The result of a multiplication operation is called a product
Now you're getting it - axb=ab. axb is Multiplication of 2 Terms, ab is the single Product. It's the reason that 8/2(1+3) and 8/2x(1+3) give different answers 🙄
Show me one textbook where a(b+c)2 gets an a2 term
I already gave you many that tell you a(b+c)=(ab+ac) Mr. Ostrich - which part of a(b+c)=(ab+ac) are you having trouble understanding?
Every textbook with an answer key says you’re full of shit
Says person who can't find a Maths textbook that says a(bxc)=(abxac) 🙄
being wrong on purpose is the point
I'm gonna presume that's why you keep claiming a(bxc)=(abxac) 🙄
The answer in either case is shut the fuck up
says person still not doing that 😂
2(n)2 is 2n2
No it isn't! 😂 2xn² is
Anything else is an inane complication nobody else believes in or uses or needs
Except for authors of Maths textbooks 😂
Right, so you cannot derive precedence order from the definition of the operations.
Yes you can. I'm not sure what you're not understanding about Division before Addition 😂
Your argument based on the definition of multiplication as repeated addition is wrong
No it isn't! 😂
We are discussing whether the answers are flat wrong or whether there is a layer of interpretation
Flat wrong, as per the rules Of Maths 🙄
Repeating that they are wrong does nothing for this discussion, so there’s no need to bother
So stop doing wrong things and I can stop saying you're doing it wrong 😂
why they ought to qualify as “wrong” even though maths works regardless
If you have 1 2 litre bottle of milk, and 4 3 litre bottles of milk, even a 3rd grader can count up and tell you how many litres there are, and that any other answer is wrong. 🙄 2+3x4=2+3+3+3+3=14 correct 2+3x4=5x4=5+5+5+5=20 wrong See how the Maths doesn't work regardless? 😂
you’ve just heard a school-level maths teacher tell you it’s done one way and believe that’s the highest possible authority
Nope, I've proven it myself - that's the beauty of Maths, that anyone at all can try it for themselves and find out. I'm guessing that you didn't try it yourself 😂
lots of things we get taught in high school are wrong
says person failing to give a single such example 🙄
it’s actually your job to understand maths at a higher level than the level at which you teach it
No it isn't. I'm required to to get the Masters degree which is required to be a teacher here, and that's the end of it.
It may be easier to to teach high school maths this way
The correct way, yes 😂
When I hear the word “rules”, I think you’re talking either about a rule of inference in first order logic or an axiom in a first-order system
Nope, neither.
So what are you talking about?
What don't you understand about 20 being a wrong answer for 2+3x4??
whatever it is you mean by “rule”
Thing which results in wrong answers if disobeyed - like 2+3x4=20 - not complicated. This is what we teach to students - if you always obey all the rules then you will always get the correct answer.
arithmetic modulo 17, and say that’s an “alternative convention”
Of course not, just a different function of Maths, that doesn't involve Arithmetic at all (other than the steps along the way in doing the long division), unlike 2+3x4 🙄
I contend that is all convention
Nope! Just a different rule to Arithmetic 🙄
What does it mean to be “bracketed without writing brackets”?
Same thing as we're adding the 2 in 2+3 without writing a plus (or a zero) in front of the 2 - all Arithmetic starts from zero on the number-line. Maths textbooks explicitly teach this, that we can leave the sign omitted at the start if it's a plus.
the symbols themselves - but we’re not writing them! So this isn’t relevant
Just like we aren't writing the plus sign in 2+3 🙄
So what you’re admitting with these phantom brackets is that a notation can evaluate operations in a different order, even though there are no written brackets.
Nope. Same order as though we did write it in a notation using Brackets, same as we always start with adding the 2 even though we didn't write a plus sign in 2+3.
So I can specify these fake brackets to always wrap the left-most operation first: (2 + 3) x 5
No you can't, because you get a wrong answer 🙄
this notation now has left-to-right order of evaluation
No it doesn't, Multiplication before Addition 🙄
If you prefer to think of there being invisible brackets there
You know we were writing this without brackets for several centuries before we started using brackets in Maths, right?? 😂
So, how do we decide whether our usual notation “has bogus brackets” or not? Convention
Nope. proven rules 🙄
We could choose one way or the other.
No we can't. Even a 3rd grader who is counting up can tell you that 🙄
Nothing breaks if we choose one or the other.
