I donβt know why, but this was intuitively my first approach
Because thatβs what we teach students to do, though technically it should be (xy-xz)
I feel like I am getting trolled
Isnβt 17 the actual right answer?
I think itβs meant to play with your expectations. Normally someoneβs take being posted is to show them being confidently stupid, otherwise it isnβt as interesting and doesnβt go viral.However, because weβre primed to view it from that lens, we feel crazy to think weβre doing the math correctly and getting the βwrong answerβ from what we assume is the βconfident dipshitβ.
Thereβs layers beyond the superficial.
Because there is no question
So Maths test says β2+3 ____β, and you write βthatβs not a questionβ on the blank line?? π
Inside the parens first, so it becomes 2 + 5*3
Then tou do multiplication before addition, so 2 + 15
Then addition, so 17
This shit take got deleted right in front of my eyes
The system works
They did the joke wrong. To do it right you need to use the Γ· symbol. Because people never use that after they learn fractions, people treat things like a + b Γ· c + d as
a + b ----- c + dOr (a + b) Γ· (c + d) when they should be treating it as a + (b Γ· c) + d.
Thatβs the most common one of these βtroll mathβ tricks. Because notating as
a + b + d - cIs much more common and useful. So people get used to grouping everything around the division operator as if theyβre in parentheses.
Well, now you might be running into syntax issues instead of PEMDAS issues depending on what theyβre confused about. If itβs 12 over 2*6, itβs 1. If itβs 12 Γ· 2 x 6, itβs 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 itβs a complex fraction in basic text form.
The P in PEMDAS means to solve everything within parentheses first
and without a(b+c)=(ab+ac), now solve (ab+ac)
there is no βdistributionβ step or rule
Itβs a LAW of Maths actually, The Distributive Law.
that says multiplying without a visible operator
Itβs not βMultiplyingβ, itβs Distributing, a(b+c)=(ab+ac)
So yes, 36 is valid here
No it isnβt. To get 36 you have disobeyed The Distributive Law, thus it is a wrong answer
Itβs mostly because
people like you try to gaslight others that thereβs no such thing as The Distributive Law
addressing the actual point (how those facts fit together)
I did address the actual point - see Maths textbooks
all youβve done is confuse yourself
Iβm not confused at all. Iβm the one who knows the difference between Distribution and Multiplication.
what I was saying
You lied about there being no such thing as βthe Distribution stepβ (Brackets), proven wrong by the textbooks
make arguments that donβt address it.
Textbooks talking about The Distributive Law totally addresses your lie that no such step exists.
Never mind that some of those micro-rebuttals arenβt even correct
You think Maths textbooks arenβt correct?? π
I have said why this style of debate is bad in greater detail here: 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 donβt think you even understand what it means to do so. I will not respond further to either thread.
I have said why this style of debate is bad in greater detail here: lemmy.world/post/39377635/21030374
Which I debunked here
no it is not a step in PE(MD)(AS)
Soβ¦ youβre saying the βPβ step in PEMDAS isnβt a step in PEMDAS?? This is hilarious given you were just talking about contradictions π
Again, you have not understood my point
Maybe because saying the βPβ step in PEMDAS isnβt a step in PEMDAS makes no sense at all π
you categorically fail to engage with any argument.
No, I comprehensively debunked all of your points and deflections. π
I donβt think you even understand what it means to do so
says person who keeps avoiding the textbook screenshots and worked examples proving them wrong
I will not respond further to either thread
Yay! Donβt let the door hit you on the way out π
Parentheses means evaluating the things inside the parentheses you nimrod
Only if youβre still in Elementary school. How old are you anyway? Hereβs a high school Algebra book, you know, after students have been taught The Distributive Lawβ¦
Now thatβs a good troll math thing because it gets really deep into the weeds of mathematical notation. There isnβt one true order of operations that is objectively correct, and on top of that, thatβs hardly the way most people would write that. As in, if you wrote that by hand, you wouldnβt use the / symbol. Youβd either use Γ· or a proper fraction.
Itβs a good candidate for nerd sniping.
