salacious conversations

So....what do two retired school teachers talk about walking to breakfast?  This morning?  Grammar.  Specifically, is it "1/3 is..." or "1/3 are..."?  Since both are usually followed by a prepositional phrase beginning with "of", my grammar background would say "is".  But clearly, in most cases, that simply doesn't sound good.  Example.  "1/3 of the people is not caring about this."  Totally wrong.  It has to be "1/3 of the people are not caring about this."  Of course, you wouldn't say "1/3 of the pie are gone."  At least, I hope you wouldn't.  Now, of course, the world would not change, nor would gravity reverse its hold if the answer to this question remained unknown.  And truthfully, when breakfast was 1/3 gone, I had forgotten the question.  However, as I was 2/3 asleep in front of the television, like a niggling itch, it reared its ugly head.  Google.  After several tries and an amazing number of mathematical responses, I did find the answer.  It came right after the suggestion to reword the question so you didn't have to worry!  Example.  "Who could possibly give a rat's rump whether it's 'is' or 'are'"?  And better still, "Who ate the pie?"  For those of you drooling for the answer, it's simple.  Break the rule.  If the object of the preposition is singular, use "is".  If it is plural, use "are".  And if you wonder where the title of this opus comes from, consider what you are thinking I should have done with the question in the first place!