I am writing an article where I am using fractions for comparison. Should I include the word ‘of’ between the fraction and the things fractioned? To me, both sound correct, but I do not know whether a) it’s wrong, or b) there’s a difference between 1) formal writing, 2) informal writing or 3) colloquial English.

Example 1:

… almost ¹⁄₃ the prisoners were born in cities, and more than ⁵⁄₆ were enumerated in one of those cities …

… almost ¹⁄₃ of the prisoners were born in cities, and more than ⁵⁄₆ were enumerated in one of those cities …

Example 2:

… disregarding the Penitentiary, they still accounted for almost ²⁄₃ the prisoners.

… disregarding the Penitentiary, they still accounted for almost ²⁄₃ of the prisoners.

The first examples, I read as ‘one third the prisoners were’ and ‘they still accounted for almost two thirds the prisoners’. Also, if an explanation of the grammar for whichever solution is considered the best could be included, that would be much appreciated.

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    I would not expect to see vulgar fractions written that way in an article in British English. I'd expect to see 'one third of the prisoners' etc. The style guide of the Guardian newspaper takes the same view. theguardian.com/guardian-observer-style-guide-f – Spagirl Nov 29 '16 at 11:22
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    You need the "of". But this sounds like an English Language Learners query to me, and would probably suit that ell.SE better. – AndyT Nov 29 '16 at 11:23
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    Of is normally required with fractions, but phrases like a third the way through are not unheard of in BrE. See this Ngram - although the version with of is significantly more common, the version without is also found in print. (NB: I had to leave off the word 'through' due to Ngram's 5-word limit.) – Lawrence Nov 29 '16 at 12:01
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    @Spagirl I agree entirely. But I would add a hyphen as in one-third of the prisoners. Not sure how the Guardian would feel about that. I am usually in agreement with the things they say. – WS2 Nov 29 '16 at 12:12
  • @WS2 Now that you mention it, if I were writing the article I would probably have said 'a third of the prisoners' rather than 'one third'. On the hyphenation, it looks as though you are correct. google.co.uk/… – Spagirl Nov 29 '16 at 13:56

There are two different constructions:

  1. Proportion of a whole: "One half of the prisoners"; "two thirds of houses". This form requires 'of', except for "half", where it can be omitted; but for me, it is required with other fractions.

  2. Comparison: "half the size of"; "produces one third the oxides". This form does not permit "of".

The numbers from the NOW corpus are:

half the        70775     half of the        98213
third[s] the      667     third[s] of the    21300
quarter[s] the   1079     quarter[s] of the  21008

so in that corpus, "half of the" is only 1.4 times as frequent as without "of"; but "third of the" is 32 times as frequent , and "quarter of the" over 20 times.

(These numbers don't distinguish the two constructions, or indeed cases where "half/third/quarter" just happens to be followed by "the" in a different constituent, such as "We lost the middle third the last day".)

Edit: I just looked through the first 50 of the 667 instances of "third the", and found precisely one instance which looks like "third of the" with 'of' deleted.

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Depends on the necessitated professionalism and precision of language the situation requires. In general though, general populace use half the, a third, a forth/quarter without the "of". The smaller the fraction the more likely the of comes out though.

EX: "I drank a fifth of vodka, dare me to drive?"

For anything requiring a concise and specific values I would use the of statement.

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