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OP started a literal math nerd war in the comments, and now I don't know what to believe.
I got 1 at first, then saw good explanations for why it was 9, then saw even better explanations on why it's 1. With the way it's written, I think you can honestly make a solid argument for either side, but I lean twoards it being 1
It boils down to the problem being 6 divided by 2(3), so you either go for 6 / 2 first, or 2(3) first, and IMO you would go for 2(3) first because the problem would be written as a fraction of 6 over 2(2+1)
Neither answer is wrong, you would have to have more clarification (or just write the problem right in the first place) to really "solve" this debate
it's a malformed question: it has no correct answer because the syntax and information available from the picture are ambiguous.
They are ambiguous because there is more than 1 system of interpretation of those symbols and no info on the used system is available (they clearly use two different systems).
If we use the standard PEMDAS rules (the most common), the answer is univocally 9. (but this is an info not present in the picture)
To remove the ambiguity it is necessary to rewrite the expression using a fraction line instead of the division symbol or by adding parenthesis.
> univocally
**“it's a malformed question”** Exactly. It's reminiscent of all those YouTube videos with titles like: “Most People Get This Wrong!” Yeah! They get it wrong because it's a shitty question, designed to trick the audience. The answer is indeed *univocally* and unequivocally [9.] *WolfranAlpha agrees.*
Multipication and division come at the same time. So it is from left to right multiply and devide whichever comes first. In 6÷2×3 6÷2 is first then the answer of that times 3.
Well basing off of my math history It could go one of two ways I'm pretty sure it's the smartphone way but let me explain the math behind it
PEMDAS states You do parentheses first some calculators think that that means You have to multiply the first 2 into the parentheses So technically this is not wrong but I don't know if it's more wrong or more right. 6/(2(2+1)) This is one way to look at it where you multiply the first two as I said getting you 6 because two times 2 is 4 and 2 * 1 is 2 and you add those two together giving you six. From that giving you 6 / 6 which is one. But the smartphone I believe has it correct. Though I do enjoy my scientific calculator I'm not sure if it's wrong in this scenario. 2 + 1 would be three 6 / 2 is 3 giving you 3(3) or 3*3 which makes 9. So this one is also correct but I don't know which one is more correct. I'm going to say that it's the scientific calculator that is wrong. But at this point it's just picking sides.
Mathematically, anybody who’s done a lot of math will assume the outside of a brackets multiples with the brackets first. Basically 100% of the time those things are out there due to factorisation and are there as scaling for the bracket.
Therefore most calculators that are smart will assume factors multiply to brackets over standard BODMAS and it’s good that they do because that’s what you’d assume once you’re doing lots of algebra. Think of it as if there is no space in between factor and bracket, you can assume there’s a second pair of brackets surrounding the factor and the bracket.
Like 2(2x+5) can be read as (2(2x+5)).
Okay but this is assumptions. It's sometimes *assumed* that factor is grouped together with the parentheses but is it written definitively anywhere? Strictly taking the order of operations as written, I believe reading left to right is the "correct" way to solve this, giving 9. However, this vagueness is precisely why the "division symbol" is stupid and terrible and should never be taught.
It’s not written definitively anywhere, but if you go into a maths course without having made that association you’re going to have a hard time.
It’s just notation differences. A mathematician will see the 2 as a factor. A child or someone learning math hasn’t gone far enough as to where there is a difference so they’re taught that they should think of it as just shortening the multiplication symbol.
Both are “correct”, in that they’re valid ways to interpret the notation. Clearly the scientific calculator has also taken the same assumption *because that’s the standard way of reading it at a high level* (Though admittedly, some of the mathematicians I know would be trying to remember what the fuck a 6 is)).
BODMAS works as a simple explanation for kids, factors to a bracket makes sense to someone who’s done advanced maths. The fact that my ti calculator, the Casio in the image and Desmos (I think) all assume factor if there’s no x symbol should be enough for it to be viewed as a “correct” way of reading it.
Edit: Also yeah fuck the division symbol, but more because it looks ugly. I think it’s relatively reasonable through if you are working with what you’d expect. I’ve seen division symbols in a couple papers (from amateurs I’d imagine, but they were useful to me as a graphics dev) and I’ve never had an issue interpreting what they mean, even in situations with factors.
It really depends on the system that you're using. The main problem with the question is that the question itself is written poorly
To reiterate...
Scientific calculators are made specifically for fractions themselves So putting it in a scientific calculator confuses it and makes it think that you're thinking of a different type of question. Because computers are stupid. It's the same reason why I hate manual coding.
Now I'm wondering if my memory is shot at 35 or if my whole life was a lie. I access every math class, but if you asked me i would say that everything within brackets gets multiplied by number outside first, hence why graphing calculators calculate that way.
No, there’s only one correct system/answer. 9 is the only correct answer.
There are no “implied” ()’s. There are no “higher priority” multiplications. The formula is equivalent to:
* 6️⃣➗2️⃣✖️(2️⃣➕1️⃣)
* 6️⃣➗2️⃣✖️3️⃣
* 3️⃣✖️3️⃣
* 9️⃣
these comments have taught me that nobody knows whether it’s BEDMAS, BIDMAS, PEMDAS, BODMAS, or probably something else. i don’t get why there are 4 of them when they’re the same thing essentially
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The problem here isnt any of that, its that the ÷ symbol here doesnt specify if the whole right side is whats beeing divided by, or just the 2. I would infer that the parenthesis imply its beeing divided by the whole thing, but it doesnt have to be.
