Elementary Algebra in Japanese

Our ancient people were smart enough and already had the verbs for basic Algebra.


1.  To add : <ta-su> (たす).  Related words:

<ta-su-ke-ru> (たすける）to help
<ta-su-ka-ru> (たすかる）to be helped.
-----
<ku-wa-e-ru> (くわえる) to add. The old form <ku-wa-u> (くわう).
<ma-su> (ます)　to increase


2.  To subtract: <hi-ku> (ひく).   Related words:　

1) hi-ku　(ひく, 引く)  to pull,
2) hi-ku　(ひく, 引く)  to draw
3) hi-ku　(ひく, 退く)  to withdraw
4) hi-ku　(ひく, 惹く)  to attract  (like gravity)

The pronunciations and intonations are all the same <hi-ku> .
 -----
5) <he-ru> (へる)  to decrease


3. To multiply: <ka-ke-ru> (かける). Related words:　

The origin of this a bit complicated algebra  is unknown. 

Related words:　

はしをかける（hashi wo ka-ke-ru）：To build a bride (across over the river)
はしごをかける（hashigo wo ka-ke-ru）：To set a ladder (to the roof to clime up to it)
あしをかける（ashi wo ka-ke-ru）：To place something (like a rope or your own foot) at the foot or feet of someone else (who is walking) to make him stumble. Or like in Judo or Sumou (Japanese traditional wrestling or their National Sport), to place the own foot at the foot or feet of the opponent (who is standing) and push somewhere at the upper part to make him stumble by using the lever effect.

For ref.

<ka-ke-ru> has several different meanings.

1) ka-ke-ru (intonation at ke - Tokyo accent)

i)   to hang ( ka-ke-ru - 懸ける when the Chinese letter used)  The old form is ka-ku.
ii)  to place something with two points of it as the supporting points against something else like a bridge and ladder shown above (also ka-ke-ru - 掛けるWhen the Chinese letter used).

iii)   to run  ( ka-ke-ru - 駆ける when the Chinese letter used). The old form is ka-ku.
iv)  to bet ( ka-ke-ru - 賭ける when the Chinese letter used). The old form is ka-ku.
v)  to scratch (ka-ku -  掻く when the Chinese letter used, ka-ke-ru means to be able to scratch, scratche-able)
vi)  to write (ka-ku -  書く　when the Chinese letter used, ka-ke-ru means to be able to write, readable)


2) ka-ke-ru (intonation at ru) or maybe ka-ke-ru (flat with no intonation) in - Tokyo accent

i) to be missing, to be insufficient  欠ける. The old form is ka-ku.


There seems to be no relation between the <multiply>  <ka-ke-ru> and the other <ka-ke-ru>s.

Wild guess - 1 (basic concept)

Please read some of the above again.

ii)   to place something with two points of it as the supporting points against something else like a bridge and ladder shown above (also ka-ke-ru - 掛ける　when the Chinese letter used).  はしをかける（hashi wo ka-ke-ru), はしごをかける（hashigo wo ka-ke-ru).

and 

あしをかける（ashi wo ka-ke-ru）：To place something (like a rope or your own foot) at the foot or feet of someone else (who is walking) to make him stumble. Or like in Judo or Sumou (Japanese traditional wrestling or their National Sport), to place the own foot at the foot or feet of the opponent (who is standing) and push somewhere at the upper part to make him stumble by using the lever effect.

There are something in common - the function of the supporting point(s). Especially あしをかける（ashi wo ka-ke-ru）by using the lever effect. See below:



The lever effect is commonly seen and used but this is a kind of magic and based on the multiplication.

Y = aX

X is multiplied by <a>. If <a> is small, say <1, 2 ,3> Y changes a little, while <a> is large, say < 10, 100, 1,000> X changes a lot.

Wild guess - 2 (historical)

I have not checked but the concept and use of ka-ke-ru (to multiply) is not so old and probably after the commercial activity started. Merchants are generally profit conscious. They may have started to use multiplication by using a factor of 1.1, 1.15, 1.20, etc to make their selling prices including their profits or even divided by a factor of 0.9, 0.85, 0.8, etc to do so. The former case was called simply 1, 1.5, 2, ect ka-ke or ga-ke and the latter case was called 0.9, 0.85, 0.8, etc ka-ke or ga-ke or uchi-ga-ke - uchi means <inner> and the front <0.> was omitted and say 9, 8.5, 8 ga-ke .


4.  To divide: <wa-ru> （わる、割る）Related words:　

<wa-ru> （わる）: to break something into pieces
<wa-ke-ru> （わける）: to divide to parts



sptt