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.