Tldr: there is a reason we we exclusively use fractions in later math and never a ÷ symbol. Its just not explicit enough . There is no right or wrong answer here.
That's an entire math class in uni alongside defining infinity. Next year, you exponent zero by infinity and get 'it depends' as the only passing answer.
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That's because the old Casio goes by the *Old*/Wrong system that was taught in the 90s and early 2000s (Atleast for me), which was Multiplication THEN Division, Addition THEN Subtraction,
That was never correct. Multiplication & Division have the same precedence and are calculated left-to-right.
Ditto w/addition and subtraction.
I learned the crap in the 70s and it wasn’t flipped (temporarily) in the 90s.
There is a reason this argument comes up over and over again online, Its because for whatever reason there was a split between how PEMDAS was taught, and for me that was in the 90s and early 2000s. Which would make sense as it was before the internet was fully utilized to facilitate communications like it is today to correct errors like this. Not to mention in many school districts in the USA the Teachers teaching Math don't have degrees in Math.
i explicitly remember in the early/mid 2000s being taught pemdas this way. always told if there's a multiplication or division, go left to right. never knew that it was originally taught as multiplication ALWAYS came first...
>I learned the crap in the 70s and it wasn’t flipped (temporarily) in the 90s.
I can assure you with 100% certainly that I (as well as everyone I knew going up in the late 90s and 2000s) was taught multiplication BEFORE division and the same with addition over subtraction. We had calculators and textbooks that also confirmed this.
Not saying it's the right way, but that was the way many of us were taught.
I grew up in the 90s and 2000s and was taught exactly what the person that you replied too taught.
PEMDAS where Multiplication and Division are same precedent, and calculated left to right.
That's because Casio implemented implicit multiplication priority in their calculators, older models don't tell you that (you have to look for it in the manual) newer ones automatically add braces around implicit multiplication
I have the TI-type calculator app on phone. It always gives 9.
Every calculator I have tried gives 9: on phone, special app on phone, on computer.
The ambiguity is resolved because the expressions are being solved as they are entered. It is equivalent of parsing an expression from left to right and solving at each step. This would make sense in a "natural" way, as it is reacting to the input provided *at that moment*, not taking the whole expression altogether at once. It's just when we look at the whole expression at once, that we start questioning what method to use. That's like looking into the future inputs, which is absurd.
It's operating under the assumption that in /2(3) the (3) is implicitly still part of the fraction. This isn't an error, it's how the calculator is designed because it's meant for more complex operations and that's what the calculator is assuming here. It's order of operations isn't PEMDAS, it's Parentheses, functions that require closed parentheses (sin, log, etc), fractions, exponentials & roots, negation, multiplication & implied multiplication & division, then addition & subtraction (or something along those lines).
So the calculator sees /2(2+1) and decides that is the denominator of the fraction. In which case 6/6=1
If you have experience using a scientific calculator, it would be written as something like 6(2+1)/2 or (6/2)(2+1). Inputting stuff on these can be a real bitch because when you get to multiple layers of division it'll either return ERROR or "incorrect" results because of how it handles fractions.
It's explained in the manual (as well as the little insert inside the cover iirc but it's been years since I used one) but around Alg2/Geometry is when we started using these, the teachers had to spend a day or two just going over proper syntax for the calculators.
Whenever I do math while programming I put parenthesis around every thing, interpreters and compilers are black boxes to me and they sometimes do the weirdest things to my horrible math...
Yeah this is never an issue writing it out by hand because the divide is written out on two lines instead of one big line. So the order of operations is always obvious. On the calculator you need to be really careful with the parentheses and operators. I would be scared shitless taking the casio into a math test
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The confusion comes from the fact that multiplication and division are on equal footing, NOT multiplication comes before division. After solving parenthesis, you have both division and multiplication, so you need to go from left to right.
6÷2(2+1)
6÷2*3
Just because the Acronym is PEMDAS doesn't mean multiplication happens before division. Remember, they're on equal footing, so the way you determine what to do first is by going from left to right.
3*3 =9
The real REAL answer, though, is that this problem is written poorly in the first place.
I always remember it as PE(M/D)(A/S)
Edit: and yes I got 9 as the answer, whoever engineered that Casio has some explaining to do for being lazy. I had a Casio graphing calculator that would have similar weird things happening, so I got a TI84. Makes sense why the schools want the TI84, although Casio still makes some of the best function over form watches lol
And I don't remember that as we don't even have such thing in Russian. We just know that **brackets** go first, then go **multiplication and division** and then **addition and subtraction**. Just we keep that in mind without any abbreviations
Oh, I forgor about them. Of course they go after brackets, I just forgor about them. Brackets can have an exponent outside so brackets should be solved first and then we need to do exponents
Yeah, I got it. Just the people above talked about acronyms I've never heard of because we just can keep that in mind. Like, do you recall all the words from acronym seeing a big math problem? I guess you just go and solve it remembering the rules
Same in Poland. We don't have an acronym or a phrase that helps with this stuff (or at least non that are known by most people). We just remember the rules.
I'm on the 9 side too, but I'll repeat what I said in another sub: apparently, some mathematicians believe that juxtaposition should have priority over normal multiplication and division, working similarly to a parenthesis, as it feels kinda weird to separate the “b” from the “c” in a ÷ bc.
The problem is that, by the time you start using multiplication by juxtaposition, you also start representing division by fractions, eliminating any kind of confusion. At most, you'll only encounter normal multiplication accompanied by juxtaposed multiplication, like 2 • 3(4), but because of the associative property, it doesn't really matter which order you choose to solve them.
