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Consider the following sentence:

八引く一は七です。
Eight minus one is seven.

This doesn't seem to obey the usual grammar rules. If I think of 引く as a verb meaning 'to subtract' then I have a relative clause 八引く modifying 一, so 八引く一 ought to be 'one where we subtract eight' i.e. the grammatical answer should be -7 rather than +7.

I suppose I ought to be suspicious of this analysis since there is no を on 八. What is the correct way to think about this sentence? Should I abandon trying to think of 引く as 'to subtract' and just use a plain 'minus'?

What if I had added the を i.e. 八を引く一は七です. Would this be grammatical? Would it change the meaning?

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  • What is the context for this sentence? Was it written out like that? Typically I see that language used not as a standalone sentence, but as a vocalization of the formula " 8 - 1 = 7 ". – SpiritTamer Apr 25 at 22:55
  • This is how, as @SpiritTamer mentioned, a line of mathematics is read. It is not how it would otherwise be expressed. – A.Ellett Apr 26 at 0:50
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    @A.Ellett You and the other commenter seem to have misssed the point of this interesting question: yes, of course that's how arithmetic is read; but how did this construction become to be considered idiomatic, in spite of its contradictory grammatical structure? (I suspect that adherence to left-to-right associativity of (western) math operator syntax was considered a more important consideration than Japanese clausal right-to-left associativity when the system was introduced in Japan (Meiji era?), but why the 連体形 istead of using the 連用形, for example「8引き1」?) – Will Apr 26 at 1:00
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    もともと(?)は、「8、引くことの7」とかだったのかな、と。(「そろばん」でそんなふうに言う) – Chocolate Apr 26 at 1:40
  • Related: japanese.stackexchange.com/q/56962/5010 – naruto Apr 26 at 8:45
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As Chocolate has already commented, it is very probably that たす and ひく originated from the teaching at そろばん塾 (soroban juku, abacus institute) which played a very important role as a private school especially in the Edo Period and has been very popular among school boys and girls even now.

Several decades ago, I was also taught calculation by the use of an abacus. In the soroban juku, a soroban teacher, first of all, called out 「ねがいましては」(Please [calculate]). Just after the calling, he said something like this:「100(円)(なり)、たすことの200(円)(なり)、ひくことの150(円)(なり)、こたえは?」. But this would be the calling for the soroban beginners and will not be heard now even in the abacus institute, because it is old-fashioned.

  • 5 たすことの 3 は 8.(5、それにたすのは 3 で、こたえは 8)5 plus 3 is 8.
  • 8 ひくことの 1 は 7.(8、それからひくのは 1 で、こたえは 7)8 minus 1 is 7.

But たすことの and ひくことの are long, so it must have been reduced or shortened to たす and ひく, especially when many numbers are added or subtracted as 「3たす5たす6たす9は」. And I have to emphasize that speed in calculation has been very important for the advanced level teaching.

Modern Japanese only recognize these たす and ひく as 'plus' and 'minus' without having any knowledge of the historical development of these expressions. I am very grateful to the questioner for letting me know their history.

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