It's a real math equation - just not used outside of school or maybe video game development. People are just forgetting one key rule of order of operations: PEMDAS/BEDMAS/BODMAS/BIDMAS or whatever depending on where you grew up. That's what leads them to wrong answers and uncertainty. Operations inside parentheses are done first, FROM LEFT TO RIGHT. Then resolve the exponents, FROM LEFT TO RIGHT. Afterwards, do the multiplication and division operations, FROM LEFT TO RIGHT. Lastly, do addition and subtraction operations, FROM LEFT TO RIGHT. I'm capitalizing here to emphasize the pattern commonly forgotten: operations are done FROM LEFT TO RIGHT. These viral math equations aren't written unclearly - people also don't recognize that a number beside parentheses are shorthand for multiplication. 6÷2(1+2), the equation on the thumbnail, is a pretty easy solve. Resolve the 1+2, then do operations from LEFT TO RIGHT. So 6÷2=3, then 3*3=9. And I'm pretty sure the obelius (this guy: ÷) doesn't indicate fractions. I don't think it ever has. Usually, if you want fractions, indicate so by using a fractional bar, or by using parentheses like (2/3) or (2+7)/(7-2). Edit: I am now realizing Math is a pretty poor construct of humanity. It's like a Git Project where conflicts are everywhere and users keep adding branches to the master branch...
Yeah... sorry but you and Fauna are wrong here. Maybe if you're writing math equations in the safe, comfy world of pure theory, but when you actually have to apply math principles they get really messy, really fast. Mostly because of other people's prior bad decisions. Applying PEMDAS in poorly written equations is a very useful skill in programming in particular. It is a stupid gotcha when advertised to the general public, but it is a bit presumptive and insulting to say that "nobody writes equations like that." My ~9 years experience in programming would beg to differ. I don't write equations like this, but I would like to think that the countless hours I've spent analyzing and rewriting garbage code written like that really existed.
Crazy Eyes (idk why ping replies don't work rn, thanks youtoob) I guess the correct way to phrase it would be "nobody *should* write them like that" then. As someone who had to take Calc III and a lot of other math class for *shudders* inorganic chemistry and electromagnetism, my teachers would have had brought us behind the uni buildings and have us "disappeared" had we ever written an equation like that lmao
so the answer to the thumbnail one would be 9 right? cause i got into an argument with someone for a similar equation and it made me rethink my math knowledge lol
The answer is "either 9 or 1" we can't know. The equation is written in an ambiguous way. People often say "oh but you can replace the division by the / symbol so it's 9" which... is wild since, when I read 6/2(1+2) I read: 6/(2(1+2) -> 6/(2x3) -> 6/6 -> 1 But people assume it's (6/2)x(1+2) -> 3x3 -> 9 So as it stands the equation can either be: 6/(2(1+2) -> 1 or (6/2)x(1+2) -> 9 The thing is that people always focus on the PEMDAS aspect when it's not the real issue here, so much as the lack of use of parentheses (I'm copying it from another comment I replied to but you'll understand that I don't feel like typing this every time lmao)
@@AlexBarbu BODMAS: BRACKET OFF DIVISION MULTIPLICATION ADDITION SUBSTRACTION We are taught that division is a higher priority than multiplication. You are taught that multiplication and division have the same priority. There's the problem.
@@AlexBarbu It's simply what we have been taught and the maths that got us through high school and college. This method has always worked for all the situations in those levels. Now if you're gonna be an astrophysicist or a math major and then claim my knowledge is wrong then it's pretty much equivalent to everyone understand Newtonian gravity but the top scientists knowing that gravity doesn't exist and Einstein's explanation of acceleration is much more accurate.
@@zan1971A bit late, but as an actual mathematician: division isn't a different operation from multiplication, as division is simply shorthand for multiplication with the multiplicative inverse of the number you are dividing by. The multiplicative inverse in the rationals and reals (the fields you usually use in real life) is simply 1 through the number you want to get the inverse of, e.g. dividing by eight is just shorthand for multiplying by one-eighth. The order in which you multiply/divide does not matter once you get rid of the ambiguity of the : sign (does not specify exactly what belongs in denominator, fractions do), and thus I have never seen it used in any textbook nor used it myself ever, only fractions instead.
Exactly I hope whoever invented ÷ for division realises what they've done to maths in the world. I'm also not fond of those ones with the fruit but then there's like secretly 2 of the fruit and they're just trying to catch you out, viral maths in shambles
I (and many others) were taught the the "P step" (parenthesis) *only* applied to numbers *within* the parenthesis and *not* numbers which were outside but touching the parenthesis. I was taught that any number touching the outside of the parenthesis was an *implied multiplication* and should be resolved during the "M step" (multiplication). so x = 2(1+1) After the P step x = 2(2) = 2*2 The E step does nothing After the M step x = 4 Done Note that I did *not* treat the "2" outside the parenthesis as part of the "P step", that part did not get resolved until the "M step". Note also that this does not "break" the distributive property just as (2+2)*(1+1) doesn't "break" the distributive property. It seems that now, students are taught that numbers touching the *outside* of parenthesis are to be treated during the "P step" and *not* during the "M step" This is the source of confusion
It's not even that This really isn't a problem of order or operations so much as it's a problem of "what the fuck is the denominator there? is it just "2" or is it "2(1+2)"? 'Cause the lack of parentheses and the use of the division sign means that it can either be (6/2)x(1+2) or 6/(2x(1+2) which respectively lead to 9 and 1 as possible answers. But again, literally anyone with a mathematic background would just... refuse to reply to such an ambiguous equation. Even in a chemistry bachelor's degree this would have gotten people straight 0's 'cause the teacher isn't going to try and read through someone's copy if they can't even use proper fractions and/or parentheses lmao
As someone who unironically loves math and science, hearing Fauna's based take on this thing makes me really happy. Honestly if this appeared on a test, once the ambiguity is pointed out it either would've been changed or straight up removed from the test.
Ultimately it's an issue of notation. Programming languages don't have this problem because programming languages define unambiguous operator precedence rules. Most programming languages define multiplication and division to have equal precedence with "left associativity" so when both operators are adjacent to each other, they are evaluated in order from left to right.
Ultimately, it is because PEMDAS is a terrible way to interpret an equation. It is so unspecific that its nearly useless. I wish school taught expression interpretation like how programming languages work. After I learned how programming languages parsed expressions into expression trees, understanding mathematical expressions was so much easier
@@SethPentolope interestingly, that's USA's elementary-middle school teachers' obsession, cause even in USA every calculus textbook uses ""PEJMDAS"" aka rememberring multiplication by juxtaposition exists and takes priority.
