6 divided by 2(1 + 2)=? Maybe 1 in 10 People Can Solve This Math Problem-Are You One of Them?

[@verkuilb]

Here’s the problem-many people in various regions around the world have been taught that for division, the “slash” symbol (/) means something different than the obelus used in your video (÷). As they were taught, the slash means division, while the obelus means a fraction. This makes sense when you consider the origin of the obelus, which is believed to be a sort of shorthand way of depicting a fraction, with the numerator being the top dot and the denominator being the bottom dot. If you think of this way, then 6 ÷ 2(1+2) is a fraction with a numerator of 6 and denominator of 2(1+2). And the standard convention for such a fraction is to consider the entire denominator to effectively be in parentheses, even though the parentheses are not actually present. In which case, as a fraction, the correct answer here is 1, not 9. This lack of uniform practice regarding the obelus is a large part of the reason that its use is not recommended in the ISO 80000-2 standard for mathematical notation.

[@gavindeane3670]

Exactly. This expression doesn't just violate ISO 80000-2 with regard to division notation, but also multiplication notation too. ISO 80000-2 states that the multiplication symbol may be omitted if no misunderstanding is possible. So clearly, this expression shouldn't be written with implicit multiplication at all.

[@ted8777]

6:2(1+2)=6/2(1+2)=3*3=9 used colon instead the division symbol, just to lazy to search for it in my menu system.

[@ted8777]

Remember to use proper math when sending spacecraft to Mars.

[@doughoffman9463]

@@ted8777 Yes. And especially in mission critical math DON'T use an ambiguous notation subject to errors. Use parentheses and avoid crashing the mission.

[@richardhay645]

@verkuilb absolutely correct. The real problem relating to this video is that US public schools in recent years have changed how they teach. Until calculators and computers division was almost always noted by a horizontal line and was interpreted as a strict fraction. Older generations (especially those taking algebra prior to the 1960s) learned it that way. Computers and calulators do not have the ability to use the horizontal line as a math operator. My phone calculator only uses ÷ for division and by computer keyboard only has / for division. This creates a problem since you can't use ÷ for fraction and an alternative symbol for division. When the problem is presented to my Android phone the problem is resolve like this: 6/2(1+2) you get 1. This is why he was emphatic about not using a calculator. But if I write it as: 6/2×(1+2) you get 9. If you solve it with Excel and write =6/2(1+2) you are greeted with a message that calls you an idiot and tells you it can only be written as =6/2*(1+2). Accepting that message causes the calculation to be 9. Unlike the calculator the 2(1+2) is not interpreted by Excel as implied multiplication and to get the entire construct to be a fraction you must write =6/(2*(1+2)) which yields 1. The conclusion at least in the US math education on this topic is a "hot mess" and has been so for the last 50+ years. The truly correct answer to this problem is "It depends". This answer will not get you very far on the typical standardized US math test!!!

[@TubeLVT]

The description is misleading. It doesn’t match John’s video interpretation of the expression in the thumbnail image. “6 divided by 2(1 + 2)” plainly means that the value 6 is divided by the product 2(1 + 2). Recognizing the ambiguity and suspecting a trap, I got both the 1 and 9 results. PEMDAS doesn’t work when natural language is embedded in a mathematical expression.

[@michaellowe5558]

It doesn't matter how it's said in English. This is math. There aren't parentheses around 2*(1+2), so the answer can only be 9.

[@gavindeane3670]

​@@michaellowe5558The point that the person you replied to was making, is that the video title and the video content do not match. The video title is written in English, and the result of the calculation it describes is 1.

[@KaelumYodi]

@@gavindeane3670 there isn’t any ambiguity here, no tricks, nothing special about written English, just math. The problem is that many teachers don’t even teach this, as it is sort of considered an archaic form of writing a math problem. It is more of a test to determine if your instructor taught you correctly, than anything else. The order of operations must always be followed, but people tend to confuse the “division” symbol with the “divided by” line. They are not the same.

[@ted8777]

@@TubeLVT this may show my little knowledge of math but all fractions are division except x/0 unless you go into i.

