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Refer to this question for more examples.

We have multiplication, which has "multiply" as the verb. But we say "a times b".

Similarly, we have division, which has "divide" as the verb. But we say "a divided by b".

First, what is the category name of "plus," "minus," "times," and "divided by"? They aren't "operators" or "operations," nor are they strictly verbs. So, what are they?

Second, what is grammatical story there? When I write that kind of sentence, what am I creating? A phrase, a clause? Grammatically, what am I doing?

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    "They aren't operators". They are, see Merriam-Webster – 3a: something and especially a symbol that denotes or performs a mathematical or logical operation. 3b: a mathematical function. Commented Jan 16 at 20:19
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    "a divided by b" is a noun phrase. It's similar to "the car driven by Joe"
    – Barmar
    Commented Jan 16 at 21:36
  • @Barmar Oh, rght. I would have said there's a passive verb. Commented Jan 17 at 0:54
  • They are prepositions. Commented Jan 17 at 2:31

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According to Huddleston & Pullum (2002), plus, minus, and times are all prepositions (p. 635). Divided is likely best taken as an adjective rather than a verb form, since unlike the verb to divide it has a stative intepretation. It's an adjective that (in the sense in question) can only occur postpositively, and requires as a complement a prepositional phrase with the preposition by.

So "five plus three" is a noun phrase in which "five" is modified by the prepositional phrase "plus three"; the same applies to "five minus three" and "five times three." "Five divided by three," however, is a noun phrase in which "five" is modified by the adjective phrase "divided by three"; in turn, "divided by three" consists of the adjective "divided" with the prepositional phrase "by three" as a dependent of it.

Of course, in the mathematical expression "5 + 3" we don't see "+ 3" as somehow a dependent of "5". But as a matter of English syntax in "five plus three" the prepositional phrase "plus three" is a modifier of "five." Of course "five plus three" refers, not to some version of the number five, but to the number two, just as "a vase broken into pieces" typically refers, not to a vase, but to the pieces produced by breaking it.

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  • The model 5 + 3 has two interpretations: 5 combined with 3 in the usual identity-retaining-of-elements sense (so you still have the 5 blue and 3 red marbles in the total of 8 marbles), or the transformation 5 increased by 3 (so the worm which once was 5cm long is now 8cm long; the 5 is history). Commented Jan 17 at 12:48
  • Where does GGEL call divided an adjective in this function? I would call it a verb in a passive construction. Commented Jan 18 at 0:09
  • @TinfoilHat They don't make any claims about that word; I would have cited a page number if they did. My reasoning is that to divide has a dynamic interpretation, whereas divided has a stative one, which is generally a test for verbal vs. adjectival passives.
    – alphabet
    Commented Jan 18 at 0:32
  • Note also that we can't add a by phrase corresponding to the subject of the verb in this use of divided: "He divided six by two and got three" is valid, but not *"Six divided by two by him was three."
    – alphabet
    Commented Jan 18 at 0:39
  • 4 divides 12; 12 is divided by 4. Commented Jan 18 at 0:51

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