit from as long as it remains in a Jew’s hands, but one may sell it to a gentile. It is not necessary to dispose of any of the mixture, because the wheat did not cause the price to rise (SA 467:10).
Rema (447:1), however, rules stringently in accordance with the opinion of a few Rishonim who maintain that since it is forbidden to derive benefit from the mixture, it is likewise forbidden to sell it to a gentile. Instead, the entire mixture must be destroyed. This is the practice of Ashkenazic Jews. However, if this will result in a very great loss, even those who follow the Ashkenazic custom may rely upon the opinion of those who permit selling the mixture to a gentile (MB 447:3).
. There is a dispute as to whether or not one is forbidden to derive benefit from a mixture of ĥametz and non-ĥametz. According to Rif, Rosh, and the majority of poskim, ĥametz causes the entire mixture to become forbidden, whereas Ramban and Raavad maintain that the mixture is only prohibited for eating, but it is permissible to derive benefit from it. SA 447:1 adopts the former view.
However, according to Rif and Rosh, if one would discard the value of the ĥametz in the mixture, he would be permitted to sell the mixture to a gentile, since ultimately he obtains no benefit from the ĥametz; rather, he merely receives payment for the portion of the mixture that is not ĥametz. The overwhelming majority of poskim, including SA 467:10, agree with this. However, Rema writes in Darkhei Moshe 447:2 that Mordechai, Terumat Ha-deshen, and Mahari Brin all adopt a stringent approach – that the entire mixture must be burned. MB 447:3 states in the name of Aĥaronim that in a situation of potential severe monetary loss one may sell such a mixture to a gentile. Additionally, SHT 467:74 in the name of Beit Meir states that if one will suffer severe monetary losses despite selling the mixture to a gentile, he may even keep the mixture until after Pesaĥ, and then eat it or sell it to a Jew.