Unironically based. I could - and will - listen to Fauna nerding out about anything. I do have 10min of her talking about Mars and space to subtitle and upload eventually lmao
To explain the actual problem here, it's that division is almost never done that way in serious maths. Under-over division is used to avoid ambiguity, and thus when you see implicit multiplication people associate it with the thing being one whole. But because there is an nonstandard divisor there, that heuristic falls apart.
I was so worried that I'd gotten so old I'd missed an entirely new math thing. Then I realised PEDMAS is the same as BEDMAS, in the UK in mathematics we call () brackets, not parenthesis.
O just like how there are those memes where its like “theres no names that start with _ and end with _ I’LL WAAAIITT” and I just see everyone “prove” the caption wrong like they got them or whatever but no this was a 3d chess move and those people fell for the trap.
It's like Henry of MinutePhysics said: PEMDAS is wrong; the real order of operations is use parentheses, then learn the operations and use them properly. Also, Nature is mathematical and Tegmark is happy.
Its been 10 years since i have graduated from college and i have yet to find the mythical grocery store that would require me to solve a pemdas equation for anything
I mean, it is written intentionally to be confusing depending on what your understanding of P.E.DM.AS is. But it's also fascinating to see how many people decide to interpret it. And yes, there is actually a "correct" way. No, it's not open to interpretation, because when you're dealing with complicated equations the order of operations is essential. But at the same time the ones who have moved on to higher math are probably not the ones spending their time arguing about P.E.DM.AS in the first place. They've got better things to do
As a math lover and enjoyer 6/2(1 + 2) could be equal to 1 since PEMDAS is parentheses, exponent and multiplication before division which is probably right but what i hate more is the object plus object images at the end they show a minus or times to f with you
Yes those equations are unanswerable because there are multiple competing conventions. For example, some but not all mathematicians would consider the implicit multiplication like 2(1+2) to have a higher precedence than explicit multiplication like 2*(1+2). "When in doubt put more parentheses" is definitely the right approach here.
The equations are absolutely answerable, you just need to be clear about which convention you are using. In C/C++ programming, for example, the convention is clear because the languages are defined unambiguously. That is, using the C/C++ specification's operator precedence rules (which most programming languages follow) multiplication and division both have equal precedence, and both have "left associativity". So you evaluate them in order from left to right (as opposed to the exponentiation operator which has "right associativity" and is evaluated from right to left).
@@Taedrin what's interesting in programming is that sometimes the order of operations can have different side effects that you don't learn in maths, like if you work with integer numbers it's better to do divisions after other operations if possible so you don't amplify rounding errors.
@@Taedrin That's exactly how operator precedence works in the real world too. You evaluate multiplication/division from left to right with equal precedence
For computers that might be true, but for pure math multiplication is multiplication no matter the symbol. As a CS student, i hate when languages try to be quirky with their math, just use the formal math goddamnit.
Okay, but about those equations. I'm most upset at people in the comments that don't realize that multiplication and division, and addition and subtraction are opposites of each other. And therefore they have the same priority. I've come across so many smug people that say "use pemdas" and they are absolutely certain that multiplication always has to go first.
Did anybody else learn it as _PEDMAS?_ Fauna wonders why multiplication comes first in the acronym, but I legit learned it PEDMAS when I was in school. edit: obviously it doesn't matter either way i just think it's curious because I've never found anybody else who learned it as PEDMAS
I don't think I've ever seen PEDMAS tbh Then again, it doesn't matter 'cause when it comes to D and M they share the same priority so you just go from left to right. And, I could be wrong, but since multiplying and divisions are commutative you can probs even go from right to left and be right.
I remember watching a Vlogbrothers video on these exact kinds of vaguely written “equations”, and it came to the exact same conclusions that Fauna did. Is Fauna really just Hank Green?
I once got into a heated argument on Facebook as a result of one of these equations, I did the part in parentheses first as that's what you're supposed to do with PEMDAS and everyone was telling me I was wrong and should've multiplied first
Well that makes no sense as no matter what order of operations you use Parentheses always come first. PEMDAS has you do multiplication first then division, whereas nowadays the two are equal and are done left to right. So with PEMDAS you would add then multiply and divide, and with current order of operations you would add then divide and finally multiply
PEMDAS DOES NOT have you multiply first, people just assumed it does. It's 4 rules not 6. It's Parentheses, Exponents, Multiplication AND Division, Addition AND Subtraction. Count the number of expressions between commas.
Reminder: the point here is that someone is doing this _on purpose_ to get people to argue, creating "engagement" for the algorithms. The people posting these don't care a fig which one is right.
As a seasoned programmer whenever I see a "÷" symbol I just automatically throw an equation back and tell the author to either use "real" division symbols ("/") or write proper fractions.
@@roadent217 Because theyre not identical hence the confusion. A forward slash is the only valid programming operator and it has a very strict execution order. The fraction symbol is not an arithmetic operator hence why I say either write full fractions the way youre supposed to or stick to standard operators with parentheses.
@@szlatyka "A forward slash is the only valid programming operator and it has a very strict execution order." Which is? What would be the answer to the thumbnail's equation in a programming language?
@@roadent217 Programming languages don't have implicit multiplication. It would evaluate 2(1+2) first, interpreting it as calling the function "2" with the argument 3, and throw an error (since 2 is not a function). if you write it with *, 6/2*(1+2), the answer is 9.
@@linawhatevs8389 Correct. So, to answer OP - a programmer has to write out explicit multiplication. And, if he does, every programming language will consider multiplication and division to be equal in the order of operations. In that case, evaluated left to right, like you said, the forward slash will be evaluated on 6 and 2. If a programming language (Matlab, GNU Octave, or something?) would support an obelus operator ÷, I don't see why it would be any different to a forward slash /.
I tried explaining it to friends too and was it with "But PEMDAS" even though I just spent like 15min explaining why it's not a PEMDAS issue in the first place lmao
Ehhhhh, as a computer programmer, you've (generally) got three choices - either have each step be its own line, use the debugger, or put the equations on lines where the operations are more easily understood. In any of the latter two cases, you've gotta know PEMDAS either by learning it or already knowing it. Edit: she points out the parenthesis trick that I myself use.
Finally, someone who gets it... Instead of following stupid, arbitrary rules, just make your damn equations clear. Worst case, evaluate the expression like computers usually do.
The problem is that division is almost never done that way in serious maths. Under-over division is used to avoid ambiguity, and thus when you see implicit multiplication people associate it with the thing being one whole. But because there is an nonstandard divisor there, that heuristic falls apart.
