Now that’s a good troll math thing because it gets really deep into the weeds of mathematical notation. There isn’t one true order of operations that is objectively correct, and on top of that, that’s hardly the way most people would write that. As in, if you wrote that by hand, you wouldn’t use the / symbol. You’d either use ÷ or a proper fraction.
Personally, I’d call that 36 as written given the context you’re saying it in, instead of calling it 1. But I’d say it’s ambiguous and you should notate in a way to avoid ambiguities. Especially if you’re in the camp of multiplication like a(b) being different from ab and/or a × b.
Please read this section of Wikipedia which talks about these topics better than I could. It shows that there is ambiguity in the order of operations and that for especially niche cases there is not a universally accepted order of operations when dealing with mixed division and multiplication. It addresses everything you’ve mentioned.
There is no universal convention for interpreting an expression containing both division denoted by ‘÷’ and multiplication denoted by ‘×’. Proposed conventions include assigning the operations equal precedence and evaluating them from left to right, or equivalently treating division as multiplication by the reciprocal and then evaluating in any order;[10] evaluating all multiplications first followed by divisions from left to right; or eschewing such expressions and instead always disambiguating them by explicit parentheses.[11]
Beyond primary education, the symbol ‘÷’ for division is seldom used, but is replaced by the use of algebraic fractions,[12] typically written vertically with the numerator stacked above the denominator – which makes grouping explicit and unambiguous – but sometimes written inline using the slash or solidus symbol ‘/’.[13]
Multiplication denoted by juxtaposition (also known as implied multiplication) creates a visual unit and is often given higher precedence than most other operations. In academic literature, when inline fractions are combined with implied multiplication without explicit parentheses, the multiplication is conventionally interpreted as having higher precedence than division, so that e.g. 1 / 2n is interpreted to mean 1 / (2 · n) rather than (1 / 2) · n.[2][10][14][15] For instance, the manuscript submission instructions for the Physical Review journals directly state that multiplication has precedence over division,[16] and this is also the convention observed in physics textbooks such as the Course of Theoretical Physics by Landau and Lifshitz[c] and mathematics textbooks such as Concrete Mathematics by Graham, Knuth, and Patashnik.[17] However, some authors recommend against expressions such as a / bc, preferring the explicit use of parenthesis a / (bc).[3]
More complicated cases are more ambiguous. For instance, the notation 1 / 2π(a + b) could plausibly mean either 1 / [2π · (a + b)] or [1 / (2π)] · (a + b).[18] Sometimes interpretation depends on context. The Physical Review submission instructions recommend against expressions of the form a / b / c; more explicit expressions (a / b) / c or a / (b / c) are unambiguous.[16]
6÷2(1+2) is interpreted as 6÷(2×(1+2)) by a fx-82MS (upper), and (6÷2)×(1+2) by a TI-83 Plus calculator (lower), respectively.
This ambiguity has been the subject of Internet memes such as “8 ÷ 2(2 + 2)”, for which there are two conflicting interpretations: 8 ÷ [2 · (2 + 2)] = 1 and (8 ÷ 2) · (2 + 2) = 16.[15][19] Mathematics education researcher Hung-Hsi Wu points out that “one never gets a computation of this type in real life”, and calls such contrived examples “a kind of Gotcha! parlor game designed to trap an unsuspecting person by phrasing it in terms of a set of unreasonably convoluted rules”.[12]
Please read this section of Wikipedia which talks about these topics better than I could
Please read Maths textbooks which explain it better than Joe Blow Your next Door neighbour on Wikipedia. there’s plenty in here
It shows that there is ambiguity in the order of operations
and is wrong about that, as proven by Maths textbooks
especially niche cases there is not a universally accepted order of operations when dealing with mixed division and multiplication
That’s because Multiplication and Division can be done in any order
It addresses everything you’ve mentioned
wrongly, as per Maths textbooks
Multiplication denoted by juxtaposition (also known as implied multiplication)
Nope. Terms/Products is what they are called. “implied multiplication” is a “rule” made up by people who have forgotten the actual rules.
s often given higher precedence than most other operations
Always is, because brackets first. ab=(axb) by definition
1 / 2n is interpreted to mean 1 / (2 · n)
As per the definition that ab=(axb), 1/2n=1/(2xn).
