Generally speaking, when a piece of forbidden food falls into permissible food, we apply the rule of "Battel Be’shishim," which means that we consider the forbidden food "nullified" if it constitutes one-sixtieth or less of the mixture. If the proportion of permissible food to forbidden food is 60:1, or more, we may consider the forbidden food null and void, such that the entire mixture becomes permissible for consumption.
When it comes to Pesah, however, this is not the case. The Shulhan Aruch, following the position of the Rif (Rav Yishak Alfasi, Morocco, 1013-1103), rules that if a piece of Hametz falls into non-Hametz food on Pesah, the mixture becomes forbidden regardless of how small a proportion the Hametz constitutes. Hametz in even the smallest proportion – a "Mashehu" – renders the entire mixture forbidden for consumption on Pesah. This is why special care must be taken on Pesah to ensure that not even a crumb or tiny morsel of Hametz comes in contact with our food or utensils.
However, this Halacha applies only when Hametz falls into food during Pesah. If a small amount of Hametz falls into food before Pesah, then we apply the standard rule of "Battel Be’shishim," and we consider the mixture free of Hametz as long as there is a proportion of 60:1 or higher of non-Hametz food to Hametz. Accordingly, the Shulhan Aruch rules (Orah Haim 477:4) that such a mixture is permissible for consumption on Pesah. Since the Hametz fell into the food before Pesah, and it was "Battel" ("nullified"), the mixture is permissible on Pesah, and we do not say that the small amount of Pesah is "reawakened" ("Hozer Ve’ne’ur") when the Hametz prohibition take effect on Ereb Pesah.
Curiously, however, the Shulhan Aruch earlier (442:4) appears to contradict his own ruling in this regard. Discussing the status of medications containing Hametz, the Shulhan Aruch writes that if medicine was prepared with Hametz before Pesah, even if the Hametz constitutes just one-sixtieth or less of the mixture, the medicine may not be ingested on Pesah. Although one may keep the Hametz in his possession on Pesah in such a case, the medicine may not be ingested. This ruling appears to directly contradict the Shulhan Aruch’s aforementioned ruling that the concept of "Battel Be’shishim" applies to Hametz that is mixed with non-Hametz before Pesah. According to that ruling, there seems to be no reason to forbid taking the medicine on Pesah, since the Hametz was "nullified" before Pesah and is not "reawakened" with the onset of the holiday.
Several different approaches have been taken to resolve this seeming contradiction. The Peri Hadash (Rav Hizkiya Da Silva, 1659-1698) explains that in the case of medication, the Hametz was intentionally mixed with the non-Hametz ingredients. The Shulhan Aruch permits food that had been mixed with Hametz before Pesah only if the Hametz was mixed in unintentionally. But if one intentionally mixed Hametz with non-Hametz, even before Pesah, the mixture is forbidden for consumption on Pesah.
The Tureh Zahab (Rav David Halevi Segal, 1586-1667) gives a different answer. He writes that in the case of medicine, the Hametz is the primary medicinal ingredient. As the Hametz substance is what gives the mixture its medicinal effect, it cannot be considered "negated," regardless of how small a proportion it constitutes. This resembles the case of a forbidden food used as a coagulating agent ("Dabar Ha’ma’amid"), which renders the product forbidden even if it comprises less than one-sixtieth of the mixture. Since the agent gives the food product its consistency, it cannot be considered "nullified." By the same token, a Hametz ingredient which produces a medicinal effect renders the medicine forbidden on Pesah even if the product was made before Pesah. Medications with Hametz may be permissible on Pesah for other reasons, as we will, please G-d, discuss in future editions of Daily Halacha, but for our purposes here, it suffices to note that, according to the Taz, the Shulhan Aruch’s ruling concerning medications marks the exception to the rule.
Hacham Ovadia Yosef, in his Yabia Omer (2:23), follows the Taz’s approach. And thus, according to the Halacha, a mixture containing a small amount of Hametz is permissible on Pesah, as long as the mixture was prepared before Pesah, even if the Hametz was mixed in intentionally.
Summary: If a piece of Hametz falls into non-Hametz food on Pesah, the entire mixture is forbidden for consumption regardless of how small a proportion the Hametz comprises. If the Hametz was mixed with the food before Pesah, then as long as the Hametz comprises no more than one-sixtieth of the mixture, the food is permissible on Pesah (with the possible exception of certain medications that contain Hametz, a subject which will be discussed in a separate context).
