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I noticed a lack of case marking particles in mathematical sentences:

  • 1足す2は3である。
  • 3掛ける4は12である。

足す and 掛ける are verbs, does subject and object analysis apply to this? Do they take on the numbers as arguments despite not being marked by case particles? What part of speech are 足す and 掛ける? They do not seem to be syntactically acting as verbs.

Compare this with the English version:

  • 1 plus 2 is 3
  • 3 times 4 is 12

After a cursory dictionary search, it is revealed that plus and times are not verbs, but prepositions. "plus 2" and "times 4" are prepositional phrases. It seems that the structure for English is 3(times 4). While the structure in Japanese appears to me as (3掛ける)4


If we parse 3 × 4 = 12 into English or Japanese, does the difference in grammatical syntax result in a different situation? Which situation comes to mind in English and in Japanese?:

a. 3 × 4 = OOOO + OOOO + OOOO
b. 3 × 4 = OOO + OOO + OOO + OOO

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    If we have to overlay English parts of speech on 1 + 2 = 3, why not call + a coordinator? But really, it seems like we're just pronouncing the symbols as English words, and + is really an infix operator, not a preposition. – snailcar Jan 31 '16 at 3:20
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    @snailboat But it seems to make sense as plain language in English, where verbs stand in between arguments. It doesn't in Japanese unless you employ reverse Polish notation... – broccoli forest Jan 31 '16 at 12:52
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They are not grammatical phrases. We just read the symbols verbatim like:

[⁠1]{いち} [+]{たす} [⁠2]{に} [=]{は} [⁠3]{さん}

It has nothing different than saying:

[⁠1]{いち} [+]{プラス} [⁠2]{に} [=]{イコール} [⁠3]{さん}

which is also commonly heard. Though we have both [+]{たす/プラス} and [−]{ひく/マイナス}, [×]{かける} and [÷]{わる} only have native pronunciations.

See this link for common readings of more advanced expressions including a [>]{だいなり} b and A [⊇]{ふくむ} B, which would be aはbより大きい and AはBを含む if read grammatically.


If we parse 3 × 4 = 12 into English or Japanese, does the difference in grammatical syntax result in a different situation? Which situation comes to mind in English and in Japanese?

It reminds me of "order of multiplication" controversy that was in Japan a while ago, but anyway, according to Japanese official teaching guidelines, multiplicand comes first and multiplier second, which results in:

b. 3 × 4 = OOO + OOO + OOO + OOO

But I'm not sure if this is grammatically elicited, because even when you say 3に4を掛ける or 3を4に掛ける in natural word order, neither of them has such implication, unless you read it 3を4回掛ける.

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