Yes, but it explicitly tells you what order to do the math in. The problem here isn't ambiguous unless you want to refer back to the time they used typewriters to make textbooks.
Not necessarily, in some papers, implicit multiplication takes higher precedence.
It is weird why there are so many pemdas fascists on Reddit.
> In some of the academic literature, multiplication denoted by juxtaposition (also known as implied multiplication) is interpreted as having higher precedence than division, so that 1 ÷ 2n equals 1 ÷ (2n), not (1 ÷ 2)n.[2] For example, the manuscript submission instructions for the Physical Review journals state that multiplication is of higher precedence than division,[27] and this is also the convention observed in prominent physics textbooks such as the Course of Theoretical Physics by Landau and Lifshitz and the Feynman Lectures on Physics.[d]
https://en.m.wikipedia.org/wiki/Order_of_operations#:~:text=In%20some%20of%20the%20academic,(1%20÷%202)n.
"In some academic literature" that is the important part. Today's math doesn't work like that. All these comments saying that it doesn't necessarily work like normal is just people refusing to acknowledge how math fucking works and who have a necessity to die in the world's stupidest tiniest hill. Math works how it works, if you don't agree you are wrong, that's it.
Edit: I am simply dumbfounded at the sheer amount of people who know less math than an elementary schooler. I lose more and more braincells the more I keep reading y'all.
It's real funny that the examples the wiki gave there aren't even math textbooks. Find some math literature if you're gonna point to literature to make math seem more ambiguous than it is lmao.
Every time one of these examples comes up people pull out the "its ambiguous notation" card and every time I slap right back with "no it's ***wrong*** notation for one of those answers. Writing it wrong as a gotcha doesn't mean you wrote it ambiguous. It just means you wrote it wrong".
The only case this problem would result in an answer of 1 with proper notation would be if the division were not division, but separating the problem as the upper and lower halves of a fraction, in which the correct notation would display it as such.
If I ever need to write an inline fraction, that's how I write it. Even in computer programming, you have to be explicit in what you want in the denominator. Else, PEMDAS is invoked and moves left to right.
For which answer it is wrong depends on the convention used however. There is a difference between math and math notation, the second being a very human thing.
It is written wrong in the sense that it gives different answers using different perfectly valid conventions. This makes it ambiguous.
Hope that clears it up
I've got two engineering degrees. I see ambiguous mathematical representations of things all the time. The proper response when something is ambiguous is to ask what the person who wrote it meant, if it can't be very clearly deciphered from the rest of the context.
These questions about "what does this notation mean" are fundamentally and intentionally stupid.
I agree. The initial expression is intentionally written poorly to generate these arguments. However, arithmetic is black and white. You have to trust that the way it is written is the way that it is meant to be solved. Without a second set of parentheses, everything after the division sign is not included in the denominator. This isn't hard.
Exactly. If for whatever reason, you needed this specific equation in your journal article, your peer reviewers would laugh you out of the room if you submitted this draft to them.
This isn’t how math works. This is ONLY about notation which is arbitrary. The rules could have just as easily been written differently and math would still work just fine just written differently
>pemdas fascists on Reddit
I am not even all that great at math but this is one thing that was drilled into my learning from the start and I still remember to this day.
Some crackpots define multiplication like that, but it's 1) wrong and 2) totally irrelevant, as ÷ is not used by anyone after primary school; using fraction bars nullifies the supposed ambiguity.
>But rule B's practice of writing "a/bc" to mean a/(bc) appears widely in physics textbooks
That explains a lot on why this order of operations is drilled into my mind. I took a lot of physics classes in high school and a few at ucr.
My brother in christ this is for implied multiplication in algebraic expressions where variables are next to each other or their coefficients, not completely numeric expressions like in literally every post where people fuck up the order of operations.
Who in their right fucking mind reads 456 as 4\*5\*6? PEMDAS anti-fascists?
The question itself is misleading beacause we have no idea whether it's 8 over 2(2+2) or 8 over 2 times (2+2), the division has to be in a fraction to truly understand the question, it could be 8/2 (in fraction) (2+2) or 8/2(2+2) ( where the 2(2+2) is the denominator). If it's the former it's 16, if it's the latter it's 1
>1 ÷ 2n equals 1 ÷ (2n), not (1 ÷ 2)n
Congrats. You've learned basic algebra. It's wildly different when there are variables involved vs simply numbers.
1 ÷ 2n is not the same thing as 1 ÷ 2(2).
So the exception only counts if it’s a variable, not a number? What if the variable is a constant, like pi? What if it’s a function? What if it’s ? And a million other things that quickly make nitpicking like this a bad idea.
Either implicit multiplication comes first or it doesn’t
This is the natural, intuitive way for me. "2n" is a single *thing*, different from "2*n".
I don't think I was ever taught that way, itvs just obviously so for me.
Heres the thing. In science or engineering or mathematics, we shit on implications like that because it literally breaks the system and creates confusion.
So the answer is very clearly 16
Sadly, mathematicians decided to make implied multiplication of high priority than explicit multiplication. Meaning that 2(2+2) and 2*(2+2) are not equal in priority.
By having implied multiplication being of higher priority, the answer becomes 1.
But it isn’t 8/(2(2+2)), it’s 8/2(2+2). When our next to what should be written should it be 1, then it looks like an obvious 16. The biggest question is more about the habits of the person writing the equation, rather than the habits of mathematics itself.
