Set the bar low, but just high enough that tons of people still trip over it.
Sit back and enjoy the comment wars.
The people who are confident but wrong are too proud to admit they were wrong even if they realize it, and comment angrily.
The people who are right and know why, comment for corrections and some to show off how S-M-R-T they are.
The people who are wrong but willing to accept that just have their realization and probably don’t think about it again. So do the people who don’t know and/or care.
But those first two groups will keep the post going in both shares and comments, because “look at all these wrong people”
In actuality, it’s because of fundamental properties of operations
Commutation
a + b = b + a
a×b = b×a
Association
(a + b) + c = a + (b + c)
(a×b)×c = a×(b×c)
Identity
a + 0 = a
a×1 = a
If you know that, then PEMDAS and such are useless because they’re derived from those properties but do not fully encompass them.
Eg.
3×2×(2+2) = 3×(4+4) = 12+12 = 24
This is a correct solution that is improper if you’re strictly adhering to PEMDAS rule as I’ve done multiplication before parenthesis from right to left.
I could even go completely out of order by doing 3×2×(2+2) = 2×(6+6) and it will still be correct
Parenthesis, exponents, (multiplication and division), (addition and subtraction).
Addition and subtraction are given the same priority, and are done in the same step, from left to right.
It’s not a great system of notation, it could be made far clearer (and parenthesis allow you to make it as clear as you like), but it’s essentially the universal standard now and it’s what we’re stuck with.
No, it should simply be “Parenthesis, exponents, multiplication, addition.”
A division is defined as a multiplication, and a substraction is defined as an addition.
I am so confused everytime I see people arguing about this, as this is basic real number arithmetics that every kid in my country learns at 12 yo, when moving on from the simplified version you learn in elementary school.
I hate most math eduction because it’s all about memorizing formulas and rules, and then memorizing exceptions. The user above’s system is easier to learn, because there’s no exceptions or weirdness. You just learn the rule that division is multiplication and subtraction is addition. They’re just written in a different notation. It’s simpler, not more difficult. It just requires being educated on it. Yes, it’s harder if you weren’t obviously, as is everything you weren’t educated on.
That’s because (strictly speaking) they aren’t teaching math. They’re teaching “tricks” to solve equations easier, which can lead to more confusion.
Like the PEMDAS thing that’s being discussed here. There’s no such thing as “order of operations” in math, but it’s easier to teach by assuming that there is.
Edit:
To the people downvoting: I want to hear your opinions. Do you think I’m wrong? If so, why?
I’m just confused as to how that is not common knowledge. The country I speak of is France, and we’re not exactly known for our excellent maths education.
Because its not really “1 plus 3”, its negative 1 plus 3 which is two. I know it seems a little weird but the minus sign is " tied" to the thing following it.
The Greeks certainly didn’t come up with PEMDAS. US teachers too lazy to teach kids actual maths did. And that’s before taking into account that the Greeks didn’t come up with Algebra.
Learning the actual algebraic laws, instead of an order of operations to mechanically replicate. PEMDAS might get you through a standardised test but does not convey any understanding, it’s like knowing that you need to press a button to call the elevator but not understand what elevators are for.
Though “lazy teachers” might actually be a bit too charitable a take given the literacy rates of US college graduates mastering in English. US maths teachers very well might not understand basic maths themselves, thinking it’s all about a set of mechanical operations.
Those two things are memorisation tasks. Maths is not about memorisation.
You are not supposed to remember that the area of a triangle is a * h / 2, you’re supposed to understand why it’s the case. You’re supposed to be able to show that any triangle that can possibly exist is half the area of the rectangle it’s stuck in: Start with the trivial case (right-angled triangle), then move on to more complicated cases. If you’ve understood that once, there is no reason to remember anything because you can derive the formula at a moment’s notice.
All maths can be understood and derived like that. The names of the colours, their ordering, the names of the planets and how they’re ordered, they’re arbitrary, they have no rhyme or reason, they need to be memorised if you want to recall them. Maths doesn’t, instead it dies when you apply memorisation.
Ein Anfänger (der) Gitarre Hat Elan. There, that’s the Guitar strings in German. Why do I know that? Because my music theory knowledge sucks. I can’t apply it, music is all vibes to me but I still need a way to match the strings to what the tuner is displaying. You should never learn music theory from me, just as you shouldn’t learn maths from a teacher who can’t prove a * h / 2, or thinks it’s unimportant whether you can prove it.