Yes it does. Again ask the 3rd grader how many litres we have, and then try doing Addition first to get that answer 😂
we could say that left-to-right evaluation is the notation “without bogus brackets”
No we can't. Ask the 3rd grader, or even try it yourself with Cuisenaire rods
Which choice we make is entirely arbitrary
Nope. proven rules 🙄
That is, unless you can find a compelling reason why one is right and the other wrong, rather than just saying it once again
Count up how many litres we have 🙄
What problems does it cause?
wrong answers 😂
you’re trying to establish that it’s a fundamental law of maths that you must do multiplication before addition
As per Maths textbooks 😂
you’ve written a post in which you document how some calculators don’t follow this
rule
said that they’re wrong is not evidence of that
says person ignoring the Maths textbooks I quoted and the actual calculators giving the correct answer 🙄
It’s just your opinion
Nope! proven rules as found in Maths textbooks 🙄
it’s really (weak) evidence that your opinion is wrong,
says person ignoring the Maths textbooks I quoted and the actual calculators giving the correct answer 🙄
you’re less of an authority than the manufacturers of calculators
Demonstrably not 😂
basic, non-scientific, non-graphing calculators all have left-to-right order of operations
No they don't! 😂
e.g. windows calculator in “standard” mode
The Windows calculator is an e-calc which was written by a programmer who didn't check that their Maths was correct. 🙄 Now try it with any actual calculator 🙄
Why is it different?
Written by a different programmer, but one who didn't know The Distributive Law, so even in Scientific mode it gives wrong answers to 8/2(1+3) 🙄
Because “standard” mode is emulating a basic calculator
No it isn't. All basic calculators obey Multiplication before Addition, 🙄 and if the programmer had tried it then they would've found that out
performs operations on that accumulated value
Instead of using the stack, to store the Multiplication first, like all actual calculators do 🙄
When you type “x 2” you are multiplying the accumulator by 2
No, the dumb programmer is. All actual calculators did the Multiplication first and put the result on the stack
the calculator has already forgotten everything that you typed to get the accumulator
But actual calculators have put that result on the stack 🙄
This was done in the early days of calculators
No it wasn't. All calculators "in the early days" used the stack
It has a different convention for a sensible reason
Nope, it's just disobeying the rules of Maths because dumb programmer didn't check their Maths was correct 🙄
it was more practical when memory looked like this:
And even then the stack existed 🙄
the fact is that this isn’t “wrong”
Yes it is! 😂 Again, ask the 3rd grader to count up and tell you the correct answer
if you expect something different then it is you who
knows the rules of Maths 🙄
What do you mean “we don’t”?
What don't you understand about "we don't"?
I just made the definition
Of the notation, not the rules 🙄
We have another notation which says to do paired operations (equivalent to being in brackets) first
And this notation says to do paired operations first, same as if they were in Brackets. You so nearly had it 🙄
plain english (like “convention”)
says person who keeps calling the rules "convention" 🙄
mathematical (like “axiom”, “definition”, etc)
You know we have Mathematical definitions of the difference between conventions and rules, right??
If you can simplify before distributing - and the PDFs you spam say you can
They say you can do that when there is Addition or Subtraction inside the Brackets. They also say you cannot Distribute over Multiplication, at all
then there is no difference
There is no difference between Addition and Multiplication?? 😂
You made it the fuck up
And yet, there it is in textbooks that were written before I was even born 😂
2(n)2 is 2n2 whether n=a+b or n=a*b=ab
Nope! a(b+c)=(ab+ac). a(bxc)=abc
If you want to square the 2, that’s (2n)2.
...or 2²xn², or 2(½n+½n)²
It’s not about the multiply sign, or grouping, or division
Yes it is! 😂 If there's a Multiply or a Divide, you cannot Distribute.
You fooled yourself into saying 2=1
Not me! 😂
Sorry but there is no math government that can enforce rules
Maths textbooks do. Try looking in some
the order of operations isn’t intrinsic either
Yes they are! 😂
It is just something people agreed upon volununtarily, aka a convention
Nope. Literally proven rules
Tell that obvious to over half the population who get this wrong
Way less than half actually. No teachers or students ever get this wrong, only adults who have forgotten the rules, and poll after poll puts this down around 40-45% of adults.
Ok, then explain prefix and postfix, where these conventions don’t apply
The conventions don't apply, the rules still apply. Maths notation and the rules of Maths aren't the same thing.
How can these be rules of math when they didn’t universally apply?
