I thought I would consider talking about this 'operator' because of its notorious nature of confusing the public. I hope to convince you of the importance of the obelus sign, and why people should not confuse this sign with the '/' division operator. In basic words, there is a reason why we don't see this operator beyond elementary school, it is because it doesn't actually represent division as myself, or any scientist would use in an algebraic sense. This is actually an operator which entails mainly computational use.
Believe it or not, the oldest account of the use of obelus used in a text I could find in this form is found in a german text from 1659 called Teutsche Algebra by Johann H. Rahn. Here is a picture below of their algebraic rules: (look for the one with the obelus)
There are other examples through texts of this nature. I personally believe the obelus has lost its meaning over the years, but in itself it does resolve a lot of the Left-Right parsing issues with division in not ambigous forms using it in general. Let me explain by using an example by denoting two alleged statements which are claimed to be the same:
[1] 6/3(3+1)
[2] 6÷3(3+1)
Now your intuition because you see '÷' you say "DIVISION, let's do it!". Take a step back and notice these are two statement with two operators. Now today in convention we just say they are the same thing to ease issues, but it evades the purpose of the ÷ sign. Here is why upon discussing with a couple peers in education why they continue to use this ONLY at the elementary level.
It is about enforcing the concepts of division, not carrying out actual division. When you write it with the obelus, it is to separate the numerator and denominator, then carry out the operator. Meaning the left, and right terms are clustered together in two arguments. So this operates less like '/' and more like a clear division. It is strict division it seems.
The obelus is usually only used with numbers, and not algebraic statements since it doesn't really have the meaning we intend for division. You can think of the obelus as an elementary school tool to hammer in the concept to take one thing and break it into other pieces and count them.
Here is a more accurate way of stating the ÷ sign in modern days:
a÷b = (a)/(b) to be consistent with older texts which used this sign more regularly.
So if we do our two example we yield [1]:
6/3(3+1) which is 2*4 which is 8.
[2] yields:
6÷3(3+1) rewrites as (6)/(3(3+1)), then is 6/12 which is 0.5.
Notice the way we write the two statements in our example makes a big difference in the way they are carried out. Older models of calculators will employ ÷ over / since it is quicker to implement, since they will assume you are doing the division where you don't have more complicated statements than a over b.
It is fundamental to understand the obelus' main place in teaching is with only simple arithmetic statements where there are only two numbers involved. In computation the obelus is more common since you can assume we can fiddle around with the two arguments of a division (much like in a programmer's arsenal) since depending on the language you will have to interpret the operator differently.
This maybe doesn't have as much relevance today since conventions in Mathematics do change over time, but I believe as a scientist that we should not use an operator which is not used properly unless it has a purpose. In general, use the '/' over the obelus, it is far more clear since it can be intended as different things. I would definitely treat them as two different types of division (one the algebraic operator, the other a binary operator with a lower precedence). Obelus is more of a computational form of division than an algebraic one anyways.
Hope this helps!
Have a beautiful day!
D R Page
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