But factorised terms are multiplications,
No, they're Distribution done in the Brackets step, a(b+c)=(ab+ac), now solve (ab+ac)
a(b+c) = a*(b+c)
Nope! a(b+c)=(ab+ac). 1/a(b+c)=1/(ab+ac), but 1/ax(b+c)=(b+c)/a.
23+25=16
(2x3+2x5) actually, or you'll get the wrong answer when it follows a Division sign. See previous point
Do you think you’re above them?
You know we're talking about Year 7 Maths, right? 😂
Elementary school teaches you the fundamentals to your future education
but NOT The Distributive Law, which is taught in high school, in Algebra
I didn’t say you were wrong about math
You said "I don’t think you’re right", and followed it up with "Ill informed", to a Maths teacher.
I said you were wrong about English that is used in relation to math
And you were wrong about that too
Clearly this isn’t a strong suit of yours
What you mean is you clearly can't rebut any of it
However, stop acting like you know everything
I know everything about high school Maths - I teach it
you clearly don’t
There you go again calling a Maths teacher wrong about Maths 😂
You’re using some very strange logic to argue you’re right
You think Maths textbooks use very strange logic??
it doesn’t make any sense
read this then. Contains Maths textbooks
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”
And he was wrong about that. 🙄
calls such contrived examples
Which notably can be found in Maths textbooks
the creator of the universe tells this guy he’s being a hypocritical crank
The creator of the universe made the laws of nature, which gave rise to the rules of Maths, which can be found in Maths textbooks 😂
You’re very rude
What do you expect to happen when you call a Maths teacher wrong about Maths?
Ill informed
Maths teachers are ill informed about Maths?? 😂
Elementary means fundamental or basic
Which therefore contradicts your argument about it being part of Arithmetic, which is taught in elementary school, Algebra isn't
I’m talking programming languages
Written by people who forget the order of operations rules, hence MathGPT is the only e-calc which gives correct answers.
We are not the same
Yep, as well as being a programmer I'm also a Maths teacher
Most languages throw a syntax error if the multiplication symbol is missing
See first point
You are the brickest wall on lemmy
Says person who hasn't looked this up in a Maths textbook 😂
Either out of undiagnosed neurodivergence or some aggravating character gimmick
Neither, I'm a Maths teacher
you pretend there is one true way to do a thing
There's no pretending involved, it's in Maths textbooks
The commutative property means addition can happen in any order
Yep, and??
But multiplication and distribution are totally different
Nope! They can also be done in any order
you will never ever shut the fuck up about splitting that hair
Got no idea who you think you're talking to, but I never said Multiplication and Division are different
It’s dogma
No, it's the rules of Maths as found in Maths textbooks 😂
You’ve internalized one set of rigid instructions
ALL Mathematicians have, if you're going to put it like that.
declared them the rules of all mathematics
As found in Maths textbooks
to the point you insist Reverse Polish Notation has parentheses
It adds them in the background, so that you don't have to - if it didn't it would return wrong answers - you not having to type them in doesn't mean they aren't getting added
It literally cannot
...give correct answers without putting each paired operation into brackets
Yet it’s an equally valid way to write and do math
and obeys the EXACT SAME RULES 🙄
It gets the same results
because it obeys the same rules 🙄
despite distribution being impossible
Not impossible at all. Someone even wrote it in one of the other comments! 😂
Last time I tried wedging this uneniable fact through any gap in your mortar
you found there were no gaps 😂
you smugly declared you’d found a way
And as these very comments show, I'm not the only one to have done so! 😂
then explained multiplication, not distribution
No, Distribution.
Zero self-awareness
Well, you have zero awareness of what's in Maths textbooks anyway 😂
To this day, you are trying to be smug about a time you proudly contradicted yourself
I have never contradicted myself. You calling Distribution "Multiplication" doesn't make it Multiplication.
I feel sorry for students who can’t just tell you
My students do very well in their exams. How about you? 😂
Go away, patience vampire
Still can't admit you were wrong then 🙄
Adults who have forgotten the rules who I work with and read/write code where it’s important
And as a consequence of that, MathGPT is the only e-calc which gives correct answers to order of operations! 😂
This is like some pure maths vs real life engineering cliché
It's a Correct Maths vs. Programmers who have forgotten the rules cliche
You’re either being deliberately obtuse or you’re painfully naive
Neither, I'm a Maths teacher
Those aren’t ‘rules of maths’,
Yes they are 😂
because math would work with other orders of operations as well.
There aren't any "other" orders of operations.
They are conventions
Nope, rules of Maths
Other cultures could have different conventions and it would work as well
They do have other conventions, they do not have other rules. The rules of Maths are universal.
I don’t think you’re right
You don't think Maths textbooks are right??
The wiki page
is full of disinformation. Note that they literally never cite any Maths textbooks
as an example of “elementary arithmetic.”
And whichever Joe Blow My Next Door Neighbour wrote that is wrong
as an example in “elementary algebra.”
Algebra isn't taught until high school
That implies that yes, this is arithmetic,
No, anything with a(b+c) is Algebra, taught in Year 7
the introduction of variables is what makes it algebra
and the rules of Algebra, which includes a(b+c)=(ab+ac). There is no such rule in Arithmetic.
It doesn’t matter what course finally teaches it to you
It does if you're going to argue over whether it's Arithmetic or Algebra.
not by definition part of that domain
The Distributive Law is 100% part of Algebra. It's one of the very first things taught (right after pronumerals and substitution).
It’s been ages since I took it
I teach it. We teach it to Year 7, at the start of Algebra
More people evaluate 2+3x4 incorrectly than 2+(3x4)
The people who have forgotten the rules of Maths, and the mnemonics even! 😂
So, no, your answer does not hold up to my observed reality
So try observing a real Maths textbook then. Students have no trouble at all with this, only adults who've forgotten the rules.
Nope. Never said anything of the sort.
No I didn't, but nice try at a strawman 😂
There is no such thing as "implied multiplication" in any language. They are called Terms/Products in whatever language that book is using.