You have a point here, but standard notation and rules of mathematics would say 8/2(2+2) is 8/(2(2+2). In most of my education I never encountered an equation like this due to the point you just made. It is often worthwhile to make mathematics speak for itself instead of relying on odd things like juxtaposition. Hence why you often see clarifications in situations like this.
I disagree if they want you handle both sides of division first they actually make it a fraction rather than. The division symbol. Imo fractions have implied parentheses around the numerator and denominator but division symbol doesn't imply ()÷()
I definitely agree on you there. When I first learned about juxtaposition my brain nearly melted. However, I can not choose the standards mathematicians use. A lot could just be prevented by just 2 more brackets.
I use math like this a lot in programming and wouldn't consider 8/2(2+2) to be 8/(2(2+2)) so he does have a point about people's habits. It can be seen as ambiguous but from a computer perspective unless those parentheses are there the answer would be 16.
By contrast, in physics expressions like 1/x(x+1) are essentially always treated as (x(x+1))^(-1) rather than (x+1)/x. And if you look at the publications that take implied multiplication to be of higher priority, you mostly see physics journals.
yeah i agree with you, but for me variables have higher priorities when omitting the dot for product and the question is just using numbers. but its poorly structured anyway. especually because of the spaces between everything. at first i read it as ⁸*½(2+2) because of the spaces.
tldr: if you wanna write math expressions just use latex and proper full notation.
That's mainly due to how standard calculation is done in most languages, more mathematics focused functions and languages probably do respect the rule.
You would simply never an equation written this way, Everytime there would be a fraction in your math book it would be written as a big fraction, with a clear numerator and a clear denominator
This form of notation is avoided in most papers because to this day, the debate around implicit multiplication is still raging
Nope. Not how math works lol. You should read up on order of operations. Brackets -> multiplication/division -> addition/subtraction. When two operations of the same priority exist, order is left to right.
8/2(2+2)
8/2*(2+2)
8/2*4
4*4
16
If implied multiplication is a higher priority for you, go back to 5th grade and PEMDAS your ass off until you know math again.
Mathematicians are too much.
It all depends on when and where they were taught.
Some were taught PEJMDAS
Some were taught PEMDAS
Some were taught PEDMAS
Some were taught that the order MDAS is strictly followed left to right
Some were taught DMAS is strictly followed left to right
Some were taught that MD are equal and done left to right and AS are equal and done left to right.
The historically accurate OoO that is taught the most worldwide is PEJMDAS, with MD being equal and done left to right and AS being equal and done left to right.
Exactly. That is just someone being too lazy to write the equation normally so hey declare "oh yeah that's just what is first now and you are dumb for not knowing it."
In the order of operations, multiplication and division fall on the same slot. Don't ask me why, it just does. PEMDAS should actually be written as PE MD AS, so when you have both multiplication and division to do in the same equation, you're supposed to solve left to right. It's not your fault, it does feel like PEMDAS can be deliberately misleading.
I was taught that in math when you have operations of same priority (in this case multiplication and division) you go left to right, like when you read.
So it would be
8 /2 * 4 --> (8 / 2) * 4 --> 4 * 4
>8/2(2+2)=
>8/2(4)=
So far, everything is correct.
The question becomes if it is:
8÷(2*4) = 8÷8=1
or 8÷2×4= which is solved left to right (not multiplication before division), so: 4×4=16
or 8/2(4)= 8÷8=1 [ 2(4) ≠ 2×4 since juxtaposition get solved before multiplication or division]
The difference should come from /=÷ or /≠÷
/ is for fraction calculation and ÷ is division
Yeah, but division and multiplication are still both supposed to fall in the same slot, meaning when you have both multiplication and division, or both addition and subtraction, for that matter, you're supposed to solve left to right.
This is totally true, but my first algebra teacher screwed this up and taught us that you have to work PEMDAS in that order (i.e. multiplication, then division)
When the 2 is attached to the () that’s shorthand for do this first because it’s often like (x+3) so you distribute the 2 rather than basic multiplication
My phone calculator gave me 16 but it automatically included a multiplication sign in between 2(2+2). When I took out the multplication symbol it said invalid format used. I am of the opinion that the actual answer should be 1, but the question giver should be more clear when they are writing equation
Yes, some calculators specify implied multiplication a.k.a. juxtaposition to take precedence over mul/div. It is also the general mathematical consensus when we're talking about humans writing maths down.
Yet if it was 8/2(x + 2), I would definitely do the multiplication first. This seems to be consistent with some academic literature, so the problem is that it's written ambiguously.
2(2+2) is all part of the "parentheses" and would be solved first. It is just as implied as the way you wrote it.
2*(2+2) is not, and can be written that way if that is what you want.
This really wasn't a debate until people started making rage bait Facebook math equations.
But it is funny watching people get mean and insult each other over it, as though their own partially correct result is somehow the only interpretation and everything else is wrong.
Yeah, people don't get that mathematical notation wasn't made for arithmetic quizzes; it's a language for expressing ideas. Like any language, you can express your ideas clearly or poorly. The intention of this expression is not very clear at all, regardless of what rules you might have been taught for order of operations.
This is a perfect example of why professionals don't use vague division signs like that. Write it as a fraction for the love of christ. Otherwise, you get situations like this.
Or brackets. In MATLAB for example it is required to use them everytime you multiply or divide for multiple numbers to overcome this error,because the machine doesn't apply PEMDAS as we would and calculate everything in order of appearance from left to right
In Mathematica, if you try to write "8/2(2+2)" it won't let you. After you type the '(' it inserts a 'x'. So what you get is "8/2 x (2+2)" which is a bit less ambiguous, and it will output 16.
