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.
I mean, any explanation of PEMDAS is clear about the parentheses
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.
And the the 2 outside the parenthesis signifies to multiply with the result of the parenthesis, so there should be no debate about that.
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 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.