Commercial minus as italic variant of division sign in German and Scandinavian context

[Leif Halvard Silli]

Thanks to our discussion in July 2012,[1] the Unicode code charts now 
says, about 00F7 ÷ DIVISION SIGN, this:

  “• occasionally used as an alternate, more visually
     distinct version of 2212 − {MINUS SIGN} or 2011 ‑ 
     {NON-BREAKING HYPHEN} in some contexts  
        [… snip …]
   → 2052 ⁒ commercial minus sign”

However, I think it can also be added somewhere that commercial minus 
is just the italic variant of ”division minus”. I’ll hereby argue for 
this based on an old German book on ”commercial arithmetics” I have 
come accross, plus what the the July 2012 discussion and what Unicode 
already says about the commercial sign:

FIRST: IDENTICAL CONTEXTS. 

   German language is an important locale for the Commercial Minus. In 
German, the Commercial minus is both referred to as ”kaufmännische 
Minus(zeichen)” and as "buchhalterische Minus" (”Commercial Minus 
Character” and ”Bookkeeper Minus”). And, speaking of ”division minus” 
in the context I know best, Norway, we find it in advertising 
(commercial context) and in book keeping documentation and taxation 
forms. Simply put, what the Unicode 6.2 ”General Punctuation” section 
says about Commercial Minus, can also be said about DIVISION SIGN used 
as minus: «U+2052 % commercial minus sign is used in commercial or tax 
related forms or publications in several European countries, including 
Germany and Scandinavia.» So, basically and for the most part, the 
commercial minus and the ”division sign minus” occur in the very same 
contexts, with very much the same meaning. This is a strong hint that 
they are the same character.

SECOND: GERMAN USE OF DIVISION SIGN FOR MINUS IN COMMERCIAL CONTEXT.

   Is there any proof that German used both an italics variant and a 
non-italics variant of the “division minus”? Seemingly yes. The book 
“Kaufmännische Arithmetik” (“Commercial arithmetics”) from 1825 by 
Johann Philipp Schellenberg. By reading section 118 «Anhang zur 
Addition und Subtraction der Brüche» [”Appendix about the addition and 
subtraction of fractions”]) at page 213 and onwards,[2] we can conclude 
that he describes as “commercial” use of the ÷ ”division minus”, where 
the ÷ signifies a _negative remainder_ of a division (while the plus 
sign is used to signify a positive remainder). Or to quote, from page 
214: «so wird das Fehlende durch das [Zei]chen ÷ (minus) bemerkt, und 
bei Berechn[nung der Preis der Waare abgezogen» [”then the lacking 
remainder is marked with the ÷ (minus) and withdrawn when the price of 
the commodity is calculated”]. {Note that some bits of the text are 
lacking, I marked my guessed in square brackets.} I did not find (yet) 
that he used the italic commercial minus, however, the context is 
correct. (My guess is that the italics variant has been put to more 
use, in the computer age, partly to separate it from the DIVISION SIGN 
or may be simply because people started to see it often in handwriting 
but seldom in print. And so would not have recognized it in the form of 
the non-italic division sign.)

THIRD: IDENTICAL INTERPRETATION

The word “abgezogen” in the above quote is interesting since the Code 
Charts for 2052 ⁒ COMMERCIAL MINUS cites the related German word 
“abzüglich”. And from the Swedish context, the charts quotes the 
expression “med avdrag”. English translation might be ”to be withdrawn” 
or ”with subtraction/rebate [for]”. Simply put, we here see the 
commercial meaning.

WHAT ABOUT COMMERCIAL MINUS AS “CORRECT” SIGN  IN SCANDINAVIAN SCHOOLS?

UNICODE 6.3 notes that in some European (e.g. Finnish, Swedish and 
perhaps Norwegian) traditions, teachers use the Commercial Minus Sign 
to signify that something is correct (whereas a red check mark is used 
to signify error). If my theory is right, that commercial minus and 
division sign minus are the same signs, how on earth is that possible? 
How can a minus sign count as positive for the student?

The answer is, I think, to be found in the Code Chart’s Swedish 
description ("med avdrag"/"with subtraction/rebate"). Because, I think 
that the correct understanding is not that it means "correct" or "OK". 
Rather, it denotes something that is counted in the customer/student’s 
favor. So, you could say it it really means "slack", or "rebate".  So 
it really mans ”good answer“. It is a ”rebate” that the student 
rightfully deserves.

FOURTH: A DEEPER MEANING

If we look at it from a very high level, then we can say that the 
division minus is used to signify something that is the result of a 
calculation - such as a price, an entry in bookkeeping or, indeed, a 
character/mark/point/score in a (home)work evaluated by a teacher. 
Whereas the ”normal” minus sign is used to when we represent negative 
data. For example, in taxation, all the numbers one reports, is the 
result of some calculation. Likewise, when a teach ticks of an answer 
as “good answer”, then it is because the teacher has evaluated (a.k.a. 
”calculated”) the answer and found it to be good and that the student 
has calculated correctly/well.

CIRCUMSTANCIAL EVIDENCE

The commercial minus looks like a percentage sign. And also, in 
programming, e.g. JavaScript, the percentage sign is often used for the 
modulo operator - which is an operator that finds the dividend of a 
division.

Hence, when we take all this together, I believe we have to conclude 
that the COMMERCIAL MINUS is just the italic variant of the DIVISION 
SIGN.

PS: For more German documentation of this custom, it would probably be 
wise to research books about bookkeeping as well as ”commercial 
arithmetics”. I also have a suspicion that it would be worth 
investigation contexts where modulo/division remainders operations are 
found - for instance, in calendar calculations.

[1] http://www.unicode.org/mail-arch/unicode-ml/y2012-m07/0053.html
[2] 
https://archive.org/stream/kaufmnnischeari00schegoog#page/n229/mode/2up
-- 
leif halvard silli