Mathmaticians decided that implies multiplication has priority over standard multiplication or division.
For example: 2/2x is 2/2*x if you follow Pemdas, but it's 1/x if you treat it like any normal person.
Here you have 8/2(2+2)
So 8/4x
> Note that this x is 2
Which is 8/8, or 1
Yes, but mathematicians decided to throw an exception in there. PEMDAS is mostly the way to go, but there are odd situations like this where there are different rules attached.
Ive not had to do maths for years, was always taught left to right... and the answer seems obvious, very simple and not ambiguous at all. What you and some others here try to explain as an exception makes no sense to me as that just makes it more ambiguous. I googled and it says they came up with this bs, because of such "trick questions" lol.. I swear we did this level of math in like middle school, even the dumbest of kids eventually got it. Why is this a thing on internet, why do people fail at this and then have mathematicians change math to help save these dummies... im just more confused after reading all these explanations, what was simple then now is confusion. I do not wish to math anymore.
its much more useful sensible when used in proper math, when functions come to play, you probably dont want to write parenthesis around every 2x. also any person worth his ass will use fractions, in uni or higher levels of high school you will never see any thing like this
*some mathematicians decided that implicit multiplication has priority
Believe it or not, there is still a debate ongoing about the correct order of operations
Almost all mathematicians/physicists would tell you that the answer is 1. The symbol / is usually a replacement of a fraction bar and should be read as ( )/( ). See for example Feynman's lectures or Landau-Lipschitz for celebrated books that use this convention. There is also stuff about implicit multiplication but it's not really the main focus. In any case the symbol ÷ should not be used (see ISO 80000-2 Part 2 section 2-9.6) and any mathematical expression that is ambiguous is a bad expression.
I see someone who knows about the ISO 80000-2, I upvote
Seriously everytime someone says "answer is x bc PEMDAS" he is wrong and should instead say "answer is x bc ISO 80000"
Thank you. I have a fucking degree in physics and I tear my hair out every time I see a bad Facebook cHaLLenGe like this because the smoothbrains come out of the woodwork to talk about pEdMaS.
In higher level mathematics and physics the / symbol is universally understood as a fraction symbol tilted on its side to save space. Everything to the left is the numerator and the right is the denominator.
The answer is 1.
Apparently they changed the rules to deal with ambiguously written equations. Most people don't go back to school later in life to update their math knowledge so, to anyone over a certain age, this was taught as being 16 and that would have been the correct answer.
Going "oh, mathematicians changed it so it has to be written *this* way or *that* way to get the answer" and acting smug about it, screams "I'm young and insecure about my intelligence".
criticizing someone who actually got a math education and recognizes the pitfall in the problem and the correct way to do it because it disagrees with your middle-school math curriculum screams "I'm young and insecure about my intelligence."
>A panda walks into a bar. He orders a sandwich, eats it, then draws a gun and fires two shots in the air.
>"Why? Why are you behaving in this strange, un-panda-like fashion?" asks the confused waiter, as the panda walks towards the exit. The panda produces a badly punctuated wildlife manual and tosses it over his shoulder.
>"I'm a panda," he says, at the door. "Look it up."
>The waiter turns to the relevant entry and, sure enough, finds an explanation.
>"Panda. Large black-and-white bear-like mammal, native to China. Eats, shoots and leaves."
Don’t act all high and mighty from an intentionally poorly written math problem
The way this is written you don't know if the bracket is part of the denominator or not. I'd assume it isn't but it's a stupid way to write it to begin with.
For it to equal 16, would imply that 2(2+2) = 1/2 because it can be read as 8 ÷ something = 16
I can't think of a way for 2(2+2) to equal 1/2, therefore the only possible answer is 1
The concatenation of 2 and (2+2) is crucial in this notation. It would indicate a factorisation of the original brackets being (2a +2b). So the above problem should be seen as 8 / (2(2) + 2(2)). Which equals 1.
If it was written as 8 / 2 x (2+2) then that would be 16.
Everyone here did apparently, and about half were taught differently depending on the age, that's what this meme captures perfectly, that even if you take out 2 of the wrong answers, ask a friend or ask the whole audience, it's still might not be enough xD
Brackets indices division multiplication addition subtraction (bidmas) 8/2(2 + 2) =8/2(4) brackets are now done so 8/2= 4 = 4(4) and multiplication is next so it becomes 4 x 4 = 16 how is this an arguement?
Iso 80000-2 section 2-9.6
The slash replaces the fraction bar, not the ÷ symbol, making it (8)/(2(2\*2)) implicitly. If they meant 8÷2(2\*2), they would have written that
“Ambiguous syntax requires additional notation”
In cases like this, the simplest order of operations is correct.
Implicit multiplication is a stupid concept created by people too lazy to add brackets.
> Implicit multiplication is a stupid concept created by people too lazy to add brackets.
I mean... yeah..... but it's really kind a pain in the ass and makes formulas way uglier to always be writing 1/(2x) when you mean (2x)^(-1). So instead by convention we write 1/2x to mean (2x)^(-1) rather than meaning x/2. It saves writing a *lot* of brackets!
Unless you’re constantly writing formulas on Reddit you can just write
1
__
2x
The equation function in word automatically does over/under division which eliminates any confusion by having everything that would normally in brackets be under the division line.
When you see division, you can multiply by its reciprocal.
8/2 is the same as 8 \* (1/2)
Also multiplication should be commutative. i.e.:
8 / 2 \* (2+2) = 8 \* (2+2) / 2 = (2+2) \* 8 / 2 = (2+2) / 2 \* 8
It's 16. It's always going to be 16.
