<p><kbd><a href="https://en.wikipedia.org/wiki/Shang_dynasty" rel="nofollow noreferrer">商</a><br><a href="https://en.wikipedia.org/wiki/Oracle_bone_script" rel="nofollow noreferrer">甲</a><br><a href="https://i.sstatic.net/1HGtG.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/1HGtG.png" alt="enter image description here"></a><br><a href="http://xiaoxue.iis.sinica.edu.tw/yanbian/Reference/JiaguwenReference" rel="nofollow noreferrer">河</a>687<br><a href="http://www.guoxuedashi.com/jgwhj/?bhfl=1&amp;bh=24225&amp;jgwfl=" rel="nofollow noreferrer">合集24225</a></kbd></p>

<p>「商」 (<em>to measure</em> > <em>calculate, approximate, discuss</em> > (1) <em>quotient</em>, (2) <em>commerce</em>) was originally comprised of <a href="http://xiaoxue.iis.sinica.edu.tw/yanbian?kaiOrder=706" rel="nofollow noreferrer">「辛」 (<em>picture of a chisel or torture weapon</em></a> > <em>hardship, difficulty</em>) and <a href="http://xiaoxue.iis.sinica.edu.tw/yanbian?kaiOrder=157" rel="nofollow noreferrer">「丙」 (<em>picture of a workshop table</em>)</a>, indicating trade professions involving <em>measurement</em> (e.g. of raw materials and dimensions). This is one of the earliest and most literal meanings of the word 「商量」.</p>

<p>「口」 was later added as a <em>proper noun mark</em>, referring to the name of the <a href="https://en.wikipedia.org/wiki/Shang_dynasty" rel="nofollow noreferrer"><em>Shang Dynasty</em></a>.</p>

<p><kbd>商<br><a href="https://en.wikipedia.org/wiki/Chinese_bronze_inscriptions" rel="nofollow noreferrer">金</a><br><a href="https://i.sstatic.net/B11kZ.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/B11kZ.png" alt="enter image description here"></a><br>商婦甗<br><a href="http://www.guoxuedashi.com/yzjwjc/?bh=867&amp;jgwfl=" rel="nofollow noreferrer">集成867</a></kbd><kbd><a href="https://en.wikipedia.org/wiki/Warring_States_period" rel="nofollow noreferrer">戰國</a>・<a href="https://en.wikipedia.org/wiki/Chu_(state)" rel="nofollow noreferrer">楚</a><br>金<br><a href="https://i.sstatic.net/ZrRKD.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/ZrRKD.png" alt="enter image description here"></a><br>曾侯乙鐘<br><a href="http://www.guoxuedashi.com/yzjwjc/?bh=290&amp;jgwfl=" rel="nofollow noreferrer">集成290</a></kbd><kbd><a href="https://en.wikipedia.org/wiki/Qin_dynasty" rel="nofollow noreferrer">秦</a><br><a href="https://en.wikipedia.org/wiki/Bamboo_and_wooden_slips" rel="nofollow noreferrer">簡</a><br><a href="https://i.sstatic.net/2PyhR.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/2PyhR.png" alt="enter image description here"></a><br><a href="http://xiaoxue.iis.sinica.edu.tw/yanbian/Reference/QinwenziReference" rel="nofollow noreferrer">日甲</a>145<br><a href="https://en.wikipedia.org/wiki/Shuihudi_Qin_bamboo_texts" rel="nofollow noreferrer">睡虎地秦簡</a></kbd><kbd>今<br><a href="https://en.wikipedia.org/wiki/Regular_script" rel="nofollow noreferrer">楷</a><br><a href="https://i.sstatic.net/5UAtx.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/5UAtx.png" alt="enter image description here"></a><br><br> 　</kbd></p>