[@gavindeane3670]

​@@KaelumYodiThe notation certainly is ambiguous. That's the entire point of it. Not only because of the use of the ÷ symbol (although that doesn't help), but it's still exactly the same ambiguity if you write it with the proper division symbol as 6/2(1+2). No teachers should be teaching this. Notation like this has no place in a classroom, unless it's during a lesson about the importance of clarity and what not to do.

[@raya.pawley3563]

9. Thank you

[@jadenmudge]

yep

[@richardschneider5248]

3(3)=9 yes!

[@tinchin6328]

Wrong. Not 9.

[@jocelynphillips6210]

@@tinchin63289 IS the correct answer.

[@reneperrin1628]

Let’s consider the expression (2 +4). You can factor out the 2 and write it at 2(1+2). Which you would write exactly as 2(1+2). In this case the denominator is 2(1+2) and the result is one. And if you read scientific papers, that is a very common notation. If you find the example contrived, replace it with 2(1+x). My issue with this example and PEMDAS is that there is a missing *. If the equation was given as 6 / 2 * (2 + 1 ). Then yes. I would apply PEMDAS, but as specified, i would consider that there is a factorization in the denominator and the result is 1.

[@gavindeane3670]

How do you decide whether the factor is 2 or 6/2?

[@KenFullman]

This is exactly how I see it too. You don't even need the brackets. When we have an expression such as 2y, this means 2 TIMES y, but we wouldn't say that 6 ÷ 2y is equal to 3y

[@joseluiscartesvaliente5924]

Correcto. El resultado es UNO, ya que 6 : 2x3 = 6 : 3x2 (Propiedad conmutativa) = 6 : 6 = UNO (1)

[@reneperrin1628]

@@gavindeane3670 The absence of the * operator. 6/2x is generally accepted as 6/(2*x) and not 6/2 * x. The issue is that this is a generally accepted convention, and not a formal rule. So it's ambiguous. So, 6/2 * (2 + 1) = 9 by PEMDAS, but 6/2(2+1) = 1 per the "2x" convention.

[@gavindeane3670]

​​@@reneperrin1628Yeah, I understand the ambiguity and how the two interpretations work. What I was getting at is the assumption that when a number is multiplied by a bracketed sum, that number must necessarily have been factored out of the brackets before. That assumption doesn't hold at all. It's POSSIBLE that this expression could arise from someone having 6/(2+4) and taking out the common factor of 2 from the brackets, so they write 6/2(1+2). It's also possible that this expression could arise from someone having 6 6 (----- 1 + ----- 2 ) 2 2 and taking out the common factor of 6/2, and they're not following the implied multiplication convention you describe so they write 6/2(1+2). And it's also possible that the 6, the 2, and the (1+2) all came together in this expression independently, and there was never any factor taken out of the brackets.

[@Stylux-z1p]

6 : 2(1 + 2 ) Is the same as multiplying by its reciprocal 2(1 + 2 ) --> 1 / 2(1 + 2 ) [6/1] x [1/ 2(1 + 2 )] [6/1] x [1/6] = 1✅ if the division operator " : " was replaced by a horizontal bar "--------" ----------------------------------------------------------------- 6 : 2(1 + 2) --> sum between parentheses has priority (1 + 2 ) = 3 6 : 2(3) --> from left to right if division comes first then it has priority above multiplication , so 6 : 2 = 3 3(3) = 9 ✅

[@MamaSapp]

yay! i got it right!

[@A.A.ron77]

I gave this comment a thumbs up cuz it also kinda makes sense. I also wondered what happens if you distribute the 2 over to the elements inside the parenthsis, so it becomes 6 ÷ 2 + 4, which is 3 + 4 = 7. or, if I left the parenthesis on it would be 6 ÷ (2+4) = 1. SO we basically have a different answer than 9, which we get from pemdas. I also tryed, substitution. X=6 Y=2 Z=1 so its x ÷ y(z + y) which is x/y(z+y) which is x/(yz + y^2) I believe thats 1 again.... Hmmm?.