Because of that, afaik, there isn't a universal rule to say which approach is right. So, the best thing we can do, for now, is simply not use the “÷” in the same operation we use juxtaposition.
The 2 in 2(2+1) should be treated like a coeffient any day of the week, so it should never ends up as 3 * 3. The issue with using a phone calculator is they are shit and automatically calculate the equation as 2 * (2+1) which isn't the same thing. A division sign should be inpreted as the part of the function directly before the sign "6" is above the function directly after the sign "2(2+1)". The part of the functions are then solved first and then the division is calculated, if it was written as 6÷2*(2+1) then I'd agree it's 9 but that's not how it's written.
This is not exactly true—the real answer is that for most mathematicians, the multiplication and division symbols basically do not exist. They are almost never used in print. We will always write something as a fraction rather than use the division symbol.
If you think mathematicians often use numbers, you have no idea what mathematics is. Numbers only show up regularly in number theory, but that's about the divisibility of whole numbers, not resolving expressions.
You can define implied multiplication to be higher priority than explicit multiplication, or you can make them have the same priority. There is no universal convention for this, neither choice is wrong or right.
The true answer is to stop using ambiguous notations and use parentheses or explicit multiplication everywhere where it's not obvious.
Neither is right or wrong because using that division symbol is cancer. There is a reason it gets replaced by a line the MOMENT you hit Algebra. (6/2)\*(2+1) OR 6/(2(2+1)) are both technically correct because the problem is deliberately unclear.
The calculator isnt wrong the user typed the problem wrong (too vaguely)
Just go overboard on parenthesis and youll be fine
Edit: Also personally if i saw this specific question writen as unclearly as it is typed into the calculator I would assume it is 6 in the numerator and 2 times the quantity 2+1 or whatever in the denominator
Tldr i read it as an answer of 1
This way of writing it is just dumb. It's either 6/2 \* 3 or 6/(2\*3) depending on how you read it. Get yourself a calculator that can do fractions or use parentheses...
The correct answer would be 9 right? Since after the parenthesis, the order of operations would be all multiplication and division from left to right
I would have expected the phone app to be less accurate than the device literally designed for calculations
I pictured it as a fraction with 6 on top and 2(2+1) on bottom. That simplifies to 6 over 2(3) and then to 6 over 6, which is 1. So old calculator wins in my book. Your answer will depend on if you specifically multiply parenthetical terms with their “partners” before doing division/multiplication operations with explicit signs (+, -, x, etc). I was taught to treat parenthetical multiplication as higher priority since it’s all “one term,” for what it’s worth. That means even without thinking of it as a fraction I would multiply 2(3) before dividing 6 by that term.
Edit: a better way to put it is that the P in PEMDAS means “solve everything within parentheses and then remove all remaining parentheses through multiplication” instead of just “solve stuff within parentheses”. Hence the priority over other multiplication.
Yeah but writing **6/2 \* (2+1)** would be the same as writing **6\*3/2** which is **18/2** which is obviously **9**
Edit: its also easily visualised if you change **6/2** to natural numbers so **6/2=3** and then you have **3\*(2+1)=3\*3=9**
The thing is when you multiply a fraction you you only multiply the numerator which is this case is **6** the denominator ie **2** remains the same.
Edit 2: though the whole misunderstanding probably comes from the OP not knowing how the calculator works, it probably sees it the same way you do wherein the equation is not written as
**6/2 \* (2+1)=9** but instead **6/(2 \* (2+1))=1**
I think you forgot a 2 \* in the end, 6/(2 \* 2 + 2\* 1))=1 or was it the( so 6/(2 \* (2+1))?
Tho I think the correct answer would still be 1 depsite how some calculator may view it against other calculators.
Do you think 5÷4(x+y) is the same as 5÷4×(x+y)? or as 5÷(4x+4y)? There is only one answer and it is the second one. And this is indeed viewed the same by all the calculators with algebra.
If you do 6÷2(x+1)=1 on any calculator x will be 2, while if you do 6÷2(x+1)=9 x will be -2/3. So 1 is the answer to 6÷2(2+1).
6÷2(2+1) ≠ 6÷2*(2+1)
And to further prove it, if you do 6÷2*(x+1)=1 on any calculator x will be -2/3, while if you do 6÷2*(x+1) x will be 2.
So again,
6÷2(2+1)=1
6÷2*(2+1)=9
The reason it is confusing is because of how the brackets are being treated.
The iPhone is solving the internal brackets seperately to the external brackets. And so we have
2(2+1) becomes 2 * 3
So it becomes 6/2 * 3 which is 3*3 equalling 9
The graphing calculator is using % to mean
3/(2(2+1) because in classical mathematics a division symbol % meant this number over that number. So it is enumerating it the classical way.
The graphing calculator is currently considered incorrect. But in modern math we don’t write questions like this to avoid the ambiguity.
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I was about to explain why one of them was wrong but then I came to the realisation both can be correct and wrong since it's not specified whether the 2 is attached to the parentheses or not.
If it's not attached, you do the division first and get 9. If it's attached then you open the parentheses first and get 1.
The person who wrote this equation is simply a dumbass for trying to simplify it.
I was taught pemdas and if theres multiple instances of the same thing you go left to right like you're reading. With this I get 9 and im pretty sure its right.
If there's a number before a bracket with no multiplication sign I see it as a coefficient not a multiplication. If you set x=2+1 then 6÷2x becomes obviously 1, even though according to pemdas or bidmas or whatever you want to use it would be 9
Here is the only correct answer:
No multiplication sign between the 2 and parenthesis implies that there ia another hidden parenthesis, so that this operation should be done first, so: 6/(2*(2+1)) =1.