On that note, did you know that the Windows calculator works differently in simple mode and in scientific mode? In simple mode it just does every operation after another while in scientific mode it takes PEMDAS into account. For example if you do 1+2*3 in simple mode it will give the (technically wrong) result 9 while in scientific mode it will give the (right) result 7. Wonder how many people just punched in the numbers into the simple windows calculator and were like "See???? I was right!!!" Also yeah, multiplication and division are kinda the same, only that division is like multiplying with the inverse of the number, so 2/3 could be rewritten as 2 * 1/3 with 1/3 being the inverse of 3. It's like subtraction is like addition but with the negated number, like 2-3 is the same as 2+(-3)
That's in fact the entire issue at hand. PEMDAS doesn't matter if proper notation isn't used. If anyone wanted an actual, inambiguous answer they'd write it either: 6/(2(1+2)) or (6/2)(1+2)
2(1+2) is just a decomposed (2+4) same as 2(x+2) == (2x+4), it's a whole that shouldn't be separated. Like 6/(2x+4) is the same as 6/2(x+2), but it's not 6/2 * (x+2) unless you add parenthesies. It's as if you started manipulating an equation to solve for X and were suddenly told "X is 1" before you finished.
I would definitely see 6/2(x+2) as 6/2 * (x+2). Imo if you can't use fractions because of the limitations of digital text, please use parantheses for everything that is supposed to be in the divisor
See in school I was taught BODMAS, which stands for Brackets, Orders, Division, Multiplication, Addition and Subtraction, so by what I was taught division would come first. It's almost like the stuff we were taught in school was intentionally taught at a basic level to make it easy to understand rather than a definitive ruling that's universally true for all eternity. Most lessons are stepping stones to other, more complicated lessons.
You need a fairly good calculator though, not one of those basic step by step ones Also depending on how it's written you need to change your input For example the thumbnail's "6/2(1+2)" would need to be changed to "6/2*(1+2)"
@@letsplaysvonaja1714 but these two equations are not the same, and it becomes more evident if there is a variable. Like 6/(2x+4) is the same as 6/2(x+2), but it's not 6/2 * (x+2) unless you add parenthesies.
@@AlexECX You're assuming that, just because the 2 is placed adjacent to the parenthesis, that the entire second part after the divisor is a denominator. Most people who write equations wouldn't assume that you would just pick up on that and they would use a proper fractional divider instead of just the forward slash character. Furthermore I've never heard of any hard and fast rules which tell you to do that. I imagine any that you might have heard are specific to your school or culture.
btw the equations arent wrong... People just arent "used to" visualizing it that way. Its not misleading. I admit I've used the argument that the equations are wrong, before, but in reality its a simple equation.
It's indeed misleading on purpose But say, if I tell you that 6÷2(1+2) is telling you that "2(1+2)" is the denominator, people are invariably going to pop up and tell me otherwise even though that's the whole point of this symbol (÷) In the end, my old Casio calc does it one way, the apparently correct way, and my phone calculator assumes that (1+2) is separate from 6÷2.
PeMDas = PoDMas P E/O MD/DM AS Division is multiplication of fractions. Treat multiplication and division the same, go from left to right Subtraction is addition with negatives. Treat addition and subtraction the same, go from left to right. 6 / 2 (1+2) =6 / 2 (3) = 6 / 2 x 3 Now that you only have division and multiplication, PoDMas=PeMDas Do all multiplication and division from left to right. That has never been unclear.
It's not a matter of order of operations, it's a matter of unclear denominator. i.e: as it stands this equation can either be: (6/2)x(1+2) or 6/(2x(1+2))
As far as I know - I'm not a native English speaker, let alone American - pree much. But they use 'parentheses' instead of 'brackets' and 'exponents' instead of 'orders' (which works for square root too and roots in general since the nth root of x is x to the power 1/n)
Funny enough I actually always called it BIDMAS instead of BODMAS with the I standing for indices, but then I learned there were other classes *in the same school* that called it BODMAS so I think that was just the one teacher I had
The answer is "either 9 or 1" we can't know. The equation is written in an ambiguous way. People often say "oh but you can replace the division by the / symbol so it's 9" which... is wild since, when I read 6/2(1+2) I read: 6/(2(1+2) -> 6/(2x3) -> 6/6 -> 1 But people assume it's (6/2)x(1+2) -> 3x3 -> 9 So as it stands the equation can either be: 6/(2(1+2) -> 1 or (6/2)x(1+2) -> 9 The thing is that people always focus on the PEMDAS aspect when it's not the real issue here, so much as the lack of use of parentheses
Eh? Does someone in the world get that 6/2 means 2 is the denominator, but 6÷2 confuses them? Or am I misunderstanding this? I mean, I sometimes do math for fun but still, the example in the thumbnail isn't confusing unless you're deliberately doing the math from left to right and not following pemdas.
Without parentheses it could also be 6/2(1+2) which give you a totally different answer "But no one would write it like that" That's the point lmao, i didn't even make this example myself, just found it online. My uni teachers would have had me 'disappeared' if I ever dared write anything like this. Then again, there's waaay too many numbers in this compared to uni maths lmao Where 'em letters and greek letters at?
I was talking with a 64 year old guy the other day and he was livid that in his multiple jobs and life experiences, he didn’t have to use any sort of algebra, calculus, or trigonometry lol His geometry class helped somehow with business but that was it lol I love my math teachers but they already require the same exact courses and higher in college for STEM degrees(some of them still seeming very pointless though), so it’s annoying they require it in highschool. A Highschool math class is worth half a college course, so worthless lol
Trig is very useful in computer graphics and engineering. Calculus is also useful for computer graphics, but it can also be used for in-depth statistical analysis. And as for algebra... I'm going to say he's just wrong on that. It's virtually impossible to go through modern life without using algebra. Algebra is just the substitution of numbers for an expression, or working backwards to find out a missing value in an equation. If you've ever budgeted for a month, then figured out how much you should spend on a particular thing to meet that budget... you've just solved for "x."
@@Lemon_Inspector I've known people who've said this unironically. Also, people who say "History class was pointless, I'm never going to be an archaeologist"...
Something is wrong with your logical thinking if you have problems with simple stuff like this. It doesn't matter how it's written, there is a simple set of rules that dictate the solving order.
Yeah, IDK. I never got higher than a D in any math class through Calc (at which point I stopped taking math classes) but I still feel like I'm better at math than most. Like, just being able to calculate a 20% tip in your head sets you in the top quarter of the bell curve.
