Math: "Can You Solve These 'Ghostly' Riddles?" Puzzle 1

The question and solution as presented by Presh Talwalkar (October 2015):
* Content: https://youtu.be/p1GUHQRUjd8 [4m 51s]
* From: https://www.youtube.com/channel/UCHnj59g7jezwTy5GeL8EA_g
* Search: https://www.youtube.com/results?search_query=Can+You+Solve+These+%22Ghostly%22+Riddles%3F

A father left 17 goats to 3 sons.

His will specified 1/2 of the goats to the oldest son, 1/3 to the midle son, and 1/9 to the youngest son.

For obvious reasons, some people have reservations about the first puzzle of the three puzzles discussed, but another way to look at it is to consider that there are in fact eighteen goats but the sons only inherit seventeen of those eighteen goats. The remaining goat either died, escaped into the wild or was to somebody else. Or alternately whatever, but it stands to reason that the eighteenth goat is not truly figurative like the brick in the second puzzle or the ascending/descending monk in the third, and that the question as presented failed to mention that the total number of goats isn't seventeen.

However, of course, it could be that the will only and literally specified the proportions and to whom each proportion is to go, and that the number of goats left to be inherited could have been arbitrary rather than multiple of two and nine. Such would destroy the riddle, and reduce the hypothetical matter to a decision rendered by a probate court unless the sons solve it on their own.

Furthermore, there is one more "however". The actual question in the riddle is as follows: But the sons could not divide 17 evenly. How did they split up the goats? This seems to insist that there are only seventeen goats in total. Assuming that the sons didn't want to butcher and divide each of (or to sell and divide the reward from) the three remaining of seventeen goats into 1/2 (for the oldest), 1/3 (for the middle), 1/9 (for the youngest) and 1/18 (for none) portions, and in making an negotiated or otherwise unlawful claim to that remaining 1/18 portion, it is reasonable in practical terms that they would divide the goats into the whole numbers that Talwalkar's solution specifies: 9/17, 6/17 and 2/17, which are respectively greater than 9/18, 6/18 and 2/18. The same outcome is achieved by rounding 9/17, 6/17 and 2/17 up apiece, or by dividing 3/17 evenly among the sons and adding the first 1/17 to 8/17, the second 1/17 to 5/17 and the third 1/17 to 1/17.

Now, supposing the sons couldn't or didn't make the negotiated or otherwise unlawful claim to the 1/18 portion, and didn't want to butcher and divide each of (or to sell and divide the reward from) the three remaining of seventeen goats, then the oldest son would have to settle for 8/17, the middle for 5/17, and the youngest for 1/17. This is a problem to whoever/whatever is entitled to the 1/18 portion, since 17/18 is not a whole number. Must he/she/it settle for 17/18 of a goat's body or a goat's value? Or is a goat and the goat's value forfeit entirely? Or can an intact goat be claimed at no charge? Either way, what happens to the two or three remaining goats? This is why I believe there are eighteen goats but that the eighteenth goat just happens to be irrelevant to the three sons.