What is a Sixth?

Shmuel states that ona’ah includes a case of a sixth of the sale price, even if it is not a sixth of the fair price. Shmuel also agrees that a sixth of the fair price is considered ona’ah. Therefore, according to Shmuel, all the cases below are ona’ah:
1. Item worth 70, sold for 60
2. Item worth 60, sold for 50
3. Item worth 60, sold for 70
4. Item worth 50, sold for 60

The Rambam (Mechira 12:3) says that anything less than a sixth is considered forgiven. The Rambam gives two examples:
1. Item worth 60, sold for 51
2. Item worth 60, sold for 69

The Magid Mishnah challenges the first case of the Rambam. In this case, a sixth of the fair price is 10, while a sixth of the sale price is 8.5. The difference in the sale is less than a sixth of the fair price, but is more than a sixth of the sale price (8.5), and should be ona’ah according to Shmuel!?

The Shulchan Aruch (HM 227:3) only discusses the second case, while the Rama (227:4) cites the first case.

The Sma (227:5,11) rules like the Magid Mishnah.

The Taz explains that the Rambam holds that Shmuel accepts either form of sixth, but only at a sixth. Any other deviation is evaluated based on the fair price only. See Drisha C”M 227:4 for more details.

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Terumah More than a Sixth

The Gemora (Kesuvos 100a) asks: Why is this case (an agent undercharging for the property of an orphan) any different than that which we learned in the following Mishna: If one tells an agent, “Separate terumah for me (without specifying an amount), he should separate according to what the agent perceives is the mindset of the owner (either one-fortieth, one-fiftieth or one-sixtieth). If he cannot ascertain what the owner would want, he should separate one-fiftieth. If the agent has separated one in forty or one in sixty as terumah, the terumah is nevertheless is valid. (It is evident that although the agent has made a mistake, his actions are nevertheless valid?)

The Gemora answers: By the terumah, the agent has a valid excuse; he can say that he figured that the owner would separate terumah in a stingy manner or generously; however, in this case (where the agent charged too little for the property), the owner may tell the agent, “You should not have made a mistake.”

The Beis Yaakov asks: Isn’t the case of terumah a case where the agent erred in an amount which is more than a sixth; everyone would agree that the sale is invalid?

He answers: Since it is extremely common to err in this regard when separating terumah; even more than a sixth is regarded as having the same halacha as precisely a sixth.

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