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The Language of Math - Order of Operations, Notation, and other subjects

I see the 8/2(4) as equalling 1, but if it was 8/2*(4) I'd see it as equalling 16.
Or:
LaTeX:
\[\frac{8}{2*4}=1\]
LaTeX:
\[\frac{8}{2}*4=16\]
We were taught the lack of separation between the 2 and the open bracket meant it was part of the bracketed section like how exponents on the closing bracket are part of the section.
But I didn't go into Maths, merely use it in my field and our equations are built with that assumption in mind.
 
Let's get into a nightmare argument. I am an engineer and a bit of a Nupas Cadmaitic system administrator. It is a software for modeling welded metal structures and preparing data for machine tools. It also allows you to create and configure a library of standard solutions. And so, as part of configuring these libraries, I came across the most damned approach. For some files, the approach works:
a+b/2+c*d => ((a+b)/2+c)*d.
shledon-bbt.gif
What in the unholy hell is that formula?
LaTeX:
\[ a+b\div2+c\times d\Rightarrow ((a+b)\div2+c)\times d \]
How does that even parse?!
 

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