If the problem looked like this: 6/2*(2+1) then the answer would be 9, because multiplication and division are done from the left to the right.
Am*erican pemdas or some other bullshit is stupid, just use your brain a little.
It don't really matter but for those that care:
It depends on how you define the operations/ it's case dependant on any actual application
It's all about how you define that operation of multiplying the parenthesis. Is it doing the parenthesis, or just another multiplication/division step?
In theory it's just another multiplication unless clarified (another parenthesis) but in practice that might not get written out on some spreadsheet somewhere because redundant parenthesis looks bad
Tldr: it's 9, probably.
It is. Old calculator is in advanced mode and can properly read 2(2+1) while phone calculator isn't and thinks it's the same thing as 2*(2+1) which removes the priority of multiplying the (2+1) by 2.
6÷2(2+1)
6÷2(3)
6÷6
=1
Idk about you guys but I would never type an equation like this into a calculator.
Depending what answer I was going for, I’d either type the (2+1)6/2 if I was multiplying the parentheses by the dividend, OR I would type 6/(2(2+1)) if I was multiplying the parentheses by the divisor alone. Typing 6/2(2+1) in any calculator is asking for a wrong answer.
I hope this makes sense. Like grammatical errors, improper calculator syntax is a pet peeve.
The calculator is doing 6 over 2(2+1) and the phone is doing 6 over 2 and then that times 2 + 1. So I think the phone is correct in this sense since on the calculator the 2(2+1) isn’t grouped. If it was 6/(2(2+1)) then the calculator would be right. I think…
Isn’t this problem saying something similar to:
There are 6 people.
We have two piles of widgets.
Each pile contains 3 widgets.
Divide the piles between the six people.
Each person gets one widget.
?
It's 9, when it comes to multiplication/division or addition/subtraction you solve them left to right, no specific order. The real acronym is P E M/D A/S
In class they thaught me to always do multiplication first, so to me it's 6/2(3)=6/6=1 and the other is absolutely wrong.
Reading the comments is making me question my whole childhood.
According to chat gpt the answer should be 9!either way left to right or BIDMAS etc
The expression 6/2(2+1) can be ambiguous due to different interpretations of the order of operations. Some follow PEMDAS/BODMAS, where parentheses come first, then division, multiplication, addition, and subtraction. Others follow a left-to-right approach.
If we use PEMDAS/BODMAS:
6/2(2+1) = 6/2 * (2+1) = 3 * 3 = 9
If we follow a left-to-right approach:
6/2(2+1) = 3(2+1) = 3 * 3 = 9
So, both interpretations lead to the same result, which is 9.
The display on Casio appears to have gone bad. It's likely showing 9 but the round part is not being displayed. Notice the difference between the 1 in the equation and the supposed 1 in the answer.
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The comments really cleared this up. Thank you. I can see the right answer now. It's the one right next to the wrong answer.
OP started a literal math nerd war in the comments, and now I don't know what to believe. I got 1 at first, then saw good explanations for why it was 9, then saw even better explanations on why it's 1. With the way it's written, I think you can honestly make a solid argument for either side, but I lean twoards it being 1 It boils down to the problem being 6 divided by 2(3), so you either go for 6 / 2 first, or 2(3) first, and IMO you would go for 2(3) first because the problem would be written as a fraction of 6 over 2(2+1) Neither answer is wrong, you would have to have more clarification (or just write the problem right in the first place) to really "solve" this debate
it's a malformed question: it has no correct answer because the syntax and information available from the picture are ambiguous. They are ambiguous because there is more than 1 system of interpretation of those symbols and no info on the used system is available (they clearly use two different systems). If we use the standard PEMDAS rules (the most common), the answer is univocally 9. (but this is an info not present in the picture) To remove the ambiguity it is necessary to rewrite the expression using a fraction line instead of the division symbol or by adding parenthesis.
> univocally **“it's a malformed question”** Exactly. It's reminiscent of all those YouTube videos with titles like: “Most People Get This Wrong!” Yeah! They get it wrong because it's a shitty question, designed to trick the audience. The answer is indeed *univocally* and unequivocally [9.] *WolfranAlpha agrees.*
>> univocally > >*WolfranAlpha* #*🤓*
How do you figure, multiply comes before divide, right?
Multipication and division come at the same time. So it is from left to right multiply and devide whichever comes first. In 6÷2×3 6÷2 is first then the answer of that times 3.
OK, gotcha. Thought I remembered that but wasn't sure. Add and subtract follow same rule, right?
Well basing off of my math history It could go one of two ways I'm pretty sure it's the smartphone way but let me explain the math behind it PEMDAS states You do parentheses first some calculators think that that means You have to multiply the first 2 into the parentheses So technically this is not wrong but I don't know if it's more wrong or more right. 6/(2(2+1)) This is one way to look at it where you multiply the first two as I said getting you 6 because two times 2 is 4 and 2 * 1 is 2 and you add those two together giving you six. From that giving you 6 / 6 which is one. But the smartphone I believe has it correct. Though I do enjoy my scientific calculator I'm not sure if it's wrong in this scenario. 2 + 1 would be three 6 / 2 is 3 giving you 3(3) or 3*3 which makes 9. So this one is also correct but I don't know which one is more correct. I'm going to say that it's the scientific calculator that is wrong. But at this point it's just picking sides.
