Mental Nuts-- Can You Crack 'em?

[BigV]

A man left nineteen sheep to three heirs. One to get one-half, one one-quarter, and one one-fifth. No sheep were to be killed, and all to be dealt fairly with.

I see how the math works out when you add one sheep to make the total twenty. But why just add one to do that, why not add eighty-one and distribute 50 and 25 and 20 then return 5? This better not be the answer, adding one...

Still, very creative friends I have here!

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A man left nineteen sheep to three heirs.

Ok, fine. This seems very straightforward. 19 sheep, heirs. Pretty unambiguous.

One to get one-half, one one-quarter, and one one-fifth.

Here's the nut that needs cracking. Half of what? A quarter of what?, a fifth of what? As y'all have pointed out, this doesn't "add up". What's missing? Or what is to be left out? How can these work out... What about half of ... the weight? Regardless, those fractions will never add up to 1, the presumptive "whole". As long as we're talking about only one kind of thing (a group of 19 sheep for example) those pieces will leave some left over.

Nothing in this nut says that 1/2 and 1/4 and 1/5 is the complete list of what was "to get".

Nothing says that the "one" who gets is a different heir. I can imagine that the same "one gets" 1/2, and 1/4, and 1/5 (of the sheep??) so this heir gets 19 sheep. Still leaves 1/20th of 19 sheep unallocated. Grrrrrrr...

Maybe these "fractions" aren't talking about fractions of the flock of sheep. What about one heir getting half the sheep, another heir getting a quarter (a twenty five cent piece or a $2.50 coin, take your pick) and another gets a jug of shine (a fifth). ... ... What am I gonna do about the other "half of nineteen sheep" (ha fucking ha)??

A man left nineteen sheep to three heirs. One to get one-half, one one-quarter, and one one-fifth. No sheep were to be killed, and all to be dealt fairly with.

still thinking...