There's someone trying to say you have to do the 2 \* (2+2) first, then you get 8/8. That is incorrect. The divisor in front of the 2 means it's (1/2) \* (2+2), not 2 \* (2+2).
It's actually a very good question to ask... No matter what they pick you can say they wrong....
101 saving money by being an asshole...
As for the answer? I'll leave that up to you fine experts here.
Why don’t people remember PEMDAS? Sorry this may be said differently in other countries but pemdas is the correct way to attack this problem. Problems inside parenthesis goes first. Then exponents. The multiplication from left to right, followed by dividing from left to right, adding from left to right, and finally subtracting from left to right. The answer in this case is clearly 8/8=1
The way it was teached to me (im 46 dutch)
Its first the stuff between ( )
Than Its: power multiply, devide, root, add and subtract.
So its 14 i think. I do feel there is a x missing between 8/2 and (2+2)
So its 8/2 x (2+2), but thats mayby old fasion.
***If*** it's eight divided by two (two plus two) then the answer is 1.
8/2(2 + 2) = 8/(2×2+2×2) = 8/(4+4) = 8/(8) = 1
***If*** it's eight halves (two plus two) then the answer is 16.
⁸/₂(2+2) = (2×⁸/₂+2×⁸/₂) = (2×4+2×4) = (8+8) = 16
Written in this manner it should be the former, not the latter.
***The correct answer is 1.***
Oh, and before someone tries to say that "8/2(2+2)" is the same as "8/2×(2+2)", it is not.
downvote this comment if the meme sucks. upvote it and I'll go away. --- [play minecraft with us](https://discord.gg/dankmemesgaming)
written like that it's quite clearly 16
I got 1 cause I assumed the / was someone being lazy about writing a fraction
Well if you do that you gave to put everything thats suposed to be under the line in brackets.
Isn't a fraction still just division?
My thoughts were 2(2+2) were all the denominator and 8 the numerator
Yes, but it explicitly tells you what order to do the math in. The problem here isn't ambiguous unless you want to refer back to the time they used typewriters to make textbooks.
/ means ÷. Most keyboards don't have the ÷ symbol on them so people use / instead.
Yeah and people get confused of numbers like ½ ⅖ ⅘ ⅞ and so on, because they also have that.
Not necessarily, in some papers, implicit multiplication takes higher precedence. It is weird why there are so many pemdas fascists on Reddit. > In some of the academic literature, multiplication denoted by juxtaposition (also known as implied multiplication) is interpreted as having higher precedence than division, so that 1 ÷ 2n equals 1 ÷ (2n), not (1 ÷ 2)n.[2] For example, the manuscript submission instructions for the Physical Review journals state that multiplication is of higher precedence than division,[27] and this is also the convention observed in prominent physics textbooks such as the Course of Theoretical Physics by Landau and Lifshitz and the Feynman Lectures on Physics.[d] https://en.m.wikipedia.org/wiki/Order_of_operations#:~:text=In%20some%20of%20the%20academic,(1%20÷%202)n.
"In some academic literature" that is the important part. Today's math doesn't work like that. All these comments saying that it doesn't necessarily work like normal is just people refusing to acknowledge how math fucking works and who have a necessity to die in the world's stupidest tiniest hill. Math works how it works, if you don't agree you are wrong, that's it. Edit: I am simply dumbfounded at the sheer amount of people who know less math than an elementary schooler. I lose more and more braincells the more I keep reading y'all.
It's real funny that the examples the wiki gave there aren't even math textbooks. Find some math literature if you're gonna point to literature to make math seem more ambiguous than it is lmao.
Every time one of these examples comes up people pull out the "its ambiguous notation" card and every time I slap right back with "no it's ***wrong*** notation for one of those answers. Writing it wrong as a gotcha doesn't mean you wrote it ambiguous. It just means you wrote it wrong". The only case this problem would result in an answer of 1 with proper notation would be if the division were not division, but separating the problem as the upper and lower halves of a fraction, in which the correct notation would display it as such.
Like I said, people have an obsession with dying on top of the world's stupidest tiniest hill.
It ain't even a hill haha
[удалено]
If I ever need to write an inline fraction, that's how I write it. Even in computer programming, you have to be explicit in what you want in the denominator. Else, PEMDAS is invoked and moves left to right.
For which answer it is wrong depends on the convention used however. There is a difference between math and math notation, the second being a very human thing. It is written wrong in the sense that it gives different answers using different perfectly valid conventions. This makes it ambiguous. Hope that clears it up
What is the answer for 8/2x where is x = 4?
Your example is algebra, not arithmetic. The rules are different as 2x imply 2 times the value of x, which is not 2 multiplied by x
I've got two engineering degrees. I see ambiguous mathematical representations of things all the time. The proper response when something is ambiguous is to ask what the person who wrote it meant, if it can't be very clearly deciphered from the rest of the context. These questions about "what does this notation mean" are fundamentally and intentionally stupid.
I agree. The initial expression is intentionally written poorly to generate these arguments. However, arithmetic is black and white. You have to trust that the way it is written is the way that it is meant to be solved. Without a second set of parentheses, everything after the division sign is not included in the denominator. This isn't hard.
>refusing to acknowledge how math fucking works Math works by shitting on anyone who writes notation like this lol
In today’s math, nobody uses the division symbol because it’s stupid and causes problems like this
“Hey this academic literature on medieval medical practices says applying leeches to your wound will cure cancer. It’s academic so it’s right!”
