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A fake Facebook event disguised as a math problem has been one of its top posts for 6 months
(www.engadget.com)
This is a most excellent place for technology news and articles.
So let's try out some different prioritization systems.
Left to right:
Right to left:
Multiplication first:
Here the path divides again, we can do the left division or right division first.
And finally division first:
It's ambiguous which one of these is correct. Hence the best method we have for "correct" is left to right.
Maybe I'm wrong but the way I explain it is until the ambiguity is removed by adding in extra information to make it more specific then all those answers are correct.
"I saw her duck"
Until the author gives me clarity then that sentence has multiple meanings. With math, it doesn't click for people that the equation is incomplete. In an English sentence, ambiguity makes more sense and the common sense approach would be to clarify what the meaning is
100% with you. "Left to right" as far as I can tell only exists to make otherwise "unsolvable" problems a kind of official solution. I personally feel like it is a bodge, and I would rather the correct solution for such a problem to be undefined.
It's not a rule, it's a convention, and it exists so as to avoid making mistakes with signs, mistakes you made in almost every example you gave where you disobeyed left to right.