[Avodah] arithmetic question

[Micha Berger]

On Wed, Jul 17, 2013 at 06:46:42PM +0300, Eli Turkel wrote:
: 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.

Se'ifim 2-4 have helpfule example.

: The Sma discusses whether the sixth is from the article or from the money.
: It seems to me that is irrelevant.

That's s"q 3.

Also remember that you're used to thinking of percentages as a fraction
of the starting value, whereas chazal more often speak in terms of a
fraction of the larger value (milevar).

So their 1/6 over is our 20%. If
    y = 120% * x
as we would phrase it, then it's just as true that
    x = y - 1/6 y
which is how Chazal would phrase it.

For some reason I asked about last Jan, the SMA doesn't use that concept.

I explained the SA's examples then, using the SMA's explanation. Quoting
myself from <http://www.aishdas.org/avodah/vol31/v31n011.shtml#13>:

> The SA's examples are (CM 227:2-4):
>     [Onaah by the buyer:]
>     - selling the value of 6 for 5 [- 1/6, underpaying by 1/6 the value]
>     - ... or the value of 7 for 6 [- 1/7, underpaying by 1/6 the price]
>     [Onaah by the seller:]
>     - or selling the value of 5 for 6 [+ 1/5, overcharging by 1/6 the price]
>     - or the value of 6 for 7 [+ 1/6, overcharging by 1/6 the value]
>     then this is ona'ah ... and he me'aneh must pay the ona'ah...

>     If the ona'ah was a kol shehu less... he doesn't have to return
>     anything... it is the norm for everyone to be machol that.

>     If the ona'ah was more than 1/6 by a kol shehu, like he sold 60
>     for 50 minus a perutah [ie 49.75, or - 1/5.85], the sale is batel,
>     and the mis'aneh may (yakhol) return the property, but the me'aneh
>     may not reneg if the other wants it...

> You'll notice that I phrased each of the four cases three ways:
>     - the SA's wording
>     - the difference in value
>     - how it comes to 1/6 -- whether that's in value or in price.

Tir'u baTov!
-Micha

-- 
Micha Berger             Rescue me from the desire to win every
micha at aishdas.org        argument and to always be right.
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