[2][10][14][15]
Did you look at the references, and note that there are no Maths textbooks listed?
the manuscript submission instructions for the Physical Review journals
Which isn’t a Maths textbook
the convention observed in physics textbooks
Also not Maths textbooks
mathematics textbooks such as Concrete Mathematics by Graham, Knuth, and Patashnik
Actually that is a Computer Science textbook, written for programmers. Knuth is a very famous programmer
More complicated cases are more ambiguous
None of them are ambiguous.
the notation 1 / 2π(a + b) could plausibly mean either 1 / [2π · (a + b)]
It does as per the rules of Maths, but more precisely it actually means 1 / (2πa + 2πb)
or [1 / (2π)] · (a + b).[18]
No, it can’t mean that unless it was written (1 / 2π)(a + b), which it wasn’t
Sometimes interpretation depends on context
Nope, never
more explicit expressions (a / b) / c or a / (b / c) are unambiguous
a/b/c is already unambiguous - left to right. 🙄
Image of two calculators getting different answers
With the exception of Texas Instruments, all the other calculator manufacturers have gone back to doing it correctly, and Sharp have always done it correctly.
6÷2(1+2) is interpreted as 6÷(2×(1+2))
6÷(2x1+2x2) actually, as per The Distributive Law, a(b+c)=(ab+ac)
(6÷2)×(1+2) by a TI-83 Plus calculator (lower)
Yep, Texas Instruments is the only one still doing it wrong
This ambiguity
doesn’t exist, as per Maths textbooks
“8 ÷ 2(2 + 2)”, for which there are two conflicting interpretations:
No there isn’t - you MUST obey The Distributive Law, a(b+c)=(ab+ac)
Mathematics education researcher Hung-Hsi Wu points out that “one never gets a computation of this type in real life”
If you believe the article is incorrect, submit your corrections to Wikipedia
You know they’ve rejected corrections by actual Maths Professors right? Just look for Rick Norwood in the talk section. Everyone who knows Maths knows Wikipedia is wrong, and looks in the right place to begin with - Maths textbooks
Again, if you have a problem with Wikipedia, take it up with Wikipedia
You’ve made the mistake of thinking they care. Again, look for Rick Norwood in the Talk sections, an actual Maths professor (bless him for continually trying to get them to correct the mistakes though)
Well, now you might be running into syntax issues instead of PEMDAS issues depending on what they’re confused about. If it’s 12 over 2*6, it’s 1. If it’s 12 ÷ 2 x 6, it’s 36.
A lot of people try a bunch of funky stuff to represent fractions in text form (like mixing spaces and no spaces) when they should just be treating it like a programmer has to, and use parenthesis if it’s a complex fraction in basic text form.
The P in PEMDAS means to solve everything within parentheses first; there is no “distribution” step or rule that says multiplying without a visible operator other than parentheses comes first. So yes, 36 is valid here. It’s mostly because PEMDAS never shows up in the same context as this sort of multiplication or large fractions
Are you under the impression that atomizing your opponents statements and making a comment about each part individually without addressing the actual point (how those facts fit together) is a good debate tactic? Because it seems like all you’ve done is confuse yourself about what I was saying and make arguments that don’t address it. Never mind that some of those micro-rebuttals aren’t even correct.
But to make a pointless effort to address your actual point, yes distribution exists, no it is not a step in PE(MD)(AS). Again, you have not understood my point because you categorically fail to engage with any argument. I don’t think you even understand what it means to do so. I will not respond further to either thread.
Parentheses means evaluating the things inside the parentheses you nimrod
Only if you’re still in Elementary school. How old are you anyway? Here’s a high school Algebra book, you know, after students have been taught The Distributive Law…
Or
12 / 2(6)
And trying to argue this is 36.
Now that’s a good troll math thing because it gets really deep into the weeds of mathematical notation. There isn’t one true order of operations that is objectively correct, and on top of that, that’s hardly the way most people would write that. As in, if you wrote that by hand, you wouldn’t use the
/symbol. You’d either use ÷ or a proper fraction.It’s a good candidate for nerd sniping.
Personally, I’d call that 36 as written given the context you’re saying it in, instead of calling it 1. But I’d say it’s ambiguous and you should notate in a way to avoid ambiguities. Especially if you’re in the camp of multiplication like
a(b)being different fromaband/ora × b.Yes there is, as found in Maths textbooks the world over
Maths textbooks write it that way
Yes you would.
Same same
Here’s one I prepared earlier to save you the trouble
And you’d be wrong
The context is Maths, you have to obey the rules of Maths. a(b+c)=(ab+ac), 5(8-5)=(5x8-5x5).
And you’d be wrong about that too
It already is notated in a way that avoids all ambiguities!
That’s not Multiplication, it’s Distribution, a(b+c)=(ab+ac), a(b)=(axb).