The rules do universally apply 🙄
The order of operations tells us how to interpret an equation without rearranging it
Yep, and you showed you don't know the rules 🙄
When you pick a different convention, you need to rearrange it to get the same answer
Not necessarily, though it makes it easier (but also leads a lot of people to make mistakes with signs, as you found out 😂 )
What you did was rearrange the equation
To show you how to correctly do "Multiplication first". 🙄
which you can only do if you are already following a specific convention
Which you didn't, hence why you ended up with a wrong answer. 🙄 There is no textbook which says put the multiplication in Brackets if doing "Multiplication first", none.
because the conventions are not laws of mathematics, they are conventions
And putting the Multiplication inside Brackets isn't a convention anywhere 🙄
They obey the laws of math. Conventions aren’t laws of math, they’re conventions
Yep, and you ignored both, hence your wrong answer 🙄
And a quick Google search will tell you that not everyone puts juxtaposition at a higher precedent than multiplication
And a quick look in the Google support forum will show you many people telling them that is wrong, and Google just closes the incident 🙄
it’s a convention
No it isn't. It's against the rules. 🙄 Again, you won't find this alleged "convention" in any Maths textbook
As long as people are using the same convention, they’ll agree on an answer and that answer is correct
Unless they disobeyed the rules, in which case they are all wrong 🙄
You can be mean all you like, that doesn’t change the nature of conventions
And you can be as ignorant of the rules and conventions of Maths as much as you want, and it's not going to change that your answer is wrong 🙄
My doctorate is irrelevant to the truth
It sure is. I've seen a PhD who didn't read the only textbook he had referenced in his thesis, which proved his idea that teachers were doing it wrong and he wasn't, was wrong. 😂 Should've listened to the people who teach it (or actually read the textbook he referenced 🙄 ).
which makes students of math feel inordinately inferior
They don't. All students get this correct. It's only adults who have forgotten the rules that get it wrong.
these gotcha-style math memes IMO deepen students’ belief that they’re just bad at math
Nope. Students never get these wrong.
proofs mean something very specific to me and I can’t yet imagine what that looks like WRT order of operations
All you have to do is see which way gives wrong answers for 2+3x4 and you've proven which ways don't work 😂
note that conventions aren’t necessarily “optional”
Yes they are.
when being understood is essential
You don't understand how to do 2+3x4-5 without knowing which conventions people use for the order of the plus and minus?
Here I am only concerned about the next generation of maths student and how viral content like this can discourage them unnecessarily
It doesn't. None of them get it wrong. 🙄
“No one” in this context meant “no one who actually does maths professionally.”
No it doesn't. Everyone who does Maths professionally does it the same way as in Maths textbooks 🙄
When I see 1+½ i can instantly say “one and a half”
And that would be wrong. It's 1 plus one half. 1½ is one and a half.
when I see 1 + 1 ÷ 2 i actually have to pause for a moment to think about order of operations
You don't know to Divide before Adding??
one I recognize the structure of the problem immediately, and one feels foreign.
Says person with "decades of maths experience outside of textbooks" 🙄
The point is that people who do maths for a living
That would be me
are probably above average in maths, tend to write things differently than people who are stopped their maths education in high school (or lower)
Nope. We all write it the same way as we were taught, even those who have done Maths at University (also me).
these types of memes are designed around making people who know high school maths feel smart
No, they're designed around getting those who have forgotten the rules to argue about it. i.e. engagement bait
and another which says “first multiply two by three, then add it to two”
No we don't. We have another notation which says to do paired operations (equivalent to being in brackets) first.
why on earth do the “rules” have anything further to say about order of operations?
Because if you don't obey them you get wrong answers 🙄
How are you gonna write 2 + 2 ÷ 2 with repeated addition?
You don't, because the second 2 is associated with a Division that has to be done before the addition. Maybe go back to school and learn how to do Maths 🙄
That doesn’t mean it has to be expanded first.
Yes it does. Everything has to be expanded before you do the addition and subtraction, or you get wrong answers 🙄
2+3x4=2+3+3+3+3=2+12=14 correct
2+3x4=5x4=5+5+5+5=20 wrong
You could expand 2 + 2 × 3 as (2+2)+(2+2)+(2+2)
Says someone who can't tell the difference between (2+2)x3=12 and 2+2x3=8 🙄
you are unable to tell me what mathematical law prohibits it
The order of operations rules 😂
reverse polish notation wouldn’t work as it does
It works because it treats every operation as bracketed without writing the brackets. Also that's only a Maths notation, not the Maths itself.
