[Avodah] arithmetic question

[Eli Turkel]

I am currently learning the laws of Onaah (BM 4th perek).
If one looks at CM 227#1 the Mechaber states that if one sells something
worth 7 for 6
or 6 for 5 (and similarly 6 for 7 or 5 for 6) then it is Onnah (ie an exact
sixth).

I am completely confused as the ratio 7/6 is not equal to 6/5.
The Sma discusses whether the sixth is from the article or from the money.
It seems to me that is irrelevant.

The SA then proceed that if the price difference is less than 1/6 ie 6.99
for 6 or 5.99 then the sale is valid. If OTOH it is more ie 7.01 for 6 or
6.01 for 5 then the kinyan is not valid.

My impression is if the sale is 7/6 = 1.16666 then the sale is valid and
the difference is refunded.
Greater than 1.16 but less than 6/5=1.2 the sale is not valid (mekach taut)
and at 1.2 it is again valid but the extra money is returned - which is
ridiculous.

The SA stress that the sale is valid but the overcharge is returned only
for an exact sixth.
This implies that this halacha holds only if the price is a multiple of 6.
If the price is 599.99 or even 400 this would never occur.
Even in the ideal case it is almost impossible as a difference of a penny
changes the halacha.

In fact the gemara in BM51a discusses that if the article is worth 5 and
the buyer pays 5.5
he is stuck with the overcharge. However, if he volunteers to pay 6 then he
gets the entire overcharge back. (The gemara gives a technical answer which
doesnt hold in general)  Again leads to strange situations

Any help is appreciated

-- 
Eli Turkel
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