"Three quarters" vs. "three fourths"

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)?

I did the obligatory Ngram, and found two things:

• three-fourths was found less often than three-quarters, and
• that difference was more pronounced in the British English corpus than in American English.

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.

I'm British, and I've only ever heard "three fourths" used a couple of times. You're correct with "three quarters".

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'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 in 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, thirds 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]).