In RPL, 2 2 + 3 × is 12
Because the way it calculates that is (2+2)x3, not complicated. Same order of operations rules as other Maths notations - just a different way of writing the same thing
If you had to expand multiplication first, how would it work?
It works because Brackets - 2 2 + = (2+2) - are before Multiplication
The same can be done with prefix notation
Another Maths notation, same rules of Maths
Different programming languages have different orders of operations
Maths doesn't
those languages work just fine
They don't actually. Welcome to most e-calcs give wrong answers because the programmers failed to deal with it correctly.
Your argument amounts to saying that it makes the most sense to do multiplication before addition
No, my argument is it's a universal rule of Maths, as found in Maths textbooks 🙄
that only gives you a convention, not a rule
Left to right is a convention (as is not writing the brackets in RPN). Brackets before Multiplication before Addition are rules.
knowledge on this subject without qualification
I'm a Maths teacher with a Masters - thanks for asking - how about you?
while ignoring my larger point
You mean your invalid point, that I debunked?
what are conventions if not agreed upon rules?
Conventions are optional, rules aren't.
here is a history of how we actually came to agree upon the aforementioned rules which you may find interesting
He's well-known to be wrong about his "history", and if you read through the comments you'll find plenty of people telling him that, including references. Cajori wrote the definitive books about the history of Maths (notation). They're available for free on the Internet Archive - no need to believe some random crank and his blog.
The rules are about how you interpret the notation
No, the notation definitions are about how to interpret the notation. The rules are about how to do the Maths.
That’s not true
Yes it is
PEDMAS: 8÷2x4 = 4x4 = 16
Yep.
PEMDAS: 8÷2x4 = 8÷8 = 1
Nope. PEMDAS: 8x4÷2 = 32÷2 = 16. What you actually did is 8÷(2x4), in which you changed the sign in front of the 4 - 8÷(2x4)= 8÷2÷4 - hence your wrong answer
PE M|D A|S: 8÷2x4 = 4x4 = 16
Yep, same answer regardless of the order 🙄
And thats not even getting into juxtaposition operations,
Which I have no doubt you don't understand how to do those either, given you don't know how to even do Multiplication first in this example.
where fields like physics use conventions that differ from most other field
Nope! The obey all the rules of Maths. They would get wrong answers if they didn't
you’re missing the point
No, you are...
It could be SAMDEP and math would still work
No it can't because no it wouldn't 😂
you’d just rearrange the equation.
Says someone who didn't rearrange "PEMDAS: 8÷2x4 = 8÷8 = 1" and got the wrong answer 😂
The rules don’t change
Hence why "PEMDAS: 8÷2x4 = 8÷8 = 1" was wrong. You violated the rule of Left Associativity
All I can assume from you is that you never did multiple choice questions in University
That would be a wrong assumption.
There’s a reason essay questions are considered easier.
They're not! 😂
Ok than I guess according to you PEMDSA doesn’t work
Oh course it does, and I have no idea why you think I would think otherwise! 😂
Or what about PEDMAS or PEDMSA maybe?
Yep, they all work
Oh wait we made up that order cuz it’s easier to say?
No, you made it up because your country has a chip on it's shoulder about doing it the same way as the rest of the world. 🙄
no one would ever write a problem like this
And yet Maths textbooks do! 😂
when was the last time I saw an X to mean multiplication
In a Maths textbook
1+1÷2 doesn’t even register in my brain properly
You don't know that the obelus means divide??
You so nearly had it, look "two things"! Yes axb is 2 Terms being Multiplied to make them one 😂
Nope! Says exactly what I already said, and I have no idea why you think it says otherwise. Now read the next page, which tells you ab is one Term and doesn't say that axb is 1 Term. 🙄 You're proven wrong by the very textbook you're quoting from! 😂
Says person trying to disprove a(b+c)=(ab+ac) by dragging a(bc)²=ab²c² to try and make a false equivalence argument 😂
No it isn't! 😂 The first is one term, the second is two terms
Says Mr. Ostrich, still ignoring the dozens of textbooks I posted saying a(b+c)=(ab+ac)
No, it produces an ab term and an ac term, a(b+c)=(ab+ac) 🙄
Says Mr. Ostrich, now completely full of shit, still ignoring the dozens of textbooks I posted, including ones written before I was even born