Disclaimer: I speak British English. I've noticed a lot of differences between the way Americans and Brits pronounce numbers.1 Since the question concerns this, I thought it might be appropriate to draw attention to it case we inadvertently confuse each other. My question is not about these differences, I just wish to highlight them in case they cause confusion.
1. You seem to happily call a quarter "a fourth" sometimes,
we always call 131 "one hundred and thirty one",
we pronounce double digits in phone numbers like 12449 as "one two double four nine", and
I think we are much more likely to use expressions like "thirteen hundred" to mean 1300.
When talking about fractions, I have frequently heard
1/2 a half 1/3 a third 1/4 a quarter 1/8 an eighth 1/64 a sixty fourth 1/56 a fifty sixth
Essentially the rule seems to be that, except for "a whole", "a half", and "a quarter", the word matches the ordinal number; that is to say:
Numeral Ordinal Fractional one first whole two second half three third third four fourth quarter five fifth fifth six sixth sixth fifty-seven fifty-seventh fifty-seventh
Even though 1/4 is a quarter, 1/64 is a sixty-fourth.
So what’s 1/62? A sixty-twoth? A sixty-second? Surely not a sixty-half!
I know that simply saying one over sixty-two can usually work, but I'm asking specifically for the word itself, i.e. if I divide a huge pizza into 21 pieces, what are the pieces? Other than baker’s twentieths.
Summary: Can anyone point me to any sources (whether style guides or common usage studies or anything else) that discuss the pronunciation of fractions; specifically one that discusses this separately from ordinal numbers, rather than how to form ordinal numbers in the first place.