It's really just a problem of unclear notation. Basically the question asked here boils down to, is the equation represented meant to represent 6/2 * (1+2), that is to say, a fraction (6/2) that is then multiplied by an integer (1+2) - or is it meant to *all* represent a *single* fraction, with 6 as the numerator and 2(1+2) as the denominator? And to avoid this, is why we write our fractions properly.
@@drascin To avoid this, we never imply multiplication. Every programming language will say that 6/2*(1+2)==9. I bet that, for languages thag support it, the obelus sign ÷ will be treated as equivalent to the forward slash /.
@@roadent217 I'm a dev myself, I'm aware - most programming languages follow a very strict parentheses then left to right parsing algorithm. But when writing things down for people, it's very important to leave things clear and unambiguous because making the math equivalent of those magic eye posters is not clever, it's just annoying. (Honestly, this maxim tends to apply to programming in many places too. Always write your code such that the next poor bastard who will have to work with it doesn't need to read your mind, people! And if you're doing complex boolean conditions put some parentheses and tree them up a bit to make them easier to parse!)
The core root of the problem comes solely from the "division symbol" being used instead of representing it as a fraction. 4÷2+2 could simultaneously means 4/(2+2), which would equal 1, due to "2+2" being the denominator in that fraction, or it could mean (4/2)+2 which would equal 4. neither answer is technically wrong, because the question itself is vague.
"John met Jimmy. He was hungry." Who was hungry? Same thing really. Can't guess unless you get some more info, which here for this math equation, would be parentheses. It was never really about PEMDAS indeed
TBF the equation is written wrong the correct equation is 6/(2(2+1))=1 BUT regardless even without the parenthesis, you should still follow PEMDAS rule.
1 There is only one correct answer and you will only get it if you had to take calculus and physics. You solve it as it is written, the intent of how it was written is irrelevant. A division is like this x/y and they drill this into your skull hard, it still baffles me schools say there's multiple answers.
"the intent of how it was written is irrelevant" This mentality makes no sense in any real world application, and furthermore makes no sense within the concepts of higher math. Also in a programming context, the answer is probably, but not definitely, 9, depending on the language being used.
There are multiple conventions that can be followed. You are possibly correct in implying that the person who wrote the expression is wrong, but if you were given this expression with no context and had to solve it, you can't just assume that is the case.
Incorrect. You evaluate division and multiplication with equal precedence, from left to right. The correct answer is 9. 6 / 2 * (1 + 2) = 6 / 2 * 3 = 3 * 3 = 9
There is, of course, some debate as to how operators with space only on one side should be treated. Some authors simply treat them as lower precedence, but as a compromise, they can be considered to be between no-space and full-space operators. Multiplication and division are left-associative, unless the terms are written together, like "ax²". Then it's right-associative.
Math is the worst subject ong addition,subtraction,multiplication,and division are honestly the only things that are really used in everyday life the rest is goofy
![VTubers React to Elementary School Math [13 POVs]](/img/1.gif)
As a wise man once said, “Communicating badly and then acting smug when you’re misunderstood is not cleverness.”
Sadly, selective cognition is getting more and more prevalent than ever.
That said, he said that after cutting off a guy's hand
"When in doubt, put more parentheses" I didnt think it was possible for me to love this Kirin more, but I was wrong
"The way it's written is unclear on purpose and no one would actually write an equation that way"
The school board making the 5th grade midterm exam:
FINALLY! Someone who understood that viral math equation meme is written unclearly on purpose!! Real math equations are not written like that!
Are they? I dunno.
Sounds like its something Gura would know. Let's all ask her about it when she comes back.
It's a real math equation - just not used outside of school or maybe video game development.
People are just forgetting one key rule of order of operations: PEMDAS/BEDMAS/BODMAS/BIDMAS or whatever depending on where you grew up. That's what leads them to wrong answers and uncertainty.
Operations inside parentheses are done first, FROM LEFT TO RIGHT. Then resolve the exponents, FROM LEFT TO RIGHT. Afterwards, do the multiplication and division operations, FROM LEFT TO RIGHT. Lastly, do addition and subtraction operations, FROM LEFT TO RIGHT. I'm capitalizing here to emphasize the pattern commonly forgotten: operations are done FROM LEFT TO RIGHT.
These viral math equations aren't written unclearly - people also don't recognize that a number beside parentheses are shorthand for multiplication.
6÷2(1+2), the equation on the thumbnail, is a pretty easy solve. Resolve the 1+2, then do operations from LEFT TO RIGHT. So 6÷2=3, then 3*3=9.
And I'm pretty sure the obelius (this guy: ÷) doesn't indicate fractions. I don't think it ever has. Usually, if you want fractions, indicate so by using a fractional bar, or by using parentheses like (2/3) or (2+7)/(7-2).
Edit: I am now realizing Math is a pretty poor construct of humanity. It's like a Git Project where conflicts are everywhere and users keep adding branches to the master branch...
Yeah... sorry but you and Fauna are wrong here. Maybe if you're writing math equations in the safe, comfy world of pure theory, but when you actually have to apply math principles they get really messy, really fast. Mostly because of other people's prior bad decisions. Applying PEMDAS in poorly written equations is a very useful skill in programming in particular. It is a stupid gotcha when advertised to the general public, but it is a bit presumptive and insulting to say that "nobody writes equations like that." My ~9 years experience in programming would beg to differ. I don't write equations like this, but I would like to think that the countless hours I've spent analyzing and rewriting garbage code written like that really existed.
You cruel, cruel monster Al Cor lmao
Crazy Eyes (idk why ping replies don't work rn, thanks youtoob) I guess the correct way to phrase it would be "nobody *should* write them like that" then.
As someone who had to take Calc III and a lot of other math class for *shudders* inorganic chemistry and electromagnetism, my teachers would have had brought us behind the uni buildings and have us "disappeared" had we ever written an equation like that lmao
Fauna is spitting facts
CompSci student here, parentheses are the GOAT
so the answer to the thumbnail one would be 9 right? cause i got into an argument with someone for a similar equation and it made me rethink my math knowledge lol
The answer is "either 9 or 1" we can't know.
The equation is written in an ambiguous way.
People often say "oh but you can replace the division by the / symbol so it's 9" which... is wild
since, when I read 6/2(1+2) I read: 6/(2(1+2) -> 6/(2x3) -> 6/6 -> 1
But people assume it's (6/2)x(1+2) -> 3x3 -> 9
So as it stands the equation can either be:
6/(2(1+2) -> 1
or
(6/2)x(1+2) -> 9
The thing is that people always focus on the PEMDAS aspect when it's not the real issue here, so much as the lack of use of parentheses
(I'm copying it from another comment I replied to but you'll understand that I don't feel like typing this every time lmao)
@@AlexBarbu
BODMAS:
BRACKET
OFF
DIVISION
MULTIPLICATION
ADDITION
SUBSTRACTION
We are taught that division is a higher priority than multiplication. You are taught that multiplication and division have the same priority. There's the problem.
