Lots of interesting feedback, but it seems this topic remains opinion rather than stating a standard procedure.
Let's use the example of adding weights. Maybe shipping items from my house and needed to get a total weight, but also note individual weight of each box. My computer desk is 100lbs, book shelf 50lbs, and books are a total weight of 300lbs, however, my books will not all fit in one box, they need to be divided into 5 boxes.
Doing the math quickly and easily in my head, I would do the division first because I can add 60lbs along with 100 and 50 easier than retaining 150, doing the division, and then adding it into the number I had to remember.
Writing the "equation" would be simply: 100 + 50 + 300 / 5.
BEDMOS or however it's spelled would apply to this equation also, but per my original question, would engineers and mathematicians actually write the equation in hopes the reader(s) would apply grade school rules to it; and is the grade school rule actually the common practice to decipher such an equation (although this is a simple equation, let's assume it's much longer with more dividing and multiplication)?
The way I'd write this would be: 100 + 50 + (300/5). This seems quite obvious the 300/5 is its own section.
The other way someone may read it left to right and get 90, or they may think it's 100 + ((50 + 300) / 5)
As it's been pointed out, those articles are clickbait (and I knew this before), and the writer isn't a mathematician, but still, the question is interesting.
If this was a five equation with five unknowns, comprised of A, B, C, D, E, several brackets and parenthesis would be used, such as: [((A+2) / B) + (C^2) - (SQRT D) ] /E
With the above, assuming all five equations and unknowns were found, now you have more freedom. I can add A+2 first without worrying about C^2 until after, or take the SQRT of D first, but know I can't divide by E until the end. With BEDMOS I'd have to divide by E before adding A+2 and so on.
Let's assume A - E is 1-5 after solving for all five unknowns.
The equation would then look like 1 + 2 / 2 + 3^2 - SQRT 4 / 5
With BEDMAS 2/2, 3^2, and the SQRT of 4/5 would all be done first; obviously giving a completely different answer.