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To express a fraction of 3 out of 4, how and when would you use three quarters, and when would you use three fourths?

To me, three quarters is what I would have used all the time — but I'm not a native English speaker, so I'm not sure. I did come across three fourths, but wasn't sure if that's something used in certain geographies and/or fields of expertise, or whether that's just a slightly too literal translation of another non-native speaker.

Are there certain walks of life, certain fields of expertise that would use three fourths instead? Or is this a question of geography (e.g. used in New Zealand, but not elsewhere)?

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    I'm British and would always use quarters, and fourths sounds strange. I think in America fourths is most common, but quarters also used depending on the context (and possibly region). – Hugo Feb 6 '13 at 6:51
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    I'd guess fourths would be more common in regions where quarters can mean other things, like coins. – Mr Lister Feb 6 '13 at 7:18
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    I, AmE native, think I tend to use three quarters most everywhere except for when talking about math. I say, three quarters of a cup of flour, three quarters of a mile away, three quarters full, but three fourths pi (although to be honest it's probably more likely three pi over four). – Jim Feb 6 '13 at 7:18
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I did the obligatory Ngram, and found two things:

I then perused through some of the results of a book search, and I found instances of three-fourths in a wide array of contexts, such as:

  • three-fourths of representatives and senators had served fewer than 12 years
  • the iceberg towers 10 stories, with three-fourths of its mass beneath the water
  • three-fourths of the score was based on the quality
  • some organizations require a three-fourths vote instead of a two-thirds vote in adopting certain types of business
  • directly behind the center of Billow's corps was formed three fourths of Pirch's corps, fifteen thousand men
  • for young people overall, approximately three-fourths of all mortality can be attributed to four causes
  • the cast and crew returned to Los Angeles with three-fourths of the film finished
  • an aggregate area of more than three-fourths inch in diameter
  • the ratio of 3:4 is the diatessaron or fourth, producing an octave lute that is three-fourths the length of the descant, which in turn is three-fourths the length of the tenor

In short, I couldn't figure out any rule where three-fourths would be considered an inappropriate substitute for three-quarters; it seems usable whether we are talking about a fraction of a sample size, a quorum, a completion rate, or how much pizza is left in the box.

  • You mean three-quarters was found more often than three-fourths, right? – aedia λ Feb 6 '13 at 16:24
  • @aediaλ: Close. I meant three-fourths was found less often than three-quarters :^) Thanks for spotting the error; I've fixed it. – J.R. Feb 6 '13 at 16:58
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    Ngrams as percentages: English / British English / American English. – Hugo Feb 7 '13 at 14:59
  • I would regard three-quarters as having a meaning which is not applicable in all cases where three-fourths would be suitable. In particular, I would regard a quarter has being half of a half, and "three quarters" as being having a strong implication that one either has a (possibly subdivided but still identifiable) half and a quarter, or has a whole minus a half-half, or is referring to a quantity which would historically have been one of the above. Someone who has a 12"x12" cake with a 6"x6" piece taken from a corner has three quarters of a cake. If the removed section... – supercat May 1 '14 at 15:22
  • ...had been 4"x9", I would say one had three fourths of a cake, but not three quarters. When the missing piece was 6"x6", it could be visualized as half of a 12"x6" half-cake, but there's no apparent way a 4"x9" piece would be seen as half of any normal subdivision. – supercat May 1 '14 at 15:35
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I'm British, and I've only ever heard "three fourths" used a couple of times. You're correct with "three quarters".

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Although the word quarter is used more often, fourth is also acceptable. This is likely because it is between a third and a fifth. Since the two immediately neighboring ordinal numbers are used for denoting fractions, it would be an awkward special case to disallow it. If one fourth were suddenly unavailable in the language, it would immediately have to be reinvented.

The one thing to watch out for, however is that 1/2 is never called a a second. The use of ordinals for the denominators of fractions begins with third. However, ordinals based on the word second are used for fractions: 1/22 is one twenty-second, and so forth.

  • I would use the term "quarter" for discrete subdivisions that are naturally "half of a half". If a whole cake is 12"x12", a 6"x6" square piece cut from a corner would be a "quarter"; a 9"x4" rectangular piece would be a "fourth" but should not, IMHO, be called a "quarter". – supercat May 2 '14 at 0:47
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I'm a native speaker of New Zealand English but as far as I'm aware this applies to any regional variant of English (although a "quarter" for 25¢ is specific to North America). A "quarter" is far more commonly used in conversation than a "fourth" but both mean "one part is four" (1/4). A "quarter" is a countable part so you can have two quarters or three quarters (such as pieces of a cake or pie). These could be separate quarter-sizes pieces or a fraction of the whole. However, a notable distinction is the there is a difference in the abbreviated or written forms commonly used in mathematics.

1/1 = 1 so it is a "whole" or "unit" (not a first)

1/2 (or 2/4) is "half" or "halves"

1/3 (or 1/3rd) and 2/3 is a "third" and "two thirds" respectively

3/4 and 3/4ths are read as "three quarters" or "three fourths" (these are not interchangeable)

Thus I would only use "fourths" in writing and mathematics, never in spoken conversation. Perhaps it is sometimes used by children or when teaching mathematics but is rarely spoken between two adults.

Notice that in these abbreviations the denominator (bottom number) corresponds to ordinal numbers: 1st "first", 2nd "second", 3rd "third", 4th "fourth", 5th "fifth", and so on. That is the convention for reading written fractions: x/y is read as x yths (not halves or quarters). The exception is "percentages": x/100 (x%) which uses the latin derived x per cent or very large numbers (such as ppm = parts per mil[lion]).

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It seems to be a location based term. Certainly in Australia and the UK I have only heard the term Quarter. I like the example of the shape cut into the cake... Really that is thirty six one hundred and forty forth's (36/144) as it is a 12x12 cake... Of course that reduces down to 1/4... And depending how you were taught... It's a quarter or a fourth... Or... 25% ;)

  • Hello, Sean. After your first two sentences, this is hardly material suitable for an 'answer' on ELU. And you need to give an answer with references, as J.R. does, rather than 'I have only heard the term ....' – Edwin Ashworth Dec 27 '15 at 0:24

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