[@shadowstar68]

I think the writing confuses it. When I was at school the sum would have been given like this 6 ÷ 2 x (1+2) Note this is not fractional. You solve the sum by using PEMDAS or BODMAS (same thing) So solving brackets first 6 ÷ 2 x 3 Then you deal whith each pair in order 6 ÷ 2 =3 3 x 3 = 9

[@churchillsmythe4284]

Actually, 9 is incorrect! The process given in the video made a simple violation. You shall not deny the content of the parenthesis of its rightful operation. Hence, 2(a + b) must be given its due operation with result = (2a + 2b). That 2 preceding the parenthesis is intended to operate on the content of the parenthesis before any other operation on said 2. Therefore, the answer is 1. 6/(2+4) = 1

[@gavindeane3670]

What you did there is called distribution. Distribution is literally multiplication. Distribution tells you nothing about whether the answer is 1 or 9. It's fine to use distribution, but you have to start by deciding whether the factor you're going to distribute is 2 (like you did) or 3 (the result of 6/2).

[@churchillsmythe4284]

@gavindeane3670 so it's obvious (to the logically inclined) that the parenthesis is a higher order and supercedes any operation preceding the 2. If you carry out 6/2 first, then you would have denied the operation 2(a + b) = (2a + 2b), unless you recognize 2(a+b) in whole as the denominator of the fraction( 6/2 (a+b) or simply (6 ÷ 2) = 3, then 3 ÷ (a+b) = 3/3 =1

[@gavindeane3670]

​​@@churchillsmythe4284Going from 2(a+b) to 2a + 2b is distribution. Distribution is - literally, by definition - multiplication. You can get both answers, 1 and 9, using distribution. So why are you giving the multiplication higher priority than the division? I'll give you a hint: the answer to that question has got absolutely nothing to do with parentheses. There's nothing wrong with the way you've interpreted the expression. Lots of people would interpret it that way. It's normal. You've just not understood how that interpretation works. It's not about parentheses. It's about implied multiplication.

[@churchillsmythe4284]

@@gavindeane3670 I'm giving the parenthesis higher priority. That's the rule. How would you go about this? 8 ÷ 2²(a - b)

[@gavindeane3670]

​@@churchillsmythe4284There's no rule about giving parentheses higher priority. The priority concept you're referring to applies to mathematical operations. Different types of operation can have higher or lower priority than each other Parentheses are not an operator so to talk about giving priority to parentheses is nonsensical. What you're actually doing is giving the multiplication higher priority than the division. Your excursion has exactly the same ambiguity as the expression in the video, so I don't evaluate it. I take it back to the person who wrote it and tell them to write it properly. To see why "giving priority to parentheses" is nonsense, think about evaluating 2(1+2)².

[@richardhay645]

I think it helps to write PEMDAS vertically as P on top then E then MD then AS on the bottom. Like this: P E MD AS

[@TheFalcor]

By your logic, if the question was 6 ÷ 2a then that would equal 3a. Given that 6 ÷ 2a is 6 ÷ 2 x a and BODMAS/PEMDAS simplifies that to 3 x a.

[@brucew845]

To a person who uses math for actual work, as opposed to simply playing with numbers, the 2(1+2) would be treated as 1 character, BC. Therefore the answer is 1. Math gamers are getting lazy by not putting in the needed to show that the 2 is not part of the (1+2). In math homework today where nobody cares about the Practical uses of math you can change the use of terms however or whenever you want. This problem is A divided by BC not A divided by B times C. When math was taught to be useful, this was true. The strict PEMDAS people want to change all of the old rules, is Pythagoras next or has it already been changed too.

[@mauriziograndi1750]

If 90% will get this wrong that means there’s 90% of engineers around.

[@randallchinn1850]

So if you simplify ab/ab, would you get 1 or b squared?

[@ryanstevens2722]

You need a follow up video showing this as a fraction of 6 over 2(2+1) =. Would you get the same answer of 9 or 1? This video is sadly incomplete since there is no explanation for the fraction method.

[@jimungvarsky6865]

1

[@saltcavern]

parenthesis first then the order from left to right.🧐

[@winterknight4176]

And the 2 is tied to the parenthesis by juxtaposition, so you do that multiplication first.

[@winterknight4176]

If you don't see it, then write the equation as a fraction, like this: ‎ ‎ ‎ ‎ ‎ 6 _________ 2(2+1)

[@meroha9427]

incorrect entry, depending on the context that the answer is 9, that 1 is correct, because depending on the context it can be either (6÷2)×(1+2) or 6÷(2(1+2)) and as a rule, if there is "nothing" before the number and brackets instead of the multiplication sign, it means that this part is responsible for one part, which should then be used as a divisor.