Nothing. And that’s why people don’t write equations like that: You either see
46 + ---2
or
6 + 4
-------
2
If you wrote 6 + 4 / 2 in a paper you’d get reviewers complaining that it’s ambiguous, if you want it to be on one line write (6+4) / 2 or 6 + (4/2) or 6 + ⁴⁄₂ or even ½(6 + 4) Working mathematicians never came up with PEMDAS, which disambiguates it without parenthesis, US teachers did. Noone else does it that way because it does not, in the slightest, aid readability.
Because it’s just a mnemonic to remember what the order of operations is, not like… What the order of operations is, which you should know already if you know the mnemonic.
Because it’s the only other thing about that system at all. OP wasn’t teaching, just showing what that system does. If you looked for a source that explains it you’d be told
I’m sure we’re all geniuses here, but just in case…
Please excuse my dear aunt Sally.
Parenthesis, exponents, multiplication, division, addition, subtraction.
Why? Because a bunch of dead Greeks say so!
3x3-3÷3+3
(3x3)-(3÷3)+3
9-1+3
8+3
11
I guess remembering grade school order of operation means you’re a guinus now? Bar has gotten pretty low…
That’s the point.
Set the bar low, but just high enough that tons of people still trip over it.
Sit back and enjoy the comment wars.
The people who are confident but wrong are too proud to admit they were wrong even if they realize it, and comment angrily.
The people who are right and know why, comment for corrections and some to show off how S-M-R-T they are.
The people who are wrong but willing to accept that just have their realization and probably don’t think about it again. So do the people who don’t know and/or care.
But those first two groups will keep the post going in both shares and comments, because “look at all these wrong people”
It’s all designed to boost engagement.
I like the version where these problems are made purposefully ambiguous so people will fight over it and raise the level of interaction
This right here is exactly why it’s been so popular for so long.
And it will go even lower as people start relying mpre on AI…
G U I N U S.
I know it’s probably a typo, but I’m enjoying it.
It’s jeenyus you moran!
All I can envision with that alternative is Whoopi Goldberg with a very fanciful hat serving drinks in space.
I would like to say it was on purpose but it was not :( I might do math, spelling is not my forte.
The “why” goes a little further than that.
In actuality, it’s because of fundamental properties of operations
a + b = b + a
a×b = b×a
(a + b) + c = a + (b + c)
(a×b)×c = a×(b×c)
a + 0 = a
a×1 = a
If you know that, then PEMDAS and such are useless because they’re derived from those properties but do not fully encompass them.
Eg.
3×2×(2+2) = 3×(4+4) = 12+12 = 24
This is a correct solution that is improper if you’re strictly adhering to PEMDAS rule as I’ve done multiplication before parenthesis from right to left.
I could even go completely out of order by doing 3×2×(2+2) = 2×(6+6) and it will still be correct
For the programmers: operator precedence.
Not a genius. But if subtraction is last, why isn’t it 9-4?
should actually be
Addition and subtraction are given the same priority, and are done in the same step, from left to right.
It’s not a great system of notation, it could be made far clearer (and parenthesis allow you to make it as clear as you like), but it’s essentially the universal standard now and it’s what we’re stuck with.
No, it should simply be “Parenthesis, exponents, multiplication, addition.”
A division is defined as a multiplication, and a substraction is defined as an addition.
I am so confused everytime I see people arguing about this, as this is basic real number arithmetics that every kid in my country learns at 12 yo, when moving on from the simplified version you learn in elementary school.
You want PEMA with knowledge of what is defined, when people can’t even understand PEMDAS. You wish for too much.
I hate most math eduction because it’s all about memorizing formulas and rules, and then memorizing exceptions. The user above’s system is easier to learn, because there’s no exceptions or weirdness. You just learn the rule that division is multiplication and subtraction is addition. They’re just written in a different notation. It’s simpler, not more difficult. It just requires being educated on it. Yes, it’s harder if you weren’t obviously, as is everything you weren’t educated on.
That’s because (strictly speaking) they aren’t teaching math. They’re teaching “tricks” to solve equations easier, which can lead to more confusion.
Like the PEMDAS thing that’s being discussed here. There’s no such thing as “order of operations” in math, but it’s easier to teach by assuming that there is.
Edit: To the people downvoting: I want to hear your opinions. Do you think I’m wrong? If so, why?