@@AlexBarbu
It's simply what we have been taught and the maths that got us through high school and college. This method has always worked for all the situations in those levels. Now if you're gonna be an astrophysicist or a math major and then claim my knowledge is wrong then it's pretty much equivalent to everyone understand Newtonian gravity but the top scientists knowing that gravity doesn't exist and Einstein's explanation of acceleration is much more accurate.
@@zan1971A bit late, but as an actual mathematician: division isn't a different operation from multiplication, as division is simply shorthand for multiplication with the multiplicative inverse of the number you are dividing by. The multiplicative inverse in the rationals and reals (the fields you usually use in real life) is simply 1 through the number you want to get the inverse of, e.g. dividing by eight is just shorthand for multiplying by one-eighth. The order in which you multiply/divide does not matter once you get rid of the ambiguity of the : sign (does not specify exactly what belongs in denominator, fractions do), and thus I have never seen it used in any textbook nor used it myself ever, only fractions instead.
Exactly I hope whoever invented ÷ for division realises what they've done to maths in the world. I'm also not fond of those ones with the fruit but then there's like secretly 2 of the fruit and they're just trying to catch you out, viral maths in shambles
It would be fine if people actually used parentheses. That's what parentheses are for in math.
Fun fact, that's why the division sign (÷) isn't recommended for use anymore. It's completely redundant
@@jimmygarza8896 it's not paranthesis but the division sign (:) that the problem
I'm lost, what's wrong with the division sign?
@@ZombieNaito Mostly it's just an unnecessary symbol that has nothing to offer other than potential confusion.
I (and many others) were taught the the "P step" (parenthesis) *only* applied to numbers *within* the parenthesis and *not* numbers which were outside but touching the parenthesis.
I was taught that any number touching the outside of the parenthesis was an *implied multiplication* and should be resolved during the "M step" (multiplication).
so
x = 2(1+1)
After the P step
x = 2(2) = 2*2
The E step does nothing
After the M step
x = 4
Done
Note that I did *not* treat the "2" outside the parenthesis as part of the "P step", that part did not get resolved until the "M step".
Note also that this does not "break" the distributive property just as (2+2)*(1+1) doesn't "break" the distributive property.
It seems that now, students are taught that numbers touching the *outside* of parenthesis are to be treated during the "P step" and *not* during the "M step"
This is the source of confusion
It's not even that
This really isn't a problem of order or operations so much as it's a problem of "what the fuck is the denominator there? is it just "2" or is it "2(1+2)"?
'Cause the lack of parentheses and the use of the division sign means that it can either be (6/2)x(1+2) or 6/(2x(1+2) which respectively lead to 9 and 1 as possible answers.
But again, literally anyone with a mathematic background would just... refuse to reply to such an ambiguous equation.
Even in a chemistry bachelor's degree this would have gotten people straight 0's 'cause the teacher isn't going to try and read through someone's copy if they can't even use proper fractions and/or parentheses lmao
The thing is, if you see that kind of math equation being used in academic other than school, it would not be that short.
Please, excuse my dear Aunt Sally.
I'm gonna be real: I had totally forgotten what PEMDAS stood for until she started talking about it here.
It has been 4yrs since I last heard that word.
As someone who unironically loves math and science, hearing Fauna's based take on this thing makes me really happy.
Honestly if this appeared on a test, once the ambiguity is pointed out it either would've been changed or straight up removed from the test.
Ultimately it's an issue of notation. Programming languages don't have this problem because programming languages define unambiguous operator precedence rules. Most programming languages define multiplication and division to have equal precedence with "left associativity" so when both operators are adjacent to each other, they are evaluated in order from left to right.
Ultimately, it is because PEMDAS is a terrible way to interpret an equation. It is so unspecific that its nearly useless. I wish school taught expression interpretation like how programming languages work. After I learned how programming languages parsed expressions into expression trees, understanding mathematical expressions was so much easier
@@SethPentolope interestingly, that's USA's elementary-middle school teachers' obsession, cause even in USA every calculus textbook uses ""PEJMDAS"" aka rememberring multiplication by juxtaposition exists and takes priority.
Parentheses really are the biggest gift to math, can never have enough of them.
As a mathematician, I agree with her take. I am now in love with her even more.
As a fellow wearer of glasses, her talking so in depth ab math with the glasses makes her a need and I love it
glasses are very versatile...
Programmers constructing logical conditions: "When in doubt, put in more parenthesis."
Fauna not only looks like 🤓
But also sounds like 🤓
Beat me to it lol
Unironically based.
I could - and will - listen to Fauna nerding out about anything.
I do have 10min of her talking about Mars and space to subtitle and upload eventually lmao
@@slowberryvtuberclips oh man guess I have to sub then
The correct answer to those stupid questions is always "this question is poorly formatted and you should feel bad for posting it"
Yes, Fauna is correct, put more parentheses in. If you can't do the proper notation in regular text, use more parentheses to position the numbers.
To explain the actual problem here, it's that division is almost never done that way in serious maths.
Under-over division is used to avoid ambiguity, and thus when you see implicit multiplication people associate it with the thing being one whole. But because there is an nonstandard divisor there, that heuristic falls apart.
"When in doubt put in more parenthesis."
That is indeed what I do x)
PEMDAS then when all actions have the same priority, you solve left to right.
I was so worried that I'd gotten so old I'd missed an entirely new math thing.
Then I realised PEDMAS is the same as BEDMAS, in the UK in mathematics we call () brackets, not parenthesis.
'when in doubt put in more parenthesis'....Fauna is god-tier software dev and doesn't even realize it.
O just like how there are those memes where its like “theres no names that start with _ and end with _ I’LL WAAAIITT” and I just see everyone “prove” the caption wrong like they got them or whatever but no this was a 3d chess move and those people fell for the trap.
fauna use big brain solution
its like whchever come first between multi and division goes first
she definitely argues with her teacher in school
I would have had too if this question came up on a test lmao
It's like Henry of MinutePhysics said: PEMDAS is wrong; the real order of operations is use parentheses, then learn the operations and use them properly.
Also, Nature is mathematical and Tegmark is happy.
