How to pronounce fractions with denominators larger than 20 where the last digit of the denominator is 1 or 2? eg 4/31

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.}

Question

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

etc.

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.

Solution 1:

You asked for sources.

• Americans pronounce fractions with denominators ending with 1, 2, 3, as in twenty-firsts, twenty-seconds, twenty-thirds. For confirmation, here is a definition from Merriam-Webster, one of the canonical American dictionaries.

thirty-second 2 : the quotient of a unit divided by 32 : one of 32 equal parts of anything <one thirty-second of the total>

The word thirty-twoth does not appear in the Merriam-Webster dictionary, no matter how you spell it. While a few people may use thirty-twoth, it's definitely non-standard.

• There is a difference when the denominator is 4. Americans use both fourths and quarters for one piece of something divided into four equal parts (except for hours, which are always quarter hours) while in the U.K., these are usually quarters. Oxford Dictionaries Online has

fourth 2. chiefly North American A quarter: 'nearly three fourths of that money is now gone'

Merriam-Webster has both

fourth : one of four equal parts of something
quarter : one of four equal parts of something

Solution 2:

In the US, the general rule is the ordinal form is based on the last element in the numeral.

• sixty-eighth
• one hundred twenty-ninth
• one thousandth
• one thousand-seventh

This does not change when the discussing the denominator of fractions, regardless of whether the numerator is singular or plural

• one thirteenth
• one sixty-first
• three thirty-fourths
• six twentieths

There are exceptions

• first
• second
• third
• fifth (although this seems to be a phonetic morph of fiveth)
• half
• whole
• quarter

The exceptions carry over to more complex ordinals

• sixty-second
• three thirty-thirds

Supplement (based on OP's further comments)

The fractional form, at least in US usage, uses the ordinal form for the denominator with only three (I think) exceptions - whole, half and quarter. And quarter is also regularly expressed as fourth.

Specifically 1/62 is either one sixty-second or a sixty-second. The 21 pizza slices are each one twenty-first of the pie (hardly worth eating!).

As to the footnotes, 131 is either one hundred thirty one or less commonly one hundred and thirty one. If it were the denominator of the fraction 1/131, it would be one one hundred thirty-first.

The pronunciation of multi-digit numbers varies based on what the numbers are used for. Telephone numbers are read differently from monetary numbers or counts of widgets, and there are variations within categories depending on the number (area code 212 is almost always pronounced two one two, rarely two twelve, never two hundred twelve, but area code 800 is read eight hundred). If you want to discuss that issue, it probably warrants a separate question.

Solution 3:

Definitely a sixty-first and a sixty-second as far as I am concerned - no doubt about it. (Mid to South England)

Not that either would come up very often!

Solution 4:

• 1/21: a twenty-first, or
• 1/22: one twenty-second
• 7/21: seven twenty-firsts
• 8/22: eight twenty-seconds