Nope, that’s exactly the same, ab=(axb) by definition
(axb) is most certainly different to axb. 1/ab=1/(axb), 1/axb=b/a
Please read this section of Wikipedia which talks about these topics better than I could. It shows that there is ambiguity in the order of operations and that for especially niche cases there is not a universally accepted order of operations when dealing with mixed division and multiplication. It addresses everything you’ve mentioned.
https://en.wikipedia.org/wiki/Order_of_operations#Mixed_division_and_multiplication
Please read Maths textbooks which explain it better than Joe Blow Your next Door neighbour on Wikipedia. there’s plenty in here
and is wrong about that, as proven by Maths textbooks
That’s because Multiplication and Division can be done in any order
wrongly, as per Maths textbooks
Nope. Terms/Products is what they are called. “implied multiplication” is a “rule” made up by people who have forgotten the actual rules.
Always is, because brackets first. ab=(axb) by definition
As per the definition that ab=(axb), 1/2n=1/(2xn).
Did you look at the references, and note that there are no Maths textbooks listed?
Which isn’t a Maths textbook
Also not Maths textbooks
Actually that is a Computer Science textbook, written for programmers. Knuth is a very famous programmer
None of them are ambiguous.
It does as per the rules of Maths, but more precisely it actually means 1 / (2πa + 2πb)
No, it can’t mean that unless it was written (1 / 2π)(a + b), which it wasn’t
Nope, never
a/b/c is already unambiguous - left to right. 🙄
With the exception of Texas Instruments, all the other calculator manufacturers have gone back to doing it correctly, and Sharp have always done it correctly.
6÷(2x1+2x2) actually, as per The Distributive Law, a(b+c)=(ab+ac)
Yep, Texas Instruments is the only one still doing it wrong
doesn’t exist, as per Maths textbooks
No there isn’t - you MUST obey The Distributive Law, a(b+c)=(ab+ac)
And he was wrong about that. 🙄
Which notably can be found in Maths textbooks
If you believe the article is incorrect, submit your corrections to Wikipedia instead of telling me.
You know they’ve rejected corrections by actual Maths Professors right? Just look for Rick Norwood in the talk section. Everyone who knows Maths knows Wikipedia is wrong, and looks in the right place to begin with - Maths textbooks
Again, if you have a problem with Wikipedia, take it up with Wikipedia.
You’ve made the mistake of thinking they care. Again, look for Rick Norwood in the Talk sections, an actual Maths professor (bless him for continually trying to get them to correct the mistakes though)
Well, now you might be running into syntax issues instead of PEMDAS issues depending on what they’re confused about. If it’s 12 over 2*6, it’s 1. If it’s 12 ÷ 2 x 6, it’s 36.
A lot of people try a bunch of funky stuff to represent fractions in text form (like mixing spaces and no spaces) when they should just be treating it like a programmer has to, and use parenthesis if it’s a complex fraction in basic text form.
The P in PEMDAS means to solve everything within parentheses first; there is no “distribution” step or rule that says multiplying without a visible operator other than parentheses comes first. So yes, 36 is valid here. It’s mostly because PEMDAS never shows up in the same context as this sort of multiplication or large fractions
and without a(b+c)=(ab+ac), now solve (ab+ac)
It’s a LAW of Maths actually, The Distributive Law.
It’s not “Multiplying”, it’s Distributing, a(b+c)=(ab+ac)
No it isn’t. To get 36 you have disobeyed The Distributive Law, thus it is a wrong answer
people like you try to gaslight others that there’s no such thing as The Distributive Law
Are you under the impression that atomizing your opponents statements and making a comment about each part individually without addressing the actual point (how those facts fit together) is a good debate tactic? Because it seems like all you’ve done is confuse yourself about what I was saying and make arguments that don’t address it. Never mind that some of those micro-rebuttals aren’t even correct.
I did address the actual point - see Maths textbooks
I’m not confused at all. I’m the one who knows the difference between Distribution and Multiplication.
You lied about there being no such thing as “the Distribution step” (Brackets), proven wrong by the textbooks
Textbooks talking about The Distributive Law totally addresses your lie that no such step exists.
You think Maths textbooks aren’t correct?? 😂
I have said why this style of debate is bad in greater detail here: https://lemmy.world/post/39377635/21030374
But to make a pointless effort to address your actual point, yes distribution exists, no it is not a step in PE(MD)(AS). Again, you have not understood my point because you categorically fail to engage with any argument. I don’t think you even understand what it means to do so. I will not respond further to either thread.
Which I debunked here
So… you’re saying the “P” step in PEMDAS isn’t a step in PEMDAS?? This is hilarious given you were just talking about contradictions 😂
Maybe because saying the “P” step in PEMDAS isn’t a step in PEMDAS makes no sense at all 😂
No, I comprehensively debunked all of your points and deflections. 😂
says person who keeps avoiding the textbook screenshots and worked examples proving them wrong
Yay! Don’t let the door hit you on the way out 😂
Parentheses means evaluating the things inside the parentheses you nimrod
Only if you’re still in Elementary school. How old are you anyway? Here’s a high school Algebra book, you know, after students have been taught The Distributive Law…