Honestly should be the same conclusion that anyone who made it out of high school algebra should know, but it shows how low the bar is for math
Its been 10 years since i have graduated from college and i have yet to find the mythical grocery store that would require me to solve a pemdas equation for anything
I mean, it is written intentionally to be confusing depending on what your understanding of P.E.DM.AS is. But it's also fascinating to see how many people decide to interpret it. And yes, there is actually a "correct" way. No, it's not open to interpretation, because when you're dealing with complicated equations the order of operations is essential.
But at the same time the ones who have moved on to higher math are probably not the ones spending their time arguing about P.E.DM.AS in the first place. They've got better things to do
fauna going ultra nerd mode
As a math lover and enjoyer
6/2(1 + 2)
could be equal to 1 since PEMDAS is parentheses, exponent and multiplication before division
which is probably right but what i hate more is the object plus object images at the end they show a minus or times to f with you
Yes those equations are unanswerable because there are multiple competing conventions.
For example, some but not all mathematicians would consider the implicit multiplication like 2(1+2) to have a higher precedence than explicit multiplication like 2*(1+2).
"When in doubt put more parentheses" is definitely the right approach here.
The equations are absolutely answerable, you just need to be clear about which convention you are using. In C/C++ programming, for example, the convention is clear because the languages are defined unambiguously. That is, using the C/C++ specification's operator precedence rules (which most programming languages follow) multiplication and division both have equal precedence, and both have "left associativity". So you evaluate them in order from left to right (as opposed to the exponentiation operator which has "right associativity" and is evaluated from right to left).
@@Taedrin what's interesting in programming is that sometimes the order of operations can have different side effects that you don't learn in maths, like if you work with integer numbers it's better to do divisions after other operations if possible so you don't amplify rounding errors.
@@Taedrin That's exactly how operator precedence works in the real world too. You evaluate multiplication/division from left to right with equal precedence
For computers that might be true, but for pure math multiplication is multiplication no matter the symbol. As a CS student, i hate when languages try to be quirky with their math, just use the formal math goddamnit.
@@Taedrin I'm pretty sure that following a 2 with an open parentheses is a syntax error in the C/C++ specification.
Okay, but about those equations. I'm most upset at people in the comments that don't realize that multiplication and division, and addition and subtraction are opposites of each other. And therefore they have the same priority.
I've come across so many smug people that say "use pemdas" and they are absolutely certain that multiplication always has to go first.
Did anybody else learn it as _PEDMAS?_ Fauna wonders why multiplication comes first in the acronym, but I legit learned it PEDMAS when I was in school.
edit: obviously it doesn't matter either way i just think it's curious because I've never found anybody else who learned it as PEDMAS
I don't think I've ever seen PEDMAS tbh
Then again, it doesn't matter 'cause when it comes to D and M they share the same priority so you just go from left to right.
And, I could be wrong, but since multiplying and divisions are commutative you can probs even go from right to left and be right.
@@slowberryvtuberclips Sorry to be pedantic, but only multiplication is commutative. 2 * 3 = 3 * 2 but 2 / 3 =/= 3/2.
I knew I was getting that wrong lmao
I forgot the mathematical word for like, when it doesn't matter which order you do operations in
oh yeah using / and ÷ was being intentionally vague
I remember watching a Vlogbrothers video on these exact kinds of vaguely written “equations”, and it came to the exact same conclusions that Fauna did.
Is Fauna really just Hank Green?
That would be super based
I once got into a heated argument on Facebook as a result of one of these equations, I did the part in parentheses first as that's what you're supposed to do with PEMDAS and everyone was telling me I was wrong and should've multiplied first
Well that makes no sense as no matter what order of operations you use Parentheses always come first. PEMDAS has you do multiplication first then division, whereas nowadays the two are equal and are done left to right. So with PEMDAS you would add then multiply and divide, and with current order of operations you would add then divide and finally multiply
@@TheJjcczz right? That's what I said and I failed math, but I had it drilled into my head that in PEMDAS parenthesis always goes first.
PEMDAS DOES NOT have you multiply first, people just assumed it does. It's 4 rules not 6. It's Parentheses, Exponents, Multiplication AND Division, Addition AND Subtraction. Count the number of expressions between commas.
Nice outro
Reminder: the point here is that someone is doing this _on purpose_ to get people to argue, creating "engagement" for the algorithms.
The people posting these don't care a fig which one is right.
As a seasoned programmer whenever I see a "÷" symbol I just automatically throw an equation back and tell the author to either use "real" division symbols ("/") or write proper fractions.
The obelus is identical to the forward slash. Why the confusion?
@@roadent217 Because theyre not identical hence the confusion. A forward slash is the only valid programming operator and it has a very strict execution order. The fraction symbol is not an arithmetic operator hence why I say either write full fractions the way youre supposed to or stick to standard operators with parentheses.
@@szlatyka "A forward slash is the only valid programming operator and it has a very strict execution order."
Which is?
What would be the answer to the thumbnail's equation in a programming language?
@@roadent217 Programming languages don't have implicit multiplication. It would evaluate 2(1+2) first, interpreting it as calling the function "2" with the argument 3, and throw an error (since 2 is not a function). if you write it with *, 6/2*(1+2), the answer is 9.
@@linawhatevs8389 Correct.
So, to answer OP - a programmer has to write out explicit multiplication. And, if he does, every programming language will consider multiplication and division to be equal in the order of operations. In that case, evaluated left to right, like you said, the forward slash will be evaluated on 6 and 2.
If a programming language (Matlab, GNU Octave, or something?) would support an obelus operator ÷, I don't see why it would be any different to a forward slash /.
When I was in school, there were a lot of them. And they were the easier math problems
Seems like most of this comment section is still completely missing the point of why Fauna is annoyed lol
I tried explaining it to friends too and was it with "But PEMDAS" even though I just spent like 15min explaining why it's not a PEMDAS issue in the first place lmao
That's 9
Ehhhhh, as a computer programmer, you've (generally) got three choices - either have each step be its own line, use the debugger, or put the equations on lines where the operations are more easily understood. In any of the latter two cases, you've gotta know PEMDAS either by learning it or already knowing it. Edit: she points out the parenthesis trick that I myself use.
Fellow programmer. Yes when unsure more parenthesis to make sure that part gets done before others lol. Definitely been guilty of it.
Finally, someone who gets it... Instead of following stupid, arbitrary rules, just make your damn equations clear. Worst case, evaluate the expression like computers usually do.
The answer to her question about multiplication and division is whichever comes first in the equation.
For starters, numbers are not even supposed to be written like those.. Use fraction for division and parenthesis for multiplication.