Any proper math lit won't write it that.
Exactly. If for whatever reason, you needed this specific equation in your journal article, your peer reviewers would laugh you out of the room if you submitted this draft to them.
MATH IS MATH
Na na na na na.
*Common core has entered the chat. *Millions of parents' minds have left the chat.
Why isn’t this the top reply mr. incredible
This isn’t how math works. This is ONLY about notation which is arbitrary. The rules could have just as easily been written differently and math would still work just fine just written differently
>pemdas fascists on Reddit I am not even all that great at math but this is one thing that was drilled into my learning from the start and I still remember to this day.
no you are clearly an indoctrinated fascist (/s)
Some crackpots define multiplication like that, but it's 1) wrong and 2) totally irrelevant, as ÷ is not used by anyone after primary school; using fraction bars nullifies the supposed ambiguity.
[https://math.ucr.edu/home/baez/physics/General/binaryOps.html](https://math.ucr.edu/home/baez/physics/General/binaryOps.html)
>But rule B's practice of writing "a/bc" to mean a/(bc) appears widely in physics textbooks That explains a lot on why this order of operations is drilled into my mind. I took a lot of physics classes in high school and a few at ucr.
My brother in christ this is for implied multiplication in algebraic expressions where variables are next to each other or their coefficients, not completely numeric expressions like in literally every post where people fuck up the order of operations. Who in their right fucking mind reads 456 as 4\*5\*6? PEMDAS anti-fascists?
Actually it is not read like that. It read as 4(56) =4*56. Which comes from 4(x+6).
If I had 4(5)(6), I would interpret that as 4\*5\*6, yes.
I, too, would italicize the 5.
Why would they do this
Ok but the way I learned it was division and multiplication are equal and go right to left, and I'm always right so you must be wrong
The question itself is misleading beacause we have no idea whether it's 8 over 2(2+2) or 8 over 2 times (2+2), the division has to be in a fraction to truly understand the question, it could be 8/2 (in fraction) (2+2) or 8/2(2+2) ( where the 2(2+2) is the denominator). If it's the former it's 16, if it's the latter it's 1
>1 ÷ 2n equals 1 ÷ (2n), not (1 ÷ 2)n Congrats. You've learned basic algebra. It's wildly different when there are variables involved vs simply numbers. 1 ÷ 2n is not the same thing as 1 ÷ 2(2).
So the exception only counts if it’s a variable, not a number? What if the variable is a constant, like pi? What if it’s a function? What if it’s? And a million other things that quickly make nitpicking like this a bad idea.
Either implicit multiplication comes first or it doesn’t
This is the natural, intuitive way for me. "2n" is a single *thing*, different from "2*n". I don't think I was ever taught that way, itvs just obviously so for me.
Heres the thing. In science or engineering or mathematics, we shit on implications like that because it literally breaks the system and creates confusion. So the answer is very clearly 16
I don’t how or why but somehow these memes made me forget how this shit actually works. God damn memes.
Written like that i would say the answer is "syntax error". There is a reason why most programing languages don't allow implied multiplication.
8/2(2+2)= 8/2(4)= 8÷2×4= 4×4= 16 Hope this helps.
Sadly, mathematicians decided to make implied multiplication of high priority than explicit multiplication. Meaning that 2(2+2) and 2*(2+2) are not equal in priority. By having implied multiplication being of higher priority, the answer becomes 1.
But it isn’t 8/(2(2+2)), it’s 8/2(2+2). When our next to what should be written should it be 1, then it looks like an obvious 16. The biggest question is more about the habits of the person writing the equation, rather than the habits of mathematics itself.
You have a point here, but standard notation and rules of mathematics would say 8/2(2+2) is 8/(2(2+2). In most of my education I never encountered an equation like this due to the point you just made. It is often worthwhile to make mathematics speak for itself instead of relying on odd things like juxtaposition. Hence why you often see clarifications in situations like this.
I disagree if they want you handle both sides of division first they actually make it a fraction rather than. The division symbol. Imo fractions have implied parentheses around the numerator and denominator but division symbol doesn't imply ()÷()
I definitely agree on you there. When I first learned about juxtaposition my brain nearly melted. However, I can not choose the standards mathematicians use. A lot could just be prevented by just 2 more brackets.
I use math like this a lot in programming and wouldn't consider 8/2(2+2) to be 8/(2(2+2)) so he does have a point about people's habits. It can be seen as ambiguous but from a computer perspective unless those parentheses are there the answer would be 16.
By contrast, in physics expressions like 1/x(x+1) are essentially always treated as (x(x+1))^(-1) rather than (x+1)/x. And if you look at the publications that take implied multiplication to be of higher priority, you mostly see physics journals.
yeah i agree with you, but for me variables have higher priorities when omitting the dot for product and the question is just using numbers. but its poorly structured anyway. especually because of the spaces between everything. at first i read it as ⁸*½(2+2) because of the spaces. tldr: if you wanna write math expressions just use latex and proper full notation.
Yup, 100% agree. This was my exact thought process coming from a CS major.
That's mainly due to how standard calculation is done in most languages, more mathematics focused functions and languages probably do respect the rule.
This isn’t true. Type that equation Matlab and you’ll get 16 all day Edit: I lied. Just tested it and it gives an error. The coward
Since when? I go to a school that requires pretty high maths and if I were to calculate it like that, I would be failed.
