[Avodah] arithmetic question

[Chesky Salomon]

On Thu, Jul 18, 2013 at 11:49 AM, Eli Turkel <eliturkel at gmail.com> wrote:
> I have no problem with the 1/6 being a fraction of the starting or final
> value. What confuses me it that the SA seems to be using both
> simultaneously. That is onaah is raising (or lowering) the price by exactly
> 1/6 of EITHER the starting or final values

It's been a while since this topic was covered in yeshiva, but here's my
memory:

Given an item with value 210, if the sale is for...
+ less than 175, the sale is void;
+ in the range 175-180, ona'ah applies:
    the sale is valid but the difference must be made up;
+ in the range 180-245, the sale is valid;
+ in the range 245-252, ona'ah applies; or
+ more than 252, the sale is void.

The ranges in which ona'ah applies are determined like this:

+ one-sixth of the starting price --
   1/6 * 210 = 35, so 210 +/- 35 = {175, 245} are ona'ah.

+ one-sixth of the final price --
   6/5 * 210 = 252 1/6 * 252 = 42 = 252210, so 252 is ona'ah ; and
   6/7 * 210 = 180 1/6 * 180 = 30 = 210180, so 180 is ona'ah.

- Chesky