Agreed. The equation is confusing because it doesn't stick to a single notation method. It should read as either [ 6÷2*(1+2) ] or [ ⁶⁄₂(1+2) ]
where i live we dont even have a fancy acronym like this and in the entirety of high school i was never ever confused by the order of operations
Literally fucking how is she this cute? It doesn't make sense
1:06 They are equal so, after doing what's in parenthesis, you just do whatever comes first from the left.
The problem is that division is almost never done that way in serious maths. Under-over division is used to avoid ambiguity, and thus when you see implicit multiplication people associate it with the thing being one whole. But because there is an nonstandard divisor there, that heuristic falls apart.
Based nature goddess 10/10
On that note, did you know that the Windows calculator works differently in simple mode and in scientific mode? In simple mode it just does every operation after another while in scientific mode it takes PEMDAS into account. For example if you do 1+2*3 in simple mode it will give the (technically wrong) result 9 while in scientific mode it will give the (right) result 7. Wonder how many people just punched in the numbers into the simple windows calculator and were like "See???? I was right!!!"
Also yeah, multiplication and division are kinda the same, only that division is like multiplying with the inverse of the number, so 2/3 could be rewritten as 2 * 1/3 with 1/3 being the inverse of 3. It's like subtraction is like addition but with the negated number, like 2-3 is the same as 2+(-3)
She’s not wrong about parentheses
That's in fact the entire issue at hand.
PEMDAS doesn't matter if proper notation isn't used.
If anyone wanted an actual, inambiguous answer they'd write it either:
6/(2(1+2))
or
(6/2)(1+2)
SMH, the true way to write is 6 2 / 1 2 + * for stack based clarity
Fr
Whats that cute outro from?
It's from a Fauna stream, the one called:
【Nintendo Switch Sports】 playing sports to fuel my virtual clothing gacha addiction
@@slowberryvtuberclips thank you uuuuuu
2(1+2) is just a decomposed (2+4) same as 2(x+2) == (2x+4), it's a whole that shouldn't be separated. Like 6/(2x+4) is the same as 6/2(x+2), but it's not 6/2 * (x+2) unless you add parenthesies.
It's as if you started manipulating an equation to solve for X and were suddenly told "X is 1" before you finished.
I would definitely see 6/2(x+2) as 6/2 * (x+2). Imo if you can't use fractions because of the limitations of digital text, please use parantheses for everything that is supposed to be in the divisor
is it 1 or 9?
Isn't it supposed to be BEDMAS? Brackets, exponents, division, multiplication, addition, subtraction?
See in school I was taught BODMAS, which stands for Brackets, Orders, Division, Multiplication, Addition and Subtraction, so by what I was taught division would come first. It's almost like the stuff we were taught in school was intentionally taught at a basic level to make it easy to understand rather than a definitive ruling that's universally true for all eternity. Most lessons are stepping stones to other, more complicated lessons.
That's why BODMAS (and alternative forms) can be harmful in the long run -- it teaches students the wrong thing at a foundational level.
PEMDAS? omg americans have abbriviatation for everething
Bruh just use a calculators... smh my head
You need a fairly good calculator though, not one of those basic step by step ones
Also depending on how it's written you need to change your input
For example the thumbnail's "6/2(1+2)" would need to be changed to "6/2*(1+2)"
@@letsplaysvonaja1714 but these two equations are not the same, and it becomes more evident if there is a variable. Like 6/(2x+4) is the same as 6/2(x+2), but it's not 6/2 * (x+2) unless you add parenthesies.
@@AlexECX except it isn't
You have to calculate from left to right, so it's basically "(6/2)*(1+2)"
Meaning "3*3", not "6/6" as you are saying
@@letsplaysvonaja1714 I'm not sure what "except it isn't" refers to, I'm guessing from "3*3, not 6/6" you mean 6/(2x+4) doesn't equal 1 if x = 1 ?
@@AlexECX You're assuming that, just because the 2 is placed adjacent to the parenthesis, that the entire second part after the divisor is a denominator. Most people who write equations wouldn't assume that you would just pick up on that and they would use a proper fractional divider instead of just the forward slash character. Furthermore I've never heard of any hard and fast rules which tell you to do that. I imagine any that you might have heard are specific to your school or culture.
btw the equations arent wrong... People just arent "used to" visualizing it that way.
Its not misleading.
I admit I've used the argument that the equations are wrong, before, but in reality its a simple equation.
It’s 9
The answer is 9
Fight me
But don’t because I fucking hate math
I'm worse than Gura when it comes to math
It's indeed misleading on purpose
But say, if I tell you that
6÷2(1+2) is telling you that "2(1+2)" is the denominator, people are invariably going to pop up and tell me otherwise even though that's the whole point of this symbol (÷)
In the end, my old Casio calc does it one way, the apparently correct way, and my phone calculator assumes that (1+2) is separate from 6÷2.
PeMDas = PoDMas
P
E/O
MD/DM
AS
Division is multiplication of fractions. Treat multiplication and division the same, go from left to right
Subtraction is addition with negatives. Treat addition and subtraction the same, go from left to right.
6 / 2 (1+2) =6 / 2 (3) = 6 / 2 x 3
Now that you only have division and multiplication, PoDMas=PeMDas
Do all multiplication and division from left to right. That has never been unclear.
It's not a matter of order of operations, it's a matter of unclear denominator.
i.e: as it stands this equation can either be: (6/2)x(1+2) or 6/(2x(1+2))
🤓🤓🤓
Is this just an American thing to call BODMAS PEMDAS?
As far as I know - I'm not a native English speaker, let alone American - pree much.
But they use 'parentheses' instead of 'brackets' and 'exponents' instead of 'orders' (which works for square root too and roots in general since the nth root of x is x to the power 1/n)
Yeah it's parentheses, exponents, multiplication, division, addition, subtraction. We call these [ ] brackets
Funny enough I actually always called it BIDMAS instead of BODMAS with the I standing for indices, but then I learned there were other classes *in the same school* that called it BODMAS so I think that was just the one teacher I had
where i live its bedmas
BIMDAS here in Australia (Brackets, Indices, Multiplication, Division, Addition, Subtraction)
Parentheses
Exponents
Multiplication/Division
Addition/Subtraction
Smart Kirin 💚
Also, the answer is 9... Right?
The answer is "either 9 or 1" we can't know.
The equation is written in an ambiguous way.
