Comments

@TheStarHawk, ive always been taught the order of operations was pemdas meaning one before the other and not that it was left to right when it comes to the set of operations considered(m/d or a/s). That or its a combination of not needing to use it/ the tine its been since ive learned it rhat i just dont remembber that detail…

@orion55, you are correct in saying that division and fractions are the same... but somewhat backwards. It's not that division = fraction, it's that all fractions are division, but if you were to write this division as a fraction it would be 6 over 2, then multiplied by 3, or 6/2 * 3/1 in fraction form, not 6/(2*3). It's really not written ambiguously, it's written specifically in the way it is, if it were 6 as a numerator over the rest of the equation, it would be written specifically as such.

@TheStarHawk, you’re treating the 2(3) as part of standard multiplication, when in fact distribution to within parentheses comes before MD if within the parentheses you had a variable, you wouldn’t say 6 divided by 2x is 3x. The same principle applies to numbers. But no one writes problems like these, or should anyway. Division symbols get replaced by numerator denominator lines pretty quickly as you advance in math

@Berzerker, It's not though? It's literally the standardized way to do mathematics. Worldwide, everyone who does math does it in these procedural steps. It was standardized to avoid confusion exactly like this in equations and it greatly saddens me that, apparently, it's not taught like it should be in schools. So, you may disagree all you like, but it is a fact, globally accepted by science and mathematic professionals.

@Berzerker, I'm sorry that you were not taught order of operations. But it is read left to right. Has been since 1917. Again, specifically to avoid confusion such as is presented here. Here's an example of why. 8÷4×3=6 (left to right) 8÷4×3=⅔ (right to left) Even simple equations can have wildly different results when solved in reverse order. Hence why the standardized system was adopted.

@Berzerker, True, you probably wouldn't use the ÷ symbol at all. But that doesn't change anything about this equation. It still solves to 9 when solved correctly. It also doesn't change anything about the order in which you solve equations, you still solve them using P E MD AS where MD and AS are evaluated left to right, in order of their priority. MD then AS.

@Aegis, you should investigate the associative property. inferring parentheses around the division fixes this, but you have to adopt a left to right bias. You could also assume parentheses around the rightmost product and get a different answer. I know where you're coming from but it's just incorrectly written, and without context from the author, there is simply no way to know what the author meant by this expression.

@Berzerker, That's... not how that rule is applied... it's also not a bias... it's a mathematical standard... but go on then. Honestly I'm tired of arguing. You win. I concede, math has no order and anyone can solve it in any fashion they choose. Left, right, up, down, in whatever operator order as well. Have a good day.
9. Is the average person that ignorant of order of operations?