<blockquote>
  <p>Compare the similar addition of 「口」 (or its derivatives <a href="http://xiaoxue.iis.sinica.edu.tw/yanbian?kaiOrder=264" rel="nofollow noreferrer">「甘」</a> and <a href="http://xiaoxue.iis.sinica.edu.tw/yanbian?kaiOrder=137" rel="nofollow noreferrer">「曰」</a>) in the characters <a href="http://xiaoxue.iis.sinica.edu.tw/yanbian?kaiOrder=802" rel="nofollow noreferrer">「周」</a> (<a href="https://en.wikipedia.org/wiki/Zhou_dynasty" rel="nofollow noreferrer"><em>Zhou Dynasty</em></a>), <a href="http://xiaoxue.iis.sinica.edu.tw/yanbian?kaiOrder=2172" rel="nofollow noreferrer">「曹」</a> (<a href="https://en.wikipedia.org/wiki/Cao_(state)" rel="nofollow noreferrer"><em>State of Cao</em></a>), <a href="http://xiaoxue.iis.sinica.edu.tw/yanbian?kaiOrder=2606" rel="nofollow noreferrer">「曾」</a> (<a href="https://en.wikipedia.org/wiki/Sui_(state)" rel="nofollow noreferrer"><em>State of Zeng</em></a>), etc.</p>
</blockquote>

<p><em>To measure</em> was later extended to mean <em>approximation</em> or <em>calculation</em>, and then specialised to mean <em>quotient</em>, derived from its use as a kind of jargon in <a href="https://en.wikipedia.org/wiki/Rod_calculus" rel="nofollow noreferrer">rod calculus</a>.</p>

<blockquote>
  <p>See a <a href="https://en.wikipedia.org/wiki/Rod_calculus#Extraction_of_Square_root" rel="nofollow noreferrer">rod calculus tutorial on computing the square root of 234567</a>. The top row in this calculation layout is called 「商」.</p>
</blockquote>

<hr>

<p><strong>References:</strong></p>

<ul>
<li>季旭昇《說文新證》</li>
<li><a href="http://xiaoxue.iis.sinica.edu.tw/" rel="nofollow noreferrer">小學堂</a></li>
<li><a href="http://www.guoxuedashi.com/" rel="nofollow noreferrer">國學大師</a>

<ul>
<li><a href="http://www.guoxuedashi.com/jgwhj/" rel="nofollow noreferrer">郭沫若《甲骨文合集》</a></li>
<li><a href="http://www.guoxuedashi.com/yzjwjc/" rel="nofollow noreferrer">中國社會科學院考古研究所《殷周金文集成》</a></li>
</ul></li>
</ul>

CC BY-SA 4.0
2020-01-30T07:18:59.317Z
"Measure" is actually a more apropos reference than one might think - and the relevant cognition appears in other cultures as well: e.g. if one looks to the classic Greek text by Euclid, the *Elements*, division of one number by another is called "measuring" the one by the other. A quotient, $a/b$, can be interpreted as "given a quantity $a$, measure it out in units of size $b$, and give its value in terms of those units". And this is also how all physical measurements work, too - in effect, you're taking the "quotient" of one physical object by another, reference
The_Sympathizer
CC BY-SA 4.0
2020-01-30T07:19:01.773Z
object (the unit), to yield a number.
The_Sympathizer
CC BY-SA 4.0
2020-01-30T07:20:19.127Z
Hence 商量, "measured quantity", is pretty much perfect: "the measured quantity [商量] formed by measuring a in units of b", is a/b.
The_Sympathizer
CC BY-SA 4.0
2018-02-03T12:05:15.820Z
2020-01-28T15:53:38.710Z
2020-01-28T15:53:38.710Z
dROOOze
<p><a href="https://en.wikipedia.org/wiki/Quotient" rel="nofollow noreferrer">Wikipedia</a> defines "quotient" as:</p>

<blockquote>
  <p>In arithmetic, a quotient (from Latin: quotiens "how many times", pronounced /ˈkwoʊʃənt/) is the quantity produced by the division of two numbers.[1]</p>
</blockquote>

<p>Does the character 「商」 have the meaning of "how many times" from its origin?<br>
Why is "quotient" translated as 「商」?</p>

<meaning><glyph-origin>
Why is "quotient" translated as 「商」 in mathematics?
# Why is "quotient" translated as 「商」 in mathematics?

