30843
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.](http://chat.stackexchange.com/transcript/message/27185395#27185395)
**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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2016-01-31T01:56:41.040
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2020-06-28T03:25:31.643
2016-01-31T02:05:41.727
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question
grammar syntax numbers mathematics
Maths sentences: 足す and 掛ける
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](https://shoyan.github.io/blog/2016/07/12/sample-of-formula/)
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](https://ja.wikipedia.org/wiki/%E3%81%8B%E3%81%91%E7%AE%97%E3%81%AE%E9%A0%86%E5%BA%8F%E5%95%8F%E9%A1%8C)
that was in Japan a while ago, but anyway, according to [Japanese official
teaching
guidelines](http://www.mext.go.jp/component/a_menu/education/micro_detail/__icsFiles/afieldfile/2009/06/16/1234931_004_2.pdf),
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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2020-06-28T03:25:31.643
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answer