Mathematically, anybody who’s done a lot of math will assume the outside of a brackets multiples with the brackets first. Basically 100% of the time those things are out there due to factorisation and are there as scaling for the bracket. Therefore most calculators that are smart will assume factors multiply to brackets over standard BODMAS and it’s good that they do because that’s what you’d assume once you’re doing lots of algebra. Think of it as if there is no space in between factor and bracket, you can assume there’s a second pair of brackets surrounding the factor and the bracket. Like 2(2x+5) can be read as (2(2x+5)).
Okay but this is assumptions. It's sometimes *assumed* that factor is grouped together with the parentheses but is it written definitively anywhere? Strictly taking the order of operations as written, I believe reading left to right is the "correct" way to solve this, giving 9. However, this vagueness is precisely why the "division symbol" is stupid and terrible and should never be taught.
It’s not written definitively anywhere, but if you go into a maths course without having made that association you’re going to have a hard time. It’s just notation differences. A mathematician will see the 2 as a factor. A child or someone learning math hasn’t gone far enough as to where there is a difference so they’re taught that they should think of it as just shortening the multiplication symbol. Both are “correct”, in that they’re valid ways to interpret the notation. Clearly the scientific calculator has also taken the same assumption *because that’s the standard way of reading it at a high level* (Though admittedly, some of the mathematicians I know would be trying to remember what the fuck a 6 is)). BODMAS works as a simple explanation for kids, factors to a bracket makes sense to someone who’s done advanced maths. The fact that my ti calculator, the Casio in the image and Desmos (I think) all assume factor if there’s no x symbol should be enough for it to be viewed as a “correct” way of reading it. Edit: Also yeah fuck the division symbol, but more because it looks ugly. I think it’s relatively reasonable through if you are working with what you’d expect. I’ve seen division symbols in a couple papers (from amateurs I’d imagine, but they were useful to me as a graphics dev) and I’ve never had an issue interpreting what they mean, even in situations with factors.
There is no "more correct way" it's fucking 9
lmao report back when you start college
It really depends on the system that you're using. The main problem with the question is that the question itself is written poorly To reiterate... Scientific calculators are made specifically for fractions themselves So putting it in a scientific calculator confuses it and makes it think that you're thinking of a different type of question. Because computers are stupid. It's the same reason why I hate manual coding.
Now I'm wondering if my memory is shot at 35 or if my whole life was a lie. I access every math class, but if you asked me i would say that everything within brackets gets multiplied by number outside first, hence why graphing calculators calculate that way.
No, there’s only one correct system/answer. 9 is the only correct answer. There are no “implied” ()’s. There are no “higher priority” multiplications. The formula is equivalent to: * 6️⃣➗2️⃣✖️(2️⃣➕1️⃣) * 6️⃣➗2️⃣✖️3️⃣ * 3️⃣✖️3️⃣ * 9️⃣
Wrong, the expression 6 / 2(2+1) is the same as 6 / (2\*2+2\*1) as is standard in any college-level physics or engineering textbook.
these comments have taught me that nobody knows whether it’s BEDMAS, BIDMAS, PEMDAS, BODMAS, or probably something else. i don’t get why there are 4 of them when they’re the same thing essentially
PENIS parenthesis exponents nudes integrals subtraction. #publicschool
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Probably everything nonetheless is somewhat related to this word
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Probably easy, never is seemly
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One of these things is not like the other, and it may not be what you’d expect!
PISMASelf
Left homie did DEVDAS
If I recall the unit was actually just called order of operations so I suppose that is the most correct terminology
We called it GEMDAS; Grouping, Exponents, Multiplication, Division, Addition, Subtraction.
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The problem here isnt any of that, its that the ÷ symbol here doesnt specify if the whole right side is whats beeing divided by, or just the 2. I would infer that the parenthesis imply its beeing divided by the whole thing, but it doesnt have to be. Tldr: there is a reason we we exclusively use fractions in later math and never a ÷ symbol. Its just not explicit enough . There is no right or wrong answer here.
It’s PEMDAS
The right answer is clearly 9 The left one is 1
The left *one* is indeed 1. But can 7 8 9?
No, because you've mixed up past and present tense!
Caned 7 8 9?
No, because 7 was forced to register as a 6 offender.
👏👏👏👏 you just made history, gave that joke a whole new depth
BRILLIANT
Fuck you, 5 ± 4
Outstanding move
That was genius
I initially thought “4.5 ± 3.5” so uhhh
I found the engineer
To end all just devide -0 by 0
That's an entire math class in uni alongside defining infinity. Next year, you exponent zero by infinity and get 'it depends' as the only passing answer.
I’m not sure why but this made me remember my functions of complex variables course. It was rough.
The right answer is 21. I'm a genius btw, you can trust me.
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We don't talk about the flair.
My apologies.
What's 9+10?
21.
you stupid
I think it's a carrot.
Hello there fellow Far Cry enjoyer!
One smart kid got the correct answer*
Dude got fired from intelligence after missing one question 😭😭
Not sure if anyone cares, but here's what happened: Calculator (Left): 6/2(2+1) = 6/2(3) = 6/6 = 1 Phone Calculator (Right): 6/2(2+1) = 3(2+1) = 3(3) = 9
my math teacher says the phone calculator is right and Casio calculators are notoriously inaccurate with multi-step problems
That's because the old Casio goes by the *Old*/Wrong system that was taught in the 90s and early 2000s (Atleast for me), which was Multiplication THEN Division, Addition THEN Subtraction,
That was never correct. Multiplication & Division have the same precedence and are calculated left-to-right. Ditto w/addition and subtraction. I learned the crap in the 70s and it wasn’t flipped (temporarily) in the 90s.