(Asked by: username_0 on 2018-02-03)

[Wikipedia](https://en.wikipedia.org/wiki/Quotient) defines "quotient" as:

> In arithmetic, a quotient (from Latin: quotiens "how many times", pronounced /ˈkwoʊʃənt/) is the quantity produced by the division of two numbers.[1]

Does the character 「商」 have the meaning of "how many times" from its origin?  
Why is "quotient" translated as 「商」?

**Tags:** meaning, glyph-origin

---

## 1 answers

### Answer by username_1 on 2018-02-03. Score: 4 | Accepted answer

`商  
甲  
![enter image description here](https://i.sstatic.net/1HGtG.png)  
河687  
合集24225`

「商」 (*to measure* > *calculate, approximate, discuss* > (1) *quotient*, (2) *commerce*) was originally comprised of [「辛」 (*picture of a chisel or torture weapon*](http://xiaoxue.iis.sinica.edu.tw/yanbian?kaiOrder=706) > *hardship, difficulty*) and [「丙」 (*picture of a workshop table*)](http://xiaoxue.iis.sinica.edu.tw/yanbian?kaiOrder=157), indicating trade professions involving *measurement* (e.g. of raw materials and dimensions). This is one of the earliest and most literal meanings of the word 「商量」.

「口」 was later added as a *proper noun mark*, referring to the name of the [*Shang Dynasty*](https://en.wikipedia.org/wiki/Shang_dynasty).

`商  
金  
![enter image description here](https://i.sstatic.net/B11kZ.png)  
商婦甗  
集成867``戰國・楚  
金  
![enter image description here](https://i.sstatic.net/ZrRKD.png)  
曾侯乙鐘  
集成290``秦  
簡  
![enter image description here](https://i.sstatic.net/2PyhR.png)  
日甲145  
睡虎地秦簡``今  
楷  
![enter image description here](https://i.sstatic.net/5UAtx.png)`

> Compare the similar addition of 「口」 (or its derivatives [「甘」](http://xiaoxue.iis.sinica.edu.tw/yanbian?kaiOrder=264) and [「曰」](http://xiaoxue.iis.sinica.edu.tw/yanbian?kaiOrder=137)) in the characters [「周」](http://xiaoxue.iis.sinica.edu.tw/yanbian?kaiOrder=802) ([*Zhou Dynasty*](https://en.wikipedia.org/wiki/Zhou_dynasty)), [「曹」](http://xiaoxue.iis.sinica.edu.tw/yanbian?kaiOrder=2172) ([*State of Cao*](https://en.wikipedia.org/wiki/Cao_(state))), [「曾」](http://xiaoxue.iis.sinica.edu.tw/yanbian?kaiOrder=2606) ([*State of Zeng*](https://en.wikipedia.org/wiki/Sui_(state))), etc.

*To measure* was later extended to mean *approximation* or *calculation*, and then specialised to mean *quotient*, derived from its use as a kind of jargon in [rod calculus](https://en.wikipedia.org/wiki/Rod_calculus).

> See a [rod calculus tutorial on computing the square root of 234567](https://en.wikipedia.org/wiki/Rod_calculus#Extraction_of_Square_root). The top row in this calculation layout is called 「商」.

---

**References:**

* 季旭昇《說文新證》
* [小學堂](http://xiaoxue.iis.sinica.edu.tw/)
* [國學大師](http://www.guoxuedashi.com/)
  + [郭沫若《甲骨文合集》](http://www.guoxuedashi.com/jgwhj/)
  + [中國社會科學院考古研究所《殷周金文集成》](http://www.guoxuedashi.com/yzjwjc/)

> **Comments:**
> **username_2**: "Measure" is actually a more apropos reference than one might think - and the relevant cognition appears in other cultures as well: e.g. if one looks to the classic Greek text by Euclid, the *Elements*, division of one number by another is called "measuring" the one by the other. A quotient, $a/b$, can be interpreted as "given a quantity $a$, measure it out in units of size $b$, and give its value in terms of those units". And this is also how all physical measurements work, too - in effect, you're taking the "quotient" of one physical object by another, reference  
> **username_2**: object (the unit), to yield a number.  
> **username_2**: Hence 商量, "measured quantity", is pretty much perfect: "the measured quantity [商量] formed by measuring a in units of b", is a/b.  

---