People often say "oh but you can replace the division by the / symbol so it's 9" which... is wild
since, when I read 6/2(1+2) I read: 6/(2(1+2) -> 6/(2x3) -> 6/6 -> 1
But people assume it's (6/2)x(1+2) -> 3x3 -> 9
So as it stands the equation can either be:
6/(2(1+2) -> 1
or
(6/2)x(1+2) -> 9
The thing is that people always focus on the PEMDAS aspect when it's not the real issue here, so much as the lack of use of parentheses
@@slowberryvtuberclips haha love it! You should pin your answer, I'm actually going back to school for exactly this sort of work too haha 😊
Ohh good luck with that!
Wtf is "new math"
Eh? Does someone in the world get that 6/2 means 2 is the denominator, but 6÷2 confuses them? Or am I misunderstanding this?
I mean, I sometimes do math for fun but still, the example in the thumbnail isn't confusing unless you're deliberately doing the math from left to right and not following pemdas.
Without parentheses it could also be 6/2(1+2) which give you a totally different answer
"But no one would write it like that"
That's the point lmao, i didn't even make this example myself, just found it online.
My uni teachers would have had me 'disappeared' if I ever dared write anything like this.
Then again, there's waaay too many numbers in this compared to uni maths lmao
Where 'em letters and greek letters at?
I was talking with a 64 year old guy the other day and he was livid that in his multiple jobs and life experiences, he didn’t have to use any sort of algebra, calculus, or trigonometry lol His geometry class helped somehow with business but that was it lol I love my math teachers but they already require the same exact courses and higher in college for STEM degrees(some of them still seeming very pointless though), so it’s annoying they require it in highschool. A Highschool math class is worth half a college course, so worthless lol
Factorio made me use algebra
Trig is very useful in computer graphics and engineering. Calculus is also useful for computer graphics, but it can also be used for in-depth statistical analysis. And as for algebra... I'm going to say he's just wrong on that. It's virtually impossible to go through modern life without using algebra. Algebra is just the substitution of numbers for an expression, or working backwards to find out a missing value in an equation. If you've ever budgeted for a month, then figured out how much you should spend on a particular thing to meet that budget... you've just solved for "x."
@@CrizzyEyes "My English classes were useless because nobody ever stops me in the street and asks me to quote Shakespeare!"
@@Lemon_Inspector
I've known people who've said this unironically.
Also, people who say "History class was pointless, I'm never going to be an archaeologist"...
Something is wrong with your logical thinking if you have problems with simple stuff like this. It doesn't matter how it's written, there is a simple set of rules that dictate the solving order.
Yeah, IDK. I never got higher than a D in any math class through Calc (at which point I stopped taking math classes) but I still feel like I'm better at math than most.
Like, just being able to calculate a 20% tip in your head sets you in the top quarter of the bell curve.
It's really just a problem of unclear notation. Basically the question asked here boils down to, is the equation represented meant to represent 6/2 * (1+2), that is to say, a fraction (6/2) that is then multiplied by an integer (1+2) - or is it meant to *all* represent a *single* fraction, with 6 as the numerator and 2(1+2) as the denominator?
And to avoid this, is why we write our fractions properly.
@@drascin To avoid this, we never imply multiplication.
Every programming language will say that 6/2*(1+2)==9. I bet that, for languages thag support it, the obelus sign ÷ will be treated as equivalent to the forward slash /.
@@roadent217 I'm a dev myself, I'm aware - most programming languages follow a very strict parentheses then left to right parsing algorithm.
But when writing things down for people, it's very important to leave things clear and unambiguous because making the math equivalent of those magic eye posters is not clever, it's just annoying.
(Honestly, this maxim tends to apply to programming in many places too. Always write your code such that the next poor bastard who will have to work with it doesn't need to read your mind, people! And if you're doing complex boolean conditions put some parentheses and tree them up a bit to make them easier to parse!)
Wtf is PEMDAS?
@@AlexBarbu so its like bedmas then?
I just put the 6 under 2(2+1) and go from there
So like 2(2+1)/6? Cause That would be 1 which wouldn’t be right
@@Poop_lord2585 but if you put more parentheses/brackets to make (2(2+1)) wouldn't the outcome be the same?
@@riskvideos if you were to put brackets like 6/(2(2+1) then yeah It would be 1 but it’s 6/2(2+1) which that one bracket makes it different
@@Poop_lord2585 I'll take your word for it. I'm no expert on maths.
The core root of the problem comes solely from the "division symbol" being used instead of representing it as a fraction.
4÷2+2 could simultaneously means 4/(2+2), which would equal 1, due to "2+2" being the denominator in that fraction, or it could mean (4/2)+2 which would equal 4.
neither answer is technically wrong, because the question itself is vague.
"John met Jimmy. He was hungry."
Who was hungry?
Same thing really. Can't guess unless you get some more info, which here for this math equation, would be parentheses.
It was never really about PEMDAS indeed
This question is flawed, some people use the old method while others use the new method
TBF the equation is written wrong the correct equation is
6/(2(2+1))=1
BUT regardless even without the parenthesis, you should still follow PEMDAS rule.
It could also be 6/2*(2+1) = 9
Funny how the one in the thumbnail is 1 either way, (6÷6 or 3÷3)
bait?
WTF is "New Math?" A new way of teaching is fine, but 2+2=4...ALWAYS. Nothing New about that.
1
There is only one correct answer and you will only get it if you had to take calculus and physics. You solve it as it is written, the intent of how it was written is irrelevant. A division is like this x/y and they drill this into your skull hard, it still baffles me schools say there's multiple answers.
You seem exactly the kind of person that likes to fight over the answer lmao
"the intent of how it was written is irrelevant" This mentality makes no sense in any real world application, and furthermore makes no sense within the concepts of higher math. Also in a programming context, the answer is probably, but not definitely, 9, depending on the language being used.
There are multiple conventions that can be followed. You are possibly correct in implying that the person who wrote the expression is wrong, but if you were given this expression with no context and had to solve it, you can't just assume that is the case.
Incorrect. You evaluate division and multiplication with equal precedence, from left to right. The correct answer is 9.
6 / 2 * (1 + 2) = 6 / 2 * 3 = 3 * 3 = 9
Precedence is actually defined by spacing. If you write the symbols closer together, they have higher precedence.
2 × 4+10 = 28
2×4 + 10 = 18
Jesus, what? No it's not, don't do that.
Lol
What a devious comment.
Please tell me you're not serious
There is, of course, some debate as to how operators with space only on one side should be treated. Some authors simply treat them as lower precedence, but as a compromise, they can be considered to be between no-space and full-space operators.
Multiplication and division are left-associative, unless the terms are written together, like "ax²". Then it's right-associative.
Math is the worst subject ong addition,subtraction,multiplication,and division are honestly the only things that are really used in everyday life the rest is goofy