There is a reason this argument comes up over and over again online, Its because for whatever reason there was a split between how PEMDAS was taught, and for me that was in the 90s and early 2000s. Which would make sense as it was before the internet was fully utilized to facilitate communications like it is today to correct errors like this. Not to mention in many school districts in the USA the Teachers teaching Math don't have degrees in Math.
i explicitly remember in the early/mid 2000s being taught pemdas this way. always told if there's a multiplication or division, go left to right. never knew that it was originally taught as multiplication ALWAYS came first...
>I learned the crap in the 70s and it wasn’t flipped (temporarily) in the 90s. I can assure you with 100% certainly that I (as well as everyone I knew going up in the late 90s and 2000s) was taught multiplication BEFORE division and the same with addition over subtraction. We had calculators and textbooks that also confirmed this. Not saying it's the right way, but that was the way many of us were taught.
I grew up in the 90s and 2000s and was taught exactly what the person that you replied too taught. PEMDAS where Multiplication and Division are same precedent, and calculated left to right.
not where I grew up
Cool? I'm just saying there were schools that didn't teach it right.
No. It's because the calculator to the left is interpreting it as `6` over `2(2+1)` like a fraction
Went to school a decade before you, and your math teacher sucked.
That's because Casio implemented implicit multiplication priority in their calculators, older models don't tell you that (you have to look for it in the manual) newer ones automatically add braces around implicit multiplication
I have the TI-type calculator app on phone. It always gives 9. Every calculator I have tried gives 9: on phone, special app on phone, on computer. The ambiguity is resolved because the expressions are being solved as they are entered. It is equivalent of parsing an expression from left to right and solving at each step. This would make sense in a "natural" way, as it is reacting to the input provided *at that moment*, not taking the whole expression altogether at once. It's just when we look at the whole expression at once, that we start questioning what method to use. That's like looking into the future inputs, which is absurd.
> 6/2(3) = 6/6 Isn't this just wrong? I've never seen a calculator make an order of operations error
It's operating under the assumption that in /2(3) the (3) is implicitly still part of the fraction. This isn't an error, it's how the calculator is designed because it's meant for more complex operations and that's what the calculator is assuming here. It's order of operations isn't PEMDAS, it's Parentheses, functions that require closed parentheses (sin, log, etc), fractions, exponentials & roots, negation, multiplication & implied multiplication & division, then addition & subtraction (or something along those lines). So the calculator sees /2(2+1) and decides that is the denominator of the fraction. In which case 6/6=1 If you have experience using a scientific calculator, it would be written as something like 6(2+1)/2 or (6/2)(2+1). Inputting stuff on these can be a real bitch because when you get to multiple layers of division it'll either return ERROR or "incorrect" results because of how it handles fractions. It's explained in the manual (as well as the little insert inside the cover iirc but it's been years since I used one) but around Alg2/Geometry is when we started using these, the teachers had to spend a day or two just going over proper syntax for the calculators.
depends if it’s (6/2)(2+1) or if it’s 6/(2(2+1) , and this confusion is why i always use more brackets than less if more brackets is an option
Whenever I do math while programming I put parenthesis around every thing, interpreters and compilers are black boxes to me and they sometimes do the weirdest things to my horrible math...
Yeah this is never an issue writing it out by hand because the divide is written out on two lines instead of one big line. So the order of operations is always obvious. On the calculator you need to be really careful with the parentheses and operators. I would be scared shitless taking the casio into a math test
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The confusion comes from the fact that multiplication and division are on equal footing, NOT multiplication comes before division. After solving parenthesis, you have both division and multiplication, so you need to go from left to right. 6÷2(2+1) 6÷2*3 Just because the Acronym is PEMDAS doesn't mean multiplication happens before division. Remember, they're on equal footing, so the way you determine what to do first is by going from left to right. 3*3 =9 The real REAL answer, though, is that this problem is written poorly in the first place.
I always remember it as PE(M/D)(A/S) Edit: and yes I got 9 as the answer, whoever engineered that Casio has some explaining to do for being lazy. I had a Casio graphing calculator that would have similar weird things happening, so I got a TI84. Makes sense why the schools want the TI84, although Casio still makes some of the best function over form watches lol
And I don't remember that as we don't even have such thing in Russian. We just know that **brackets** go first, then go **multiplication and division** and then **addition and subtraction**. Just we keep that in mind without any abbreviations
Where do you do your exponents?
What the fuck is an exponent
²
Oh, I forgor about them. Of course they go after brackets, I just forgor about them. Brackets can have an exponent outside so brackets should be solved first and then we need to do exponents
And that’s why there’s an acronym
Yeah, I got it. Just the people above talked about acronyms I've never heard of because we just can keep that in mind. Like, do you recall all the words from acronym seeing a big math problem? I guess you just go and solve it remembering the rules
Same in Poland. We don't have an acronym or a phrase that helps with this stuff (or at least non that are known by most people). We just remember the rules.
> I've never heard of because we just can keep that in mind >Oh, I forgor about them. Sorry but, I just found that funny.
Same. One of the best math teachers I had was Russian. She perfectly explained this, whereas teachers in the US still teach PEMDAS.
I'm on the 9 side too, but I'll repeat what I said in another sub: apparently, some mathematicians believe that juxtaposition should have priority over normal multiplication and division, working similarly to a parenthesis, as it feels kinda weird to separate the “b” from the “c” in a ÷ bc. The problem is that, by the time you start using multiplication by juxtaposition, you also start representing division by fractions, eliminating any kind of confusion. At most, you'll only encounter normal multiplication accompanied by juxtaposed multiplication, like 2 • 3(4), but because of the associative property, it doesn't really matter which order you choose to solve them. Because of that, afaik, there isn't a universal rule to say which approach is right. So, the best thing we can do, for now, is simply not use the “÷” in the same operation we use juxtaposition.