I’m just confused as to how that is not common knowledge. The country I speak of is France, and we’re not exactly known for our excellent maths education.
Because its not really “1 plus 3”, its negative 1 plus 3 which is two. I know it seems a little weird but the minus sign is " tied" to the thing following it.
Addition/subtraction work out the same regardless of how you order the operations. If you do subtraction last you start with the original:
9-1+3
and you are adding 3 to the result of (9-1). Since you are trying to perform it before the (9-1) operation is carried out, you can add 3 to the 9:
12-1 = 11
or you can add three to the -1 and get:
9+2 = 11
You only end up with 9-4 if you were subtracting 3 rather than adding three. It all becomes more obvious if you read the original as:
9 + (-1) + 3
It’s multiplication or division from left to right followed by addition or subtraction, also from left to right.
That’s where a lot of people fuck up.
The Greeks certainly didn’t come up with PEMDAS. US teachers too lazy to teach kids actual maths did. And that’s before taking into account that the Greeks didn’t come up with Algebra.
What’s lazy about learning PEMDAS? And what’s the non-lazy/superior way?
I’m a BEDMAS man myself
Learning the actual algebraic laws, instead of an order of operations to mechanically replicate. PEMDAS might get you through a standardised test but does not convey any understanding, it’s like knowing that you need to press a button to call the elevator but not understand what elevators are for.
Though “lazy teachers” might actually be a bit too charitable a take given the literacy rates of US college graduates mastering in English. US maths teachers very well might not understand basic maths themselves, thinking it’s all about a set of mechanical operations.
This guy is the the guy posting the answer and then spending hours fighting the idiots who got it wrong on Facebook.
Nerd.
x/0 is the set {+inf,-inf}, fite me IRL.
Is it also lazy to learn Roy G. Biv to know the color spectrum instead of learning all the physics and optical properties behind that?
Or what about My Very Elderly Mother Just Served Us Nine Pickles to know the planets instead of learning orbital dynamics and astrophysics?
Christ man, it’s a mnemonic device for elementary schoolers.
Those two things are memorisation tasks. Maths is not about memorisation.
You are not supposed to remember that the area of a triangle is
a * h / 2, you’re supposed to understand why it’s the case. You’re supposed to be able to show that any triangle that can possibly exist is half the area of the rectangle it’s stuck in: Start with the trivial case (right-angled triangle), then move on to more complicated cases. If you’ve understood that once, there is no reason to remember anything because you can derive the formula at a moment’s notice.All maths can be understood and derived like that. The names of the colours, their ordering, the names of the planets and how they’re ordered, they’re arbitrary, they have no rhyme or reason, they need to be memorised if you want to recall them. Maths doesn’t, instead it dies when you apply memorisation.
Ein Anfänger (der) Gitarre Hat Elan. There, that’s the Guitar strings in German. Why do I know that? Because my music theory knowledge sucks. I can’t apply it, music is all vibes to me but I still need a way to match the strings to what the tuner is displaying. You should never learn music theory from me, just as you shouldn’t learn maths from a teacher who can’t prove
a * h / 2, or thinks it’s unimportant whether you can prove it.What fundamental property of the universe says that
6 + 4 / 2 is 8 instead of 5?
Nothing. And that’s why people don’t write equations like that: You either see
4 6 + --- 2or
6 + 4 ------- 2If you wrote
6 + 4 / 2in a paper you’d get reviewers complaining that it’s ambiguous, if you want it to be on one line write(6+4) / 2or6 + (4/2)or6 + ⁴⁄₂or even½(6 + 4)Working mathematicians never came up with PEMDAS, which disambiguates it without parenthesis, US teachers did. Noone else does it that way because it does not, in the slightest, aid readability.You might be smart, but you’re still wrong about the importance of order of operations; especially in algebra.
As far as teachers go, you’re being a dick by generalizing all (US) teachers are lazy and do not understand math.
Pro tip: opinions are like assholes; you too have one, and yes it too stinks.
just say you like the smell of your own farts, it would be less text for us to read for the same result
deleted by creator
Multiplication and Division, and Addition and Subtraction are executed at the same level and done in left to right order.
deleted by creator
Because it’s just a mnemonic to remember what the order of operations is, not like… What the order of operations is, which you should know already if you know the mnemonic.
Because it’s the only other thing about that system at all. OP wasn’t teaching, just showing what that system does. If you looked for a source that explains it you’d be told