Yes, she votes, as do millions just like her
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This is why it's a troll. Apparently somewhere along the way--possibly a generational change or a widespread math-teaching policy change--what constitutes "resolving the parenthetical" involves.
I'm going to guess I'm older than you, because that is how this usually goes. To me, resolving the parenthetical (which is PEMDAS priority numero uno) means resolving that chunk together, which includes the 2 stuck to the outside of the parenthesis. That "clause" becomes "2 * 1 + 2 * 2." PEMDAS again, and that portion becomes "2 + 4." Solve, "=6."
YM obviously MV, but I find it very odd to not treat the parenthetical as a whole clause, in the absence of an operator between the 2 and the parenthesis.
Now, I'm no slouch. SAT/GMAT scores with math in the top 1%, back in the day, and having tutored statistics at the graduate level. So I don't think this is me remembering it wrong. Somehow at one point I managed to not get these questions wrong on standardized testing, relying on this method.
My best guess is some time between scenes, what was considered SOP, or at least was taught by primary school math teachers, changed. Maybe it wasn't even a universal change, leaving some people to know it one way, and some people to know it another. What you're left with is a "Gif/Jif" fight where people are largely just so used to their certainty, that the other guy's usage causes them frustration and discomfort.
I mean, any explanation of PEMDAS is clear about the parentheses
https://pemdas.info/
And the the 2 outside the parenthesis signifies to multiply with the result of the parenthesis, so there should be no debate about that.
LOL, we're using different definitions of "clear," I think. It twice says that Parentheses come first, but then declines to show an example, or to address the conundrum that is the equation at the heart of this forum.
Yes. 2(1+2) is read either as "1+2, * 2, which gets you 6, or "2 * 1 + 2 * 2," which is also 6. That's not where we're stuck. We're stuck at the "6 / 2(" beforehand. Some people's (and my) view is that even though there's a division sign between 6 and 2, which would make that a priority over addition and subtraction, that the 2 is stuck to the parenthetical without an operation between makes the 2( part of the parenthetical equation that must be resolved before the "6 / " can be addressed. "Six divided by the product of 2 times the sum of one plus two." Is how I read it.
Kiernan called this a matter of language, and I concur (and mathematics is symbolic language). It is clear to me that 2(1+2) is a symbolic chunk, a "clause" that constitutes a parenthetical. The more modern view, which I think is more unclear in intent (thus making a poor linguistic choice) says that 2( is irrelevant, the parenthetical is only what is contained inside the parentheses, concluding that 6 / 2 is a "clause" and "(1 + 2)" is another.
Doesn't make sense to me, as it introduces this ambiguity, that could easily have been avoided by presenting the equation as: 6 / 2 * (1 + 2). "Six divided by two, times the sum of one plus two." Bada bing, bada boom. The modern view considers this clarification extraneous and unnecessary. I think the resulting confusion and agitation demonstrate that it's not.
I've seen people claim pre-1917 methods would give you the "1" answer, but it - assuming we're not all crazy - went on well past that. Pretty sure I was also taught what you're talking about and, and I think I was like top 3% in SAT mathematics too, although it's been ages. No graduate level stuff, but I'd say I'm decent (if now rusty) at math concepts.
To be fair, I'm not sure there were these kind of weird questions; it's just an odd layout, a trick.
I'm thinking something like that too. That said, I do think "9" is largely correct here, but I absolutely see the other angle too, and think it's just a bizarre equation anyway, and that's the real issue.
I think I can best describe the split as what I came up with responding to user20461. The two ways of reading it are:
A)"Six divided by the product of 2 times the sum of one plus two."
B)"Six divided by two, times the sum of one plus two."
Which of these does "6 / 2(1+2)" really say? B), what seems to be the most common modern view, invents a comma not indicated by the symbology. A) doesn't require it to be understood clearly and simply. I tie my horse to A) for clarity's sake.
WELL THEN MOTHERFUCKING PISTOLS AT DAWN SIR
I'll have to decline, for I have once again changed my mind because this equation is intentionally retarded and I keep talking myself around in circles.
The issue is this is not made to be read clearly or unambiguously, and so is worthless.
Indeed. I even went another step and found this unhelpful thing, on the wiki regarding multiplication:
"In algebra, multiplication involving variables is often written as a juxtaposition (e.g., xy for x times y or 5x for five times x), also called implied multiplication. The notation can also be used for quantities that are surrounded by parentheses (e.g., 5(2) or (5)(2) for five times two). This implicit usage of multiplication can cause ambiguity when the concatenated variables happen to match the name of another variable, when a variable name in front of a parenthesis can be confused with a function name, or in the correct determination of the order of operations."
Then it says "CITATION NEEDED," meaning THEY'RE FIGHTING ABOUT IT THERE TOO.
I'm quitting it before I develop an eye-twitch.