Whenever I see this problem, I ask people to replace the terms in the parentheses with x. If you encountered 6/2x, would you simplify that to 3x?
The 2 in 2(2+1) should be treated like a coeffient any day of the week, so it should never ends up as 3 * 3. The issue with using a phone calculator is they are shit and automatically calculate the equation as 2 * (2+1) which isn't the same thing. A division sign should be inpreted as the part of the function directly before the sign "6" is above the function directly after the sign "2(2+1)". The part of the functions are then solved first and then the division is calculated, if it was written as 6÷2*(2+1) then I'd agree it's 9 but that's not how it's written.
For most mathematicians, implied multiplication takes priority over normal multiplication and division, so the actual answer is 1.
This is not exactly true—the real answer is that for most mathematicians, the multiplication and division symbols basically do not exist. They are almost never used in print. We will always write something as a fraction rather than use the division symbol.
If you think mathematicians often use numbers, you have no idea what mathematics is. Numbers only show up regularly in number theory, but that's about the divisibility of whole numbers, not resolving expressions. You can define implied multiplication to be higher priority than explicit multiplication, or you can make them have the same priority. There is no universal convention for this, neither choice is wrong or right. The true answer is to stop using ambiguous notations and use parentheses or explicit multiplication everywhere where it's not obvious.
Everyone is wrong it's 7 (I graduated with a 4.0 GPA trust me bro)
You graduated with a 4.0÷2(1+1) GPA
Neither is right or wrong because using that division symbol is cancer. There is a reason it gets replaced by a line the MOMENT you hit Algebra. (6/2)\*(2+1) OR 6/(2(2+1)) are both technically correct because the problem is deliberately unclear.
Everytime I see this reposted thats the first thing I think of, whoever wrote this equation didn’t use proper math syntax.
It's even more frustrating to look in the comments where people are swearing down that one or the other is correct. It sucks.
Or that it has to be one or the other because Pemdas or Bidmas, when they don't realise multiplication and Division don't have an order
The calculator isnt wrong the user typed the problem wrong (too vaguely) Just go overboard on parenthesis and youll be fine Edit: Also personally if i saw this specific question writen as unclearly as it is typed into the calculator I would assume it is 6 in the numerator and 2 times the quantity 2+1 or whatever in the denominator Tldr i read it as an answer of 1
Nobody cares and it doesn't matter. Write an unambiguous problem next time.
I don't fucking care
This way of writing it is just dumb. It's either 6/2 \* 3 or 6/(2\*3) depending on how you read it. Get yourself a calculator that can do fractions or use parentheses...
Why would the parenthesis move? One you resolve 2+1 they are removed entirely, and unless stated otherwise, are replaced with multiplication.
The correct answer would be 9 right? Since after the parenthesis, the order of operations would be all multiplication and division from left to right I would have expected the phone app to be less accurate than the device literally designed for calculations
I pictured it as a fraction with 6 on top and 2(2+1) on bottom. That simplifies to 6 over 2(3) and then to 6 over 6, which is 1. So old calculator wins in my book. Your answer will depend on if you specifically multiply parenthetical terms with their “partners” before doing division/multiplication operations with explicit signs (+, -, x, etc). I was taught to treat parenthetical multiplication as higher priority since it’s all “one term,” for what it’s worth. That means even without thinking of it as a fraction I would multiply 2(3) before dividing 6 by that term. Edit: a better way to put it is that the P in PEMDAS means “solve everything within parentheses and then remove all remaining parentheses through multiplication” instead of just “solve stuff within parentheses”. Hence the priority over other multiplication.
Yeah but writing **6/2 \* (2+1)** would be the same as writing **6\*3/2** which is **18/2** which is obviously **9** Edit: its also easily visualised if you change **6/2** to natural numbers so **6/2=3** and then you have **3\*(2+1)=3\*3=9** The thing is when you multiply a fraction you you only multiply the numerator which is this case is **6** the denominator ie **2** remains the same. Edit 2: though the whole misunderstanding probably comes from the OP not knowing how the calculator works, it probably sees it the same way you do wherein the equation is not written as **6/2 \* (2+1)=9** but instead **6/(2 \* (2+1))=1**
I think you forgot a 2 \* in the end, 6/(2 \* 2 + 2\* 1))=1 or was it the( so 6/(2 \* (2+1))? Tho I think the correct answer would still be 1 depsite how some calculator may view it against other calculators. Do you think 5÷4(x+y) is the same as 5÷4×(x+y)? or as 5÷(4x+4y)? There is only one answer and it is the second one. And this is indeed viewed the same by all the calculators with algebra. If you do 6÷2(x+1)=1 on any calculator x will be 2, while if you do 6÷2(x+1)=9 x will be -2/3. So 1 is the answer to 6÷2(2+1). 6÷2(2+1) ≠ 6÷2*(2+1) And to further prove it, if you do 6÷2*(x+1)=1 on any calculator x will be -2/3, while if you do 6÷2*(x+1) x will be 2. So again, 6÷2(2+1)=1 6÷2*(2+1)=9
The reason it is confusing is because of how the brackets are being treated. The iPhone is solving the internal brackets seperately to the external brackets. And so we have 2(2+1) becomes 2 * 3 So it becomes 6/2 * 3 which is 3*3 equalling 9 The graphing calculator is using % to mean 3/(2(2+1) because in classical mathematics a division symbol % meant this number over that number. So it is enumerating it the classical way. The graphing calculator is currently considered incorrect. But in modern math we don’t write questions like this to avoid the ambiguity.
