How To Calculate A Sixth

Mr. Lerner was discussing the Business Weekly at the Shabbos table with his family. One of the articles addressed onaah, unfair pricing, and distinguished between discrepancies of less than a sixth, a sixth, and more than a sixth.

“How do you calculate a sixth?” his ten-year-old son, Shimon, asked.

“You learned that already,” replied Mrs. Lerner. “You divide by six; that’s a sixth.”

“A sixth of what, though?” asked their fifteen-year-old son, Moshe.

“I assume it means a sixth of what the item should cost,” replied Mr. Lerner. “For example, if something costs $60, a sixth is $10 extra.”

“Or maybe it should mean a sixth of what the customer paid?” asked Moshe.

“Maybe,” replied Mr. Lerner. “I’m not sure if there’s really a difference.”

“Perhaps a sixth really means a fifth,” chimed in their 18-year-old son, Menachem. “We learned that in various halachos, such as redeeming maaser sheini, a fifth mentioned in the Chumash is really a quarter, which is 1/5 of the total sum received after adding the 1/4.”

“You’re raising good questions!” Mr. Lerner complimented his children. “We can ask Rabbi Dayan!”

After Shabbos, Mr. Lerner emailed Rabbi Dayan and asked:

“How do we calculate a sixth?”

“The simplest calculation is a 1/6 variance from the fair market value, whether underpayment or overpayment,” replied Rabbi Dayan. “Thus, for an item worth $60, a sales price of $50 or $70 – a variance of $10 – is considered 1/6 onaah and warrants adding the $10 underpayment or returning the $10 overcharge (C.M. 227:2).

“Rav and Shmuel (B.M. 49b) dispute whether to also calculate a sixth of the payment. The halacha is like Shmuel, that this is also considered 1/6. Thus, if a person paid $60 for an item worth $50 or worth $70, this is also onaah of 1/6 since the $10 differential is 1/6 of the amount paid.

“Mathematically, this corresponds to a 1/5 overpayment of value (e.g., $60 for a $50 item) or a 1/7 underpayment of value (e.g., $60 for a $70 item).

“Thus, for a $60 item, presumably a payment of $51.43 or $72 would also be considered 1/6 underpayment or overpayment, respectively, since the differential of $8.57 or $12 from the $60 value is exactly 1/6 of the $51.43 or $72 paid.

“This dual calculation led the poskim to a dilemma. As mentioned, whether a person paid $70 or $72 for a $60 item, this is considered an exact 1/6 variance – in which case the sale is valid, but the aggrieved party can claim the $10 or $12 differential. However, what if the person paid $71? From the perspective of fair value, this is a differential of more than a sixth (11/60), in which case the aggrieved party can annul the sale, whereas from the perspective of payment, this is a differential of less than a sixth (11/71), which is considered mechilah!

“Rambam and Rema (227:3) write that, as a rule, we calculate based on the value, so that – for a $60 item – $51 is considered less than a sixth differential and $71 more than a sixth. Only when the differential is exactly a sixth of the payment ($51.43 or $72) do we make an exception and consider this also a sixth (Sma 227:11; Taz 227:3; Ketzos 227:2).

“However, Maggid Mishneh and seemingly Shulchan Aruch rule that the entire range, $50-$51.43 or $70-$72, is considered a sixth, so that only a payment of more than $51.43 is considered a differential of less than 1/6, and only more than $72 is considered a differential of more than 1/6 for a $60 item (Sma 227:5; Pis’chei Choshen, Onaah 11:6).

“This discussion is mostly theoretical, though,” concluded Rabbi Dayan, “since there are very few items with a specific fair market value that enables us to determine an exact 1/6. Almost all items have a price range, so that only a great discrepancy would invoke onaah.”

Verdict: In the laws of onaah, unfair pricing, a discrepancy of 1/6 is calculated primarily based on the fair value of the item, but also based on the amount paid.

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This article is intended for learning purposes and cannot be used for final halachic decision. There are also issues of dina d’malchusa to consider in actual cases.

1. To regrow or repair damaged tissues or cells.
2. To restore or renew something that has been lost or destroyed.
3. To revitalize or breathe new life into something.

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