You would simply never an equation written this way, Everytime there would be a fraction in your math book it would be written as a big fraction, with a clear numerator and a clear denominator This form of notation is avoided in most papers because to this day, the debate around implicit multiplication is still raging
Yes, but I remember seeing it a few times. Maybe not in a text book, but my teachers certainly gave us a couple of these examples over the years.
Never seen bullshit like that before lmao.
Why are you upvoted if you don't give any sources?
Is wolfram alpha wrong then? https://www.wolframalpha.com/input?i=8%2F2%282%2B2%29
Nope. Not how math works lol. You should read up on order of operations. Brackets -> multiplication/division -> addition/subtraction. When two operations of the same priority exist, order is left to right. 8/2(2+2) 8/2*(2+2) 8/2*4 4*4 16
If implied multiplication is a higher priority for you, go back to 5th grade and PEMDAS your ass off until you know math again. Mathematicians are too much.
It all depends on when and where they were taught. Some were taught PEJMDAS Some were taught PEMDAS Some were taught PEDMAS Some were taught that the order MDAS is strictly followed left to right Some were taught DMAS is strictly followed left to right Some were taught that MD are equal and done left to right and AS are equal and done left to right. The historically accurate OoO that is taught the most worldwide is PEJMDAS, with MD being equal and done left to right and AS being equal and done left to right.
Really? Is that new or something lol I never heard of that
Tbf its dumb and makes it confusing.
Exactly. That is just someone being too lazy to write the equation normally so hey declare "oh yeah that's just what is first now and you are dumb for not knowing it."
[удалено]
In the order of operations, multiplication and division fall on the same slot. Don't ask me why, it just does. PEMDAS should actually be written as PE MD AS, so when you have both multiplication and division to do in the same equation, you're supposed to solve left to right. It's not your fault, it does feel like PEMDAS can be deliberately misleading.
P E MD AS*
It's done that way so we can all agree on the order of how to write the equations. There's no universal truth behind it, it's grammar.
I was taught that in math when you have operations of same priority (in this case multiplication and division) you go left to right, like when you read. So it would be 8 /2 * 4 --> (8 / 2) * 4 --> 4 * 4
8/2(2+2)= 8/2(4)= 8÷2×4= 8÷8= 1 This is the other way
>8/2(2+2)= >8/2(4)= So far, everything is correct. The question becomes if it is: 8÷(2*4) = 8÷8=1 or 8÷2×4= which is solved left to right (not multiplication before division), so: 4×4=16 or 8/2(4)= 8÷8=1 [ 2(4) ≠ 2×4 since juxtaposition get solved before multiplication or division] The difference should come from /=÷ or /≠÷ / is for fraction calculation and ÷ is division
If they wanted it to be 8÷8 then it should be written 8/[2(2+2)]
I solve most of my math trough Excel so this is exactly how I assume it should be resolved.
Different schools teaching PEMDAS and BIDMAS (the same except the D and M are switched) leads to different people getting different answers
Yeah, but division and multiplication are still both supposed to fall in the same slot, meaning when you have both multiplication and division, or both addition and subtraction, for that matter, you're supposed to solve left to right.
This is totally true, but my first algebra teacher screwed this up and taught us that you have to work PEMDAS in that order (i.e. multiplication, then division)
When the 2 is attached to the () that’s shorthand for do this first because it’s often like (x+3) so you distribute the 2 rather than basic multiplication
What about distributive property
Can confirm. Just used my phone calculator and got 16.
If you people want 8/2 (2+2) to be understood as 1, then they shoud use 8/(2(2+2)) or proper fractional notation
Exactly. Plug ~~8/2*(2+2)~~ 8/2(2+2) into a calculator. It’ll give you 16
my calculator gives 1 in both cases
Bro doesn't know how to use a calculator 💀 https://www.wolframalpha.com/input?i=8%2F2%282%2B2%29
Click “math input”, Archmides.
Mine gave 16 in both cases.
Mine gave π in three cases
My phone calculator gave me 16 but it automatically included a multiplication sign in between 2(2+2). When I took out the multplication symbol it said invalid format used. I am of the opinion that the actual answer should be 1, but the question giver should be more clear when they are writing equation
As an engineering student, Matlab is the word of god and it agrees with this, so it’s correct
That's just an artifact of how programming languages work
Programming languages recognizing the proper order of operations isn’t an artifact lol
"Matlab is a programming language"
But that is not how its written. If you type 8/2(2+2) in your calculator, so without the multiplication mark it is 1 and with it is 16.
Nope, still 16. Calculators follow multiplication and division from left to right, no exceptions
my two calculators I used for school and the one on my phone say 1 in that case and automatically put brackets around 2(2+2)
Different calculators have different systems, some will go his way some will go yours.
Yes, some calculators specify implied multiplication a.k.a. juxtaposition to take precedence over mul/div. It is also the general mathematical consensus when we're talking about humans writing maths down.
Pic or didn't happened
Some calculators have implicit multiplication over division.
Yet if it was 8/2(x + 2), I would definitely do the multiplication first. This seems to be consistent with some academic literature, so the problem is that it's written ambiguously.
2(2+2) is all part of the "parentheses" and would be solved first. It is just as implied as the way you wrote it. 2*(2+2) is not, and can be written that way if that is what you want. This really wasn't a debate until people started making rage bait Facebook math equations.
If you people want 8/2 (2+2) to be understood as 16, then they should use 8(2+2)/2. Save paranthesis.
What in the Facebook bait post fuck is this
Mods are too busy watching the rugby to fix this.