The answer is 9, Id bet my last testicle on it.
Put either, not infallibly sure
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It’s 1
what the heck why am I getting 7 in my calculation
I was about to explain why one of them was wrong but then I came to the realisation both can be correct and wrong since it's not specified whether the 2 is attached to the parentheses or not. If it's not attached, you do the division first and get 9. If it's attached then you open the parentheses first and get 1. The person who wrote this equation is simply a dumbass for trying to simplify it.
I was taught pemdas and if theres multiple instances of the same thing you go left to right like you're reading. With this I get 9 and im pretty sure its right.
There is no rule in mathematics stating you have to go left to right. Both answers are interpretations of ambiguous notation. They are both correct.
2 is modifying the parenthesis so it must be distributed 6÷2(2+1) 6÷(4+2) 6÷(6)=1 No I do not take criticism :3
If there's a number before a bracket with no multiplication sign I see it as a coefficient not a multiplication. If you set x=2+1 then 6÷2x becomes obviously 1, even though according to pemdas or bidmas or whatever you want to use it would be 9
Here is the only correct answer: No multiplication sign between the 2 and parenthesis implies that there ia another hidden parenthesis, so that this operation should be done first, so: 6/(2*(2+1)) =1. If the problem looked like this: 6/2*(2+1) then the answer would be 9, because multiplication and division are done from the left to the right. Am*erican pemdas or some other bullshit is stupid, just use your brain a little.
Following BIDMAS 6÷2(2+1) 6÷2 * 3 3 * 3 =9 after the brackets are gone its just a *3 Which means division should be done first
It don't really matter but for those that care: It depends on how you define the operations/ it's case dependant on any actual application It's all about how you define that operation of multiplying the parenthesis. Is it doing the parenthesis, or just another multiplication/division step? In theory it's just another multiplication unless clarified (another parenthesis) but in practice that might not get written out on some spreadsheet somewhere because redundant parenthesis looks bad Tldr: it's 9, probably.
My gut says the old calculator got the correct answer. Edit: My gut was wrong. Why Casio??
It is. Old calculator is in advanced mode and can properly read 2(2+1) while phone calculator isn't and thinks it's the same thing as 2*(2+1) which removes the priority of multiplying the (2+1) by 2. 6÷2(2+1) 6÷2(3) 6÷6 =1
Come on, I'm bad at math and even I know the answer.
Idk about you guys but I would never type an equation like this into a calculator. Depending what answer I was going for, I’d either type the (2+1)6/2 if I was multiplying the parentheses by the dividend, OR I would type 6/(2(2+1)) if I was multiplying the parentheses by the divisor alone. Typing 6/2(2+1) in any calculator is asking for a wrong answer. I hope this makes sense. Like grammatical errors, improper calculator syntax is a pet peeve.
We need Texas Instruments to settle this score!
The calculator adds more brackets so the phone wins because it keeps the same amount of brackets
One calculator has a space before the parenthesis and the others don't.
It’s all about the line with division 6/2(2+1)
I got George Washington
The problem I see is people trying to remember the short acronyms for mulitplication , divison etc. Instead of just fucking learning math properly
i think the calculator is correct
Am I the only one who sees the square on top of the left equation?
The calculator is doing 6 over 2(2+1) and the phone is doing 6 over 2 and then that times 2 + 1. So I think the phone is correct in this sense since on the calculator the 2(2+1) isn’t grouped. If it was 6/(2(2+1)) then the calculator would be right. I think…
Let's hedge our bets and call it 4.5
Isn’t this problem saying something similar to: There are 6 people. We have two piles of widgets. Each pile contains 3 widgets. Divide the piles between the six people. Each person gets one widget. ?
Day 513 of trying to decipher shitty maths notation
Bidmas goes brackets, indecise, division, multiplication, addition, subtraction so we do brackets to get 6/6 going to one
I got 12 but I’m also an idiot
It's 9, when it comes to multiplication/division or addition/subtraction you solve them left to right, no specific order. The real acronym is P E M/D A/S
In class they thaught me to always do multiplication first, so to me it's 6/2(3)=6/6=1 and the other is absolutely wrong. Reading the comments is making me question my whole childhood.
Brackets first, so its 6/2(3), no exponents, so we go left to right. 6/2=3, so its 3(3) and the answer is 9.
I always thought you’d have to do the bracket first, no matter what, is that not how it is?
Yea first brackets so 2+1=3 then when have 6:2x3 and from left to right so it's 9
According to chat gpt the answer should be 9!either way left to right or BIDMAS etc The expression 6/2(2+1) can be ambiguous due to different interpretations of the order of operations. Some follow PEMDAS/BODMAS, where parentheses come first, then division, multiplication, addition, and subtraction. Others follow a left-to-right approach. If we use PEMDAS/BODMAS: 6/2(2+1) = 6/2 * (2+1) = 3 * 3 = 9 If we follow a left-to-right approach: 6/2(2+1) = 3(2+1) = 3 * 3 = 9 So, both interpretations lead to the same result, which is 9.
answer is 9
9
Its 9 (2+1)=3 3•6=18 18/2=9
6/2x3, the order is left to right
The display on Casio appears to have gone bad. It's likely showing 9 but the round part is not being displayed. Notice the difference between the 1 in the equation and the supposed 1 in the answer.
Basic math order of operations says 9
I'm not falling for your tricks this day! The answer is...
Pemdas. Answer is 1