Personally, Iβd call that 36 as written given the context youβre saying it in, instead of calling it 1. But Iβd say itβs ambiguous and you should notate in a way to avoid ambiguities. Especially if youβre in the camp of multiplication like a(b) being different from ab and/or a Γ b.
There isnβt one true order of operations that is objectively correct
Yes there is, as found in Maths textbooks the world over
thatβs hardly the way most people would write that
Maths textbooks write it that way
you wouldnβt use the / symbol
Yes you would.
Youβd either use Γ·
Same same
Itβs a good candidate for nerd sniping.
Hereβs one I prepared earlier to save you the trouble
Iβd call that 36
And youβd be wrong
as written given the context youβre saying it in
The context is Maths, you have to obey the rules of Maths. a(b+c)=(ab+ac), 5(8-5)=(5x8-5x5).
But Iβd say itβs ambiguous
And youβd be wrong about that too
you should notate in a way to avoid ambiguities
It already is notated in a way that avoids all ambiguities!
Especially if youβre in the camp of multiplication like a(b)
Thatβs not Multiplication, itβs Distribution, a(b+c)=(ab+ac), a(b)=(axb).
being different from ab
Nope, thatβs exactly the same, ab=(axb) by definition
and/or a Γ b
(axb) is most certainly different to axb. 1/ab=1/(axb), 1/axb=b/a
1/3 #MathsMonday Order of operations thread index #Mathematics #Maths #Math Introduction https://dotnet.social/@SmartmanApps/110807192608472798 1 The Distributive Law #DontForgetDistribution https://dotnet.social/@SmartmanApps/110819283738912144 2 Terms #MathsIsNeverAmbiguous https://dotnet.social/@SmartmanApps/110846452267056791 3 Factorising<->The Distributive Law https://dotnet.social/@SmartmanApps/110886637077371439 4 implicit multiplication, mnemonics https://dotnet.social/@SmartmanApps/110925761375035558 5 1917 (i) - Left Associativity https://dotnet.social/@SmartmanApps/110965810374299599 6 1917 (ii) - Lennes' letter (Terms and operators) https://dotnet.social/@SmartmanApps/111005247356655843 ...
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 youβve mentioned.
en.wikipedia.org/wiki/Order_of_operations#Mixed_dβ¦
There is no universal convention for interpreting an expression containing both division denoted by βΓ·β and multiplication denoted by βΓβ. 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 βΓ·β 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 β which makes grouping explicit and unambiguous β but sometimes written inline using the slash or solidus symbol β/β.[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. 1β/β2n is interpreted to mean 1β/β(2βΒ·βn) rather than (1β/β2)βΒ·βn.[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 aβ/βbc, preferring the explicit use of parenthesis aβ/β(bc).[3]
More complicated cases are more ambiguous. For instance, the notation 1β/β2Ο(aβ+βb) could plausibly mean either 1β/β[2ΟβΒ·β(aβ+βb)] or [1β/β(2Ο)]βΒ·β(aβ+βb).[18] Sometimes interpretation depends on context. The Physical Review submission instructions recommend against expressions of the form aβ/βbβ/βc; more explicit expressions (aβ/βb)β/βc or aβ/β(bβ/βc) are unambiguous.[16]
6Γ·2(1+2) is interpreted as 6Γ·(2Γ(1+2)) by a fx-82MS (upper), and (6Γ·2)Γ(1+2) by a TI-83 Plus calculator (lower), respectively.
