# How to pronounce fractions larger than a twentieth, where the last digit of the denominator is a 1 or a 2? i.e. one thirtieth is to 30 as _ is to 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.

• I always go "... twentyoneth, twentytooth, twentythreeth, ...". (But I suppose I would call that microscopic piece of pizza "one twentyfirst", if I were worried about getting a strange look from the orderly at this resort where I'm staying.) – Hot Licks Jul 29 '15 at 0:11
• it's a big pizza. edited for clarification – Some_Guy Jul 29 '15 at 0:13
• The question that this is supposedly a duplicate of was not nearly as specific as this one, nor did the answers to that question address the specific issues raised here. The aims of the two questions are clearly divergent. The guidance of "If those answers do not fully address your question, please ask a new question" is pretty frustrating, because the question asked here (by Some_Guy) is that new question. – John Y Jul 29 '15 at 3:50
• This is not a duplicate of the cited question: that one specifically excludes the usual "seven eighths" type of expression (dunno why), and doesn't really even mention the real question here, i.e. what happens to 1 and 2 when they happen to be the last digit of the denominator. – Marthaª Jul 29 '15 at 3:51
• Your question doesn't seem to be clear (if the responses you already got are not satisfactory there must be some misunderstanding). Fractions are not pronounced any differently than ordinals except for half and quarter, which you can consider as special cases. – msam Aug 5 '15 at 14:55

• 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

• @PeterShor thanks for the concise, to the point, well sourced answer :) – Some_Guy Aug 6 '15 at 8:11

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.

• I think the OP doesn't reallize that denominatorrs are ordinals, but your first sentence seems to assume they already know that. – tchrist Jul 29 '15 at 5:47
• Why is fifth an exception? – T. Verron Jul 29 '15 at 13:34
• @T.Verron, if it weren't an exception, we would say "five-th". – Hellion Jul 29 '15 at 13:46
• Oh never mind, sorry, I thought you were still talking about the relationship between ordinals and fractions. But rereading the answer now, isn't it clear that the OP knows how to form ordinals? – T. Verron Jul 29 '15 at 14:36
• @j_random_hacker: eighth and ninth are exceptions only so far as spelling; they're pronounced regularly. – Peter Shor Jul 29 '15 at 14:51

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!

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

I feel that while "a thirty-second" is a perfectly good way to express 1/32, it's ambiguous and unusual. I would want to add the slightly archaic "part" onto the end: "a thirty-second part of this pizza" etc.

• I think that's why some people find themselves using the clearly clunky "thirty twoth". It may be odd sounding, and said with a sense of irony, but it's also unambiguous – Some_Guy Aug 5 '15 at 10:07

When using fractions in speech, the numerator is properly spoken as a cardinal ("one", "two", "three"). Except in certain cases, the denominator is properly spoken as an ordinal ("third", "fourth", "fifth"). The exceptions are "whole" (one part) and "half" (two parts). There is at least one alternate denominator where "quarter" can be used instead of "fourth".

When speaking numbers in American English, "and" properly indicates a decimal point or the breaking point between the whole and fractional parts of a compound fraction; it doesn't belong anywhere else. British English doesn't have this prescription and practice certainly deviates from this in America as well, introducing the potential for confusion.

In American English, the numeral 131 would properly be read "one hundred thirty-one", though, as you indicated, it would be common to hear it as "one hundred and thirty-one". The fraction 1/131 would be read "one one-hundred-thirty-first", "one over one hundred thirty-one", or "one over one hundred and thirty-one", but "one one-hundred-and-thirty-first" certainly sounds wrong to my ear. The confusion enters when someone says something like "one hundred and thirty-one thousandths": Are we talking about 131/1000 (0.131) or 100-31/1000 (100.031)?

Music is one of the few places where you'll encounter these sorts of fractions anymore because note durations are negative powers of two. Instead of going with a long stream of semi-, hemi-, and demi- prefixes, the ordinal is used in English, so you will encounter:

• whole notes and whole rests
• half notes and half rests
• quarter notes and quarter rests
• eighth notes and eighth rests
• sixteenth notes and sixteenth rests
• thirty-second notes and thirty-second rests
• sixty-fourth notes and sixty-fourth rests
• one-hundred-twenty-eighth notes and one-hundred-twenty-eighth rests

It's rare to see sixty-fourth notes or one-hundred-twenty-eighth notes, but the language of music certainly allows for it. Note "thirty-second notes": Per the rule, this complies with using the ordinal to speak the denominator.

• There's confusion using the American way, as well. Does one thousand three hundred twenty-sevenths mean 1000/327 or 1300/27? If you inserted the and, it would be unambiguous: 1000/327. This is why you should always read complicated fractions as one thousand over three hundred twenty-seven. – Peter Shor Aug 5 '15 at 15:10
• You're right, though the use of "and" could still be ambiguous: we might be talking about 1320/7. It's the nature of English. It helps me appreciate the Japanese method, which would roughly translate to "131 of 1,000 parts" or whatever fraction you actually wanted to use. – Paul Rowe Aug 5 '15 at 15:21

I agree with "chasly from uk" and add that (1) the same applies in the City of London and (2) from "Dizionario di Inglese - Volume Secondo - Italiano-Inglese (Paravia 2002, but originally Oxford University Press 2001): 21° = twenty-first, 22° = twenty-second, 31° = thirty-first, 32° = thirty-second, etc.