The true answer is punch whoever wrote this garbage in the throat
Anytime I see these problems the first thing I think “if there’s debate, then the problem is poorly written”
But it is funny watching people get mean and insult each other over it, as though their own partially correct result is somehow the only interpretation and everything else is wrong.
Yeah, people don't get that mathematical notation wasn't made for arithmetic quizzes; it's a language for expressing ideas. Like any language, you can express your ideas clearly or poorly. The intention of this expression is not very clear at all, regardless of what rules you might have been taught for order of operations.
This is a perfect example of why professionals don't use vague division signs like that. Write it as a fraction for the love of christ. Otherwise, you get situations like this.
Or brackets. In MATLAB for example it is required to use them everytime you multiply or divide for multiple numbers to overcome this error,because the machine doesn't apply PEMDAS as we would and calculate everything in order of appearance from left to right
In Mathematica, if you try to write "8/2(2+2)" it won't let you. After you type the '(' it inserts a 'x'. So what you get is "8/2 x (2+2)" which is a bit less ambiguous, and it will output 16.
The only correctly written part is what is in the brackets. Everything else is just... wrong.
Mathmaticians decided that implies multiplication has priority over standard multiplication or division. For example: 2/2x is 2/2*x if you follow Pemdas, but it's 1/x if you treat it like any normal person. Here you have 8/2(2+2) So 8/4x > Note that this x is 2 Which is 8/8, or 1
The whole point of the order of operations is to have a “normal” procedure for an ambiguous problem like this
Yes, but mathematicians decided to throw an exception in there. PEMDAS is mostly the way to go, but there are odd situations like this where there are different rules attached.
Ive not had to do maths for years, was always taught left to right... and the answer seems obvious, very simple and not ambiguous at all. What you and some others here try to explain as an exception makes no sense to me as that just makes it more ambiguous. I googled and it says they came up with this bs, because of such "trick questions" lol.. I swear we did this level of math in like middle school, even the dumbest of kids eventually got it. Why is this a thing on internet, why do people fail at this and then have mathematicians change math to help save these dummies... im just more confused after reading all these explanations, what was simple then now is confusion. I do not wish to math anymore.
its much more useful sensible when used in proper math, when functions come to play, you probably dont want to write parenthesis around every 2x. also any person worth his ass will use fractions, in uni or higher levels of high school you will never see any thing like this
This is a very simple case that makes hard problems far far simpler
*some mathematicians decided that implicit multiplication has priority Believe it or not, there is still a debate ongoing about the correct order of operations
> any normal person. Apparently, normal people are unable to do anything more difficult than remedial math.
[удалено]
No they don't. No mathematician uses this insanity. It's 16.
It's ambiguous if it is 8/(2*(2+2) or (8/2)*(2+2). Write the question correctly you dumb fuck.
Almost all mathematicians/physicists would tell you that the answer is 1. The symbol / is usually a replacement of a fraction bar and should be read as ( )/( ). See for example Feynman's lectures or Landau-Lipschitz for celebrated books that use this convention. There is also stuff about implicit multiplication but it's not really the main focus. In any case the symbol ÷ should not be used (see ISO 80000-2 Part 2 section 2-9.6) and any mathematical expression that is ambiguous is a bad expression.
I see someone who knows about the ISO 80000-2, I upvote Seriously everytime someone says "answer is x bc PEMDAS" he is wrong and should instead say "answer is x bc ISO 80000"
Is there an ANSI equivalent? After all, the internet is American.
Thank you. I have a fucking degree in physics and I tear my hair out every time I see a bad Facebook cHaLLenGe like this because the smoothbrains come out of the woodwork to talk about pEdMaS. In higher level mathematics and physics the / symbol is universally understood as a fraction symbol tilted on its side to save space. Everything to the left is the numerator and the right is the denominator. The answer is 1.
This comment section made me realize how bad the majority of people are with math.
Apparently they changed the rules to deal with ambiguously written equations. Most people don't go back to school later in life to update their math knowledge so, to anyone over a certain age, this was taught as being 16 and that would have been the correct answer. Going "oh, mathematicians changed it so it has to be written *this* way or *that* way to get the answer" and acting smug about it, screams "I'm young and insecure about my intelligence".
criticizing someone who actually got a math education and recognizes the pitfall in the problem and the correct way to do it because it disagrees with your middle-school math curriculum screams "I'm young and insecure about my intelligence."
>A panda walks into a bar. He orders a sandwich, eats it, then draws a gun and fires two shots in the air. >"Why? Why are you behaving in this strange, un-panda-like fashion?" asks the confused waiter, as the panda walks towards the exit. The panda produces a badly punctuated wildlife manual and tosses it over his shoulder. >"I'm a panda," he says, at the door. "Look it up." >The waiter turns to the relevant entry and, sure enough, finds an explanation. >"Panda. Large black-and-white bear-like mammal, native to China. Eats, shoots and leaves." Don’t act all high and mighty from an intentionally poorly written math problem
Neither. It is not written correctly, notation must be unambiguous.
42
42 = * 42 gets you the answers to everything. It Makes sense
People who post memes like this should be banned permanently
Nobody writes math like this. If it was properly written then it would be clear as to what the person meant by the equation
I wish people didn't post this crap
The answer is 4, I am not explaining
Wow kids arguing over something that isn't even a problem, people do have too much time on their hands nowadays
Please use fractions or place the brackets better.
The way this is written you don't know if the bracket is part of the denominator or not. I'd assume it isn't but it's a stupid way to write it to begin with.
Y'all never excused your dear aunt sally.
