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Image a company that earned 500,000 dollars last year.

Some guys are talking about that company in a bar.

That company earned half a million dollars last year.

Some news paper would also "half a million" when reporting that company.

What I'm trying to say is that, it seems that people use "half of a million" both in informal situation (casual talk) and formal situation(news report).

Cambridge Dictionary gives these examples

half a dozen

Roughly half (of) the class are Spanish and the others are a mixture of nationalities.

which seems to indicate that the "of" is unnecessary when "half" precedes a number.

However, Google Ngram shows that people might use "half of a million" sometimes.

the question is that, in what kind of situation, people use "half of a million". Could someone please give a hint? Thanks in advance.

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  • If you click the date ranges below the graph in your ngram link, you can see examples of the usages Google found.
    – The Photon
    Apr 14 '20 at 0:55
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We use one half of in sentences like:

One half of the population of this country are rich.

And, half a in sentences like:

Half a minute ago...

Half a million dollars... etc.

If you are looking for a rule the rule will be like this:

We normally use "half a" before units of measurement.

But exceptions abound.

Hope that helped.

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  • Thank you. Are "One half of the population" and "half (of) the class" the same usage?
    – WXJ96163
    Apr 14 '20 at 1:57
  • @WXJ96163 the most natural will be: "one half of the class". By the way you can upvote the answer if it helped.
    – user100323
    Apr 14 '20 at 2:00
  • Thanks for your comprehensive explanation. Would you please name some exceptions about that rule?
    – WXJ96163
    Apr 17 '20 at 6:04

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