Arithmetic and relative clauses


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?




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.




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.