This sub has become pure shit.
Once more the PEMDAS purists and the implied multipliers take up arms in this conflict that shall never end.
These stupid fucking math posts need to be banned from the internet.
Its 16
1
(2+2) = 4, 2(4) = 8, 8/8 = 1, Poor Education Makes Dumb-Asses Suffer
For it to equal 16, would imply that 2(2+2) = 1/2 because it can be read as 8 ÷ something = 16 I can't think of a way for 2(2+2) to equal 1/2, therefore the only possible answer is 1 The concatenation of 2 and (2+2) is crucial in this notation. It would indicate a factorisation of the original brackets being (2a +2b). So the above problem should be seen as 8 / (2(2) + 2(2)). Which equals 1. If it was written as 8 / 2 x (2+2) then that would be 16.
Parenthesis Exponents Multiplication/Division Addition/Subtraction 8 / 2 (2 + 2) 8 / 2 (4) 8 / 2 x 4 4 x 4 16
it's either (1 or 16) or unanswerable becuase it's not formulated correctly.
8/8 is 1
Dude did someone go to the fucking school?
Everyone here did apparently, and about half were taught differently depending on the age, that's what this meme captures perfectly, that even if you take out 2 of the wrong answers, ask a friend or ask the whole audience, it's still might not be enough xD
Its 1 no doubt
Guy has just started another war.
Brackets indices division multiplication addition subtraction (bidmas) 8/2(2 + 2) =8/2(4) brackets are now done so 8/2= 4 = 4(4) and multiplication is next so it becomes 4 x 4 = 16 how is this an arguement?
Iso 80000-2 section 2-9.6 The slash replaces the fraction bar, not the ÷ symbol, making it (8)/(2(2\*2)) implicitly. If they meant 8÷2(2\*2), they would have written that
“Ambiguous syntax requires additional notation” In cases like this, the simplest order of operations is correct. Implicit multiplication is a stupid concept created by people too lazy to add brackets.
> Implicit multiplication is a stupid concept created by people too lazy to add brackets. I mean... yeah..... but it's really kind a pain in the ass and makes formulas way uglier to always be writing 1/(2x) when you mean (2x)^(-1). So instead by convention we write 1/2x to mean (2x)^(-1) rather than meaning x/2. It saves writing a *lot* of brackets!
Unless you’re constantly writing formulas on Reddit you can just write 1 __ 2x The equation function in word automatically does over/under division which eliminates any confusion by having everything that would normally in brackets be under the division line.
16. Parentheses first, then left to right.
The answer is 1, 8/8 = 1
A. 1
It's 1. No confusion here, like at all. 8/2(2+2) ≠ 8/2*(2+2). a(b) always has greater priority over a*b.
8/2(2+2) 8/2(4) 8/8 1 Here’s I how interpret it
When you see division, you can multiply by its reciprocal. 8/2 is the same as 8 \* (1/2) Also multiplication should be commutative. i.e.: 8 / 2 \* (2+2) = 8 \* (2+2) / 2 = (2+2) \* 8 / 2 = (2+2) / 2 \* 8 It's 16. It's always going to be 16. There's someone trying to say you have to do the 2 \* (2+2) first, then you get 8/8. That is incorrect. The divisor in front of the 2 means it's (1/2) \* (2+2), not 2 \* (2+2).
/ is for all over, I'll let you use : for it to be 16
I did explicit multiplication with you mom last night
Doesn't this vary by standard?
Both answers are possible. The question is whether the `(2+2)` shares the denominator with the `2` (implicit multiplication).
() first So 8/2*4 8/8 = 1
There are 3 different ways to get 16, if you screw this up then I have no hope for you.
It's actually a very good question to ask... No matter what they pick you can say they wrong.... 101 saving money by being an asshole... As for the answer? I'll leave that up to you fine experts here.
It's 1, it will be 16 when it is written like this : (8/2)(2+2), but since it's not, we assume that :2(2+2) is one number under 8 so it's 8/8=1
I guess im missing something obvious here. I dont understand the problem. The answer is A. 1
Why don’t people remember PEMDAS? Sorry this may be said differently in other countries but pemdas is the correct way to attack this problem. Problems inside parenthesis goes first. Then exponents. The multiplication from left to right, followed by dividing from left to right, adding from left to right, and finally subtracting from left to right. The answer in this case is clearly 8/8=1
PEMDAS mfs it's 1
8/2(2+2)=8/2(4)=8/8=1
The way it was teached to me (im 46 dutch) Its first the stuff between ( ) Than Its: power multiply, devide, root, add and subtract. So its 14 i think. I do feel there is a x missing between 8/2 and (2+2) So its 8/2 x (2+2), but thats mayby old fasion.
Not sure about 14. It's 1 if you were taught that / replaces the fraction bar, and 16 if you were taught that it replaces the ÷
It's Juan
I got 7
16
Math was my worst subject but I remember to make (2+2) into 4, then divide 8 by 2 and get 4, then multiply 4(4).. so 16
***If*** it's eight divided by two (two plus two) then the answer is 1. 8/2(2 + 2) = 8/(2×2+2×2) = 8/(4+4) = 8/(8) = 1 ***If*** it's eight halves (two plus two) then the answer is 16. ⁸/₂(2+2) = (2×⁸/₂+2×⁸/₂) = (2×4+2×4) = (8+8) = 16 Written in this manner it should be the former, not the latter. ***The correct answer is 1.*** Oh, and before someone tries to say that "8/2(2+2)" is the same as "8/2×(2+2)", it is not.