An obelus was added to the mathematical language in the 1600's to write simple ratios. The orginal symbol for this looked like this ÷ . Eventually overtime especially with typewriters the symbol became looking like this : .
A viniculum was added shortly after an obelus and to write an equation that had an obelus into a equation using a vinculum you would write
6÷2×(3+3) into. _____×(3+3)
But this can also be written as 6:2×(3+3)
A solidus / was added to the mathematical language in the 1700's in order to write complex fractions that would normally require the use of a vinculum in the "inline fraction form". The use of a vinculum in math can easily require 3 times more paper use. The length of the equation is equal to the longest of either the denominator or numerator respectively, and even if one of the 2 is only 1 character, and the other is 32 characters long. You are wasting 31 extra characters on a vinculum and also the opossing side of the fraction. For this fact a solidus is not only a needed symbol in mathematics but also a cost saving method.
6/2(3+3) written with a vinculum would look like
Scientific calculator in the programming can switch between if they recognize a solidus or an obelus. Very expensive calculators can utilize both symbols in the same equation. Many physics professors will have 2 identical calculators with a label on each that states obelus, or solidus; or use the corresponding symbol on the label. This is done to help teach students that do not understand the difference.
If you have an equation such as ab÷cd and have a calculator set up to only solve for solidus than you need to convert that into a(b/c)d for the calculator to solve that equation correctly.
If you have an equation such as ab/cd and have a calculator only capable of solving for obelus(ratio) equation than it will need to be converted into (ab)÷(cd)
In the 1900's a printing press thought a solidus looked better than an obelus. So instead of placing the key for an obelus down as they where suppose to do, they changed the symbol and printed that mathematical text wrong. Still to this day there are many examples of this still found in high-school math text books.
For example when they have an excel spread sheet of mathematical notation a vinculum is referenced as being a horizontal or a vertical line and the horizontal symbol is removed from the symbols column. With ÷ and : symbols they are in there own column together and they both simply reference division symbols and not there intended references of being simple ratio symbols. In a column far away from obelus symbols generally next to a vinculum it has a solidus / symbol. Again only referencing it as a division symbol, instead of writing in-line fraction bar. If they could actually be used interchangeably than the orginal pre-printing company edits would have had all 3 symbols on the same excel column.
During the 1900's many public education school teachers wouldn't even have an associates degree. As a result many of the books sold to schools where never peered reviewed after printing.
A good scientific calculator not only should be able to switch between if it reads a solidus and obelus in the equation by going into setting. But also when it is set to obelus; to show an obelus on the screen. When it is set to do math in terms of a solidus than it shows a solidus on screen.
All these problems exist solely do to publishers such as wolfram misprinting mathematical textbooks. They have a web page dedicated to the fact that all peer reviewed mathematical textbooks used by people with phd. and peer reviewed by people with Phd's have the solidus and obelus meaning different things.
For this reason wolfram is not used in any college that teaches physics, programming, engineering or any other degrees that require advanced mathematics. As they would be peer reviewed and thrown out do to the level of misprinted textbooks they produce.
Instead of wolfram correcting there misprinted textbooks and printing a retraction and an apology to the mathematical community and public educational facilities, they ask others to join in with them for there misprints on there web page that dedicated to the fact that all peer reviewed advanced math text books would have 6÷2×(3+3)=18 and 6/2(3+3)=1÷2
A solidus is a necessary symbol in mathematics, it allows for easier reading of complex fractions, it saves on paper, ink.