Question: 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?

Answer: 
> 
> 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.  
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> **食べると**太ってしまう  
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> **明るいと**眠れない  
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> **静かだと**勉強がはかどる  
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> 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  
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> いや**だと**言う -- "(say) that..." ← と can follow various words
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> 
> 

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

---

> 
> "14**は**10**と**いくつ？"
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> 

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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> 
>
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?*)