It is not ambiguous at all, there absolutely is one right answer, and it is 16.
You're taking something you learned when you were like 9 years old and assuming it's correct in every situation forever.
Unfortunately this isn't the case and you're incorrect.
Inaccurate, this has nothing to do with the mnemonic PEMDAS, this has to do with the actual order of operations it tries to instill. That order of operations is not ambiguous, there is a correct way to solve simple equations like the one above, and there is one and only one correct answer to it. That answer is 16.
And in the "actual" order of operations, if we want to pretend one exists, 2( binds more tightly than ÷
if you're going via prescriptivism, then you're wrong, because there are plenty of authoritative sources following the left hand model
if you're going via descriptivism, then you're wrong, because this thread exists
No, 2( does not bind more tightly than ÷. 2( is simply 2×(..., and ÷ and × occur at the same level of priority. After resolving the addition in the parentheses, the remaining operations are resolved left to right.
if you're going via prescriptivism, then you're wrong, because there are plenty of authoritative sources following the left hand model
if you're going via descriptivism, then you're wrong, because this thread exists
No, the fact that a good many people are incorrect about how math works does not entail that math is an open question. It's not, math has actual rules to its equations and an unambiguous right answer. In this case, that answer is 16.
math has actual rules to its equations and an unambiguous right answer
you know you could've just started this by admitting you've never touched the subject at a higher level than high school and saved us all this bother
I'm well familiar with math and the rules by which it works. Those who persist in arguing the case here could save the rest of us the bother by admitting they were stumped by a simple gotcha equation and are embarrassed, rather than wasting everyone's time by insisting that math is nothing but a lawless, rules-free wasteland where the answer to an equation depends on your feelings at the time.
I’m well familiar with math and the rules by which it works
i know you won't realise this because you never got past basic calculus, but this is a very funny statement to anybody that did
they know all the "math rules" guys. which ones? ALL of them
but okay these rules: where do they come from, then?
Fortunately, the rules necessary to resolve the equation in this post are extremely elementary, so none of what you're referencing has any bearing whatever.
There are exactly three things to consider in here to determine priority: parentheses, multiplication/division, and addition. The addition happens first due to the parentheses, and the remaining is evaluated left-to-right. The only correct answer here is 16.
All your deflection from your embarrassment at misreading a simple equation doesn't detract from this.
Fortunately, the rules necessary to resolve the equation in this post are extremely elementary, so none of what you’re referencing has any bearing whatever.
this would be like trying to tell a chemical engineer they didn't know what they were doing based on your understanding of the atom as a ball of protons with electrons wooshing round it like they were moons
very cute
unfortunately, if you give the expression 1 / 2x to anybody who knows what they're doing they'll interpret it as 1 / (2x) because it would be absurd not to
for reference, that's why the calculator works like this. because it's a tool designed primarily for people who actually know what they're doing with numbers, so it works how they expect it to work
And there you've proven exactly what I've been saying all along. 2x works the way it does because there's a variable involved, and natural reading of that treats it as a single entity. There are no variables in the equation in the post, there are only definite numbers, parentheses, and simple mathematical operations. 8/2(2+2) is nothing more than 8/2×(2+2). There is nothing special about 2(..., this is not the equivalent of 2x.
It is not ambiguous at all, there absolutely is one right answer, and it is 16.
You're taking something you learned when you were like 9 years old and assuming it's correct in every situation forever.
Unfortunately this isn't the case and you're incorrect.
Inaccurate, this has nothing to do with the mnemonic PEMDAS, this has to do with the actual order of operations it tries to instill. That order of operations is not ambiguous, there is a correct way to solve simple equations like the one above, and there is one and only one correct answer to it. That answer is 16.
And in the "actual" order of operations, if we want to pretend one exists,
2(binds more tightly than÷if you're going via prescriptivism, then you're wrong, because there are plenty of authoritative sources following the left hand model
if you're going via descriptivism, then you're wrong, because this thread exists
No, 2( does not bind more tightly than ÷. 2( is simply 2×(..., and ÷ and × occur at the same level of priority. After resolving the addition in the parentheses, the remaining operations are resolved left to right.
No, the fact that a good many people are incorrect about how math works does not entail that math is an open question. It's not, math has actual rules to its equations and an unambiguous right answer. In this case, that answer is 16.
you know you could've just started this by admitting you've never touched the subject at a higher level than high school and saved us all this bother
I'm well familiar with math and the rules by which it works. Those who persist in arguing the case here could save the rest of us the bother by admitting they were stumped by a simple gotcha equation and are embarrassed, rather than wasting everyone's time by insisting that math is nothing but a lawless, rules-free wasteland where the answer to an equation depends on your feelings at the time.
i know you won't realise this because you never got past basic calculus, but this is a very funny statement to anybody that did
they know all the "math rules" guys. which ones? ALL of them
but okay these rules: where do they come from, then?
Fortunately, the rules necessary to resolve the equation in this post are extremely elementary, so none of what you're referencing has any bearing whatever.
There are exactly three things to consider in here to determine priority: parentheses, multiplication/division, and addition. The addition happens first due to the parentheses, and the remaining is evaluated left-to-right. The only correct answer here is 16.
All your deflection from your embarrassment at misreading a simple equation doesn't detract from this.
this would be like trying to tell a chemical engineer they didn't know what they were doing based on your understanding of the atom as a ball of protons with electrons wooshing round it like they were moons
very cute
unfortunately, if you give the expression
1 / 2xto anybody who knows what they're doing they'll interpret it as1 / (2x)because it would be absurd not tofor reference, that's why the calculator works like this. because it's a tool designed primarily for people who actually know what they're doing with numbers, so it works how they expect it to work
And there you've proven exactly what I've been saying all along. 2x works the way it does because there's a variable involved, and natural reading of that treats it as a single entity. There are no variables in the equation in the post, there are only definite numbers, parentheses, and simple mathematical operations. 8/2(2+2) is nothing more than 8/2×(2+2). There is nothing special about 2(..., this is not the equivalent of 2x.
No it isn't. 2(a+b)=(2a+2b) The Distributive Law