The Torah law concerning a ḥametz mixture is complicated, subject to dispute among Tanna’im, Amora’im, Rishonim, and Aḥaronim. We shall summarize its laws here succinctly.
The Torah declares that one who eats a kezayit of ḥametz on Pesaḥ incurs karet. If ḥametz that was mixed with other foods such that there was a kezayit of ḥametz within a shi’ur akhilat pras (three or four eggs’ bulk), and one ate a shi’ur pras of the mixture, then according to Ramban and other Rishonim, he incurs karet, while Rif and Rambam maintain that his punishment is only malkot (lashes). (According to Rabbeinu Tam, even if he ate only a kezayit of the mixture, he incurs punishment from the Torah, as cited by Rosh, Ḥullin 7:31.)
If the mixture does not contain a kezayit of ḥametz within a shi’ur akhilat pras, and one ate a quantity of the mixture that has a kezayit of ḥametz: according to Ha-ma’or and Itur, he incurs malkot, but according to Tur, whether he ate a lot of the mixture or just a little, if the mixture has the taste of ḥametz, he has violated a Torah prohibition, but he does not incur lashes; according to Rambam, he has violated only a rabbinic prohibition. (According to Rambam and SA 453:2, in a mixture of wheat and rice, if the taste of the ḥametz is discernible, eating only a kezayit constitutes a violation of a Torah prohibition.)
If ḥametz was mixed with food of the same type – for example, leavened flour with unleavened flour – since they taste the same, the ḥametz flour is nullified by the majority (batel be-rov) at the Torah level, but it is still rabbinically prohibited (SA 447:1).
Regarding the prohibition against keeping ḥametz on Pesaḥ, if a kezayit of ḥametz becomes mixed with other food, as long as it is less than sixty times the quantity of the ḥametz, one violates bal yera’eh and bal yimatzei. If the mixture is more than sixty times the quantity of the ḥametz, the ḥametz is batel at the Torah level and no prohibition is violated. Likewise, if the ḥametz becomes mixed with its own kind – for example, leavened flour with unleavened flour – that has the same taste, if there is more kosher flour than ḥametz flour, then according to Torah law the ḥametz is batel and no prohibition is violated. Nevertheless, even though no Torah prohibition is violated in these scenarios, the Sages ordained that the mixture must be eliminated, lest one eat it on Pesaḥ.