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I was playing some math games intended for children, in Japanese, and the subject was 引き算.

The isolated question came up "14は10といくつ?" In the context of 引き算 it makes sense that the answer turned out to be 4, but I don't understand the question structurally. How does it imply "If you take 10 away from 14, what's left?" Is this to be understood only in the context? Assuming the と is conditional, my rough translation is "As for 14... if (you take away) 10... how much(left)?" with everything in parenthesis being only implied. Is this correct? Are the は and と particles doing what I think?

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Is this to be understood only in the context? Assuming the と is conditional

The と is not conditional, and you can tell that from the word followed by the と.

The conditional と should follow 活用語の終止形/the terminal form of a conjugatable word, such as verb, i/na-adjective, auxiliary, eg 「話す」「寒い」「静かだ」「〇〇だ」「~ない」. It cannot follow a 体言(unconjugatable word).

Eg.
食べると太ってしまう
明るいと眠れない
静かだと勉強がはかどる
佐藤さんがいないと困る

When と is attached to a 体言 (unconjugatable word) as in your example where と is attached to 「10」, it should be the case particle (格助詞).
The case particle と can attach to words of various part-of-speech (because of its quotative usage). It can be used for saying "~ and ~" (enumeration), "with (someone)", (same/different) as/from..." (comparison), "(saying) that..."(quotation), etc., as you probably know.

Eg.
13と14 -- "~ and ~" ← と follows 体言
リンゴとバナナとヨーグルト -- "~ and ~" ← と follows 体言
妹と一緒に勉強する -- "with (someone)" ← と follows 体言
山田さんと同じクラス -- "(same) as ~" ← と follows 体言
いやだと言う -- "(say) that..." ← と can follow various words

And as you can see, と in the sense "~ and ~" would make the most sense in your example.


"1410いくつ?"

I'd say the は is the topic marker, or the thematic は (主題の「は」).

lit. As for 14, 10 and how many (is it)?

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    FWIW, as colloquial English, my first thought for a translation was: "14 is 10 and how many?" The word "much" is usually used for non-countable amounts, while "many" is used for countables. :) Jul 15 at 16:14
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    @Eiríkr あ、how much は「いくつ」より「いくら」ですよね、どっちかっちゅーと・・
    – Chocolate
    Jul 16 at 0:32
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I think it is an odd way to ask, but the structure is:

  • 14 は 10 と いくつ
  • 14 = 10 + ?

so that it is essentially a subtraction.

Grammatically, は is the subject marker and と is and (In words, 14 is 10 and how many?)

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  • Ha! I just commented on Chocolate's, and look further down the page and you'd posted the same translation. Cheers! 😄 Jul 15 at 16:15
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    @Eiríkr, すみません、sundowner さんのほうが先に投稿していらして +2 入っていたんですが、なぜか私のほうに✔が… (私は "conditional と" ではないことを見分ける方法を説明したかったのですが長くなるのでコメントでなく回答に書き換えたんです)
    – Chocolate
    Jul 16 at 1:04

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