This ambiguity has been the subject of Internet memes such as β8βΓ·β2(2β+β2)β, for which there are two conflicting interpretations: 8βΓ·β[2βΒ·β(2β+β2)] = 1 and (8βΓ·β2)βΒ·β(2β+β2) = 16.[15][19] Mathematics education researcher Hung-Hsi Wu points out that βone never gets a computation of this type in real lifeβ, and calls such contrived examples βa kind of Gotcha! parlor game designed to trap an unsuspecting person by phrasing it in terms of a set of unreasonably convoluted rulesβ.[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. thereβs 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
Thatβs because Multiplication and Division can be done in any order
It addresses everything youβve mentioned
wrongly, as per Maths textbooks
Multiplication denoted by juxtaposition (also known as implied multiplication)
Nope. Terms/Products is what they are called. βimplied multiplicationβ is a βruleβ 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
1β/β2n is interpreted to mean 1β/β(2βΒ·βn)
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 isnβt 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 1β/β2Ο(aβ+βb) could plausibly mean either 1β/β[2ΟβΒ·β(aβ+βb)]
It does as per the rules of Maths, but more precisely it actually means 1β/β(2Οaβ+β2Οb)
or [1β/β(2Ο)]βΒ·β(aβ+βb).[18]
No, it canβt mean that unless it was written (1β/β2Ο)(aβ+βb), which it wasnβt
Sometimes interpretation depends on context
Nope, never
more explicit expressions (aβ/βb)β/βc or aβ/β(bβ/βc) are unambiguous
a/b/c is already unambiguous - left to right. π
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.
6Γ·2(1+2) is interpreted as 6Γ·(2Γ(1+2))
6Γ·(2x1+2x2) actually, as per The Distributive Law, a(b+c)=(ab+ac)
(6Γ·2)Γ(1+2) by a TI-83 Plus calculator (lower)
Yep, Texas Instruments is the only one still doing it wrong
This ambiguity
doesnβt exist, as per Maths textbooks
β8βΓ·β2(2β+β2)β, for which there are two conflicting interpretations:
No there isnβt - you MUST obey The Distributive Law, a(b+c)=(ab+ac)
Mathematics education researcher Hung-Hsi Wu points out that βone never gets a computation of this type in real lifeβ
And he was wrong about that. π
calls such contrived examples
Which notably can be found in Maths textbooks
1/3 #MathsMonday Order of operations thread index #Mathematics #Maths #Math Introduction https://dotnet.social/@SmartmanApps/110807192608472798 1 The Distributive Law #DontForgetDistribution https://dotnet.social/@SmartmanApps/110819283738912144 2 Terms #MathsIsNeverAmbiguous https://dotnet.social/@SmartmanApps/110846452267056791 3 Factorising<->The Distributive Law https://dotnet.social/@SmartmanApps/110886637077371439 4 implicit multiplication, mnemonics https://dotnet.social/@SmartmanApps/110925761375035558 5 1917 (i) - Left Associativity https://dotnet.social/@SmartmanApps/110965810374299599 6 1917 (ii) - Lennes' letter (Terms and operators) https://dotnet.social/@SmartmanApps/111005247356655843 ...
If you believe the article is incorrect, submit your corrections to Wikipedia
You know theyβve 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
Youβve 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)
Take it up with them if you have a problem with them
I see youβre not even reading what I said. No wonder you donβt know how to do Mathsβ¦
I did read everything you said
Clearly you didnβt, given you keep telling me to take it up with Harvard/Wiki
enact the change you want to see in Wikipedia
See?? There you go again ignoring what I told you about Wikipedia π
I havenβt ignored anything you said.
Youβve ignored everything Iβve said about Wikipedia.
Iβm telling you that if you have a problem with those that you should contact them to fix them
and you have again ignored what I told you about them π
a + b/c + d as a + b/(c + d) I can almost understand, I was guilty of doing that in school with multiplication, but auto-parenthesising the first part is really crazy take, imo
Thatβs a really odd way to parse it.
a + b ----- c + bTreat a + b/c + d as a + b/(c + d)
No donβt. That rule was changed more than 130 years ago. a+b/c+d=a+(b/c)+d, Division before Addition
Because people never use that after they learn fractions,
Yes they do, because not every division is a fraction
math.berkeley.edu/~wu/order5.pdf
I already said he was wrong about that. Quoting him saying it doesnβt change that heβs wrong about it
Take it up with Berkeley then
What for? Youβre only the second person ever to have quoted him. Youβre not the first person to refuse to look in Maths textbooks though π
Take it up with Berkeley
Says person refusing to look in Maths textbooks π
I cannot stress this enough. If you have a problem with that, contact the author or Berkeley, not me
I cannot stress this enough - look in Maths textbooks, not random University blogs π