[@gregc.mariano9226]

Shouldn't we multiply 3 to 2 first as it is inside the parenthesis so the answer would be (6\6) =1 instead of (6/2x3)=9 as it was explained. However, you forgot to mention that ( ) is a parenthesis and at the same time a multiplication x. So which one should take precedence? Isn't it the parenthesis? This is where the confusion lies.

[@stevendebettencourt7651]

Parentheses always takes precedence, always, always, always. Also, when you see 2(1+2), it is understood this means 2*(1+2). When in doubt, add the missing multiplication sign and all confusion should vanish.

[@gavindeane3670]

Precedence is a concept that applies to operations. Parentheses are not an operator, so the question you're asking is completely misconceived. Parentheses can not take precedence over anything. Only operations can take precedence over each other. When "order of operations" is taught with stupid acronyms like PEMDAS, we're used to the common misunderstandings about doing M before D or A before S because that's what the acronym appears to suggest. But actually I think the most serious problem with the acronyms is the amount of misunderstanding they create about what parentheses mean and what they are for. Parentheses should not be part of "order of operations" at all. The difference between the two interpretations of the expression in this video has got absolutely nothing to do with parentheses. The difference is solely and entirely about the precedence of implied multiplication relative to division. Have a read about implied multiplication in the order of operations, and PEMDAS vs PEJMDAS. That's what's going on here.

[@xaiyab6892]

@@gavindeane3670 And people who were taught PEMDAS also KNOW that MD are on the same level but are prioritized LEFT TO RIGHT , as is AS. No confusion there if people pay attention in math class. If you are ignorant of how PEMDAS works, it's not the fault of PEMDAS, that is your ignorance at fault. Correct the ignorance and the problem disappears.

[@paulfrank8738]

Perhaps this will clarify; perform the operation *inside* the parenthesis first. Only the addition operation, "1+2" is inside the parenthesis, so that's the only operation performed during the parenthesis step. What we're left with are only multiplication and division operations, 6/2x3 or 6/2(3). The first form has explicit multiplication. The second form has implied multiplication or multiplication by juxtaposition.

[@noraimecomla9843]

Correct answer is 1

[@jamiemccubbins2289]

You can't remove ( ) until juxtaposition is satisfied. The x sign is only removed when a juxtaposition is formed. This can easily be proved through Algebra and substitution.

[@gavindeane3670]

It can't be proved at all. Sometimes you see people try and algebraically prove that the answer to this must be 1. Inevitably, their "proof" turns out to just be a circular argument - a logical fallacy that proves nothing. Attempting to prove it either way is a category error. It's completely misconceived. This is not a mathematics issue, it's a notation issue. It's not susceptible to mathematical proof.

[@buzzybola]

That sneaky hidden multiplication sign is an easy way to throw someone off :D

[@MargotHypnos]

So if you chose division before multiply because of the way it was written. Does that same method apply for PEMD(AS). if subtraction is operation is first in equation you do that before addition?????

[@gavindeane3670]

Yes. PEMDAS is a 4 step process not a 6 step process. P, then E, then M&D, then A&S If you want to use an acronym for this stuff, the 4 letter variations like PEMA are better for exactly this reason.

[@MargotHypnos]

@@gavindeane3670 Thank so much for clearing this up.

[@PatrickEmeka-l6s]

Refer back to old established principle of BODMAS that is unambiguous in solving this type of mathematical expression. It gives you 9 without much mental stress.

[@craigfoster354]

This left to right reading of equations might be OK in English and many other languages, but Hebrew, Yiddish and many middle eastern languages (from whom we get algebra and other maths) are read right to left. They have a more cogent argument that the answer is 1, don't you think?

[@gavindeane3670]

No. "Left to right" is really just saying that when we read things, we begin at the beginning. So if you're reading something that is meant to be read right to left, "begin at the beginning" means starting at the right. But here we're dealing with writing that starts on the left.

[@courtneyksf]

Can you use " pls excuse my Dear Aunt Sally Louise Reacher" parentheses, exponent, multipcation, divison, addition, subtraction, left, right

[@michaelh7394]

In all of my science classes the implied multiplication - 2(1+2) - takes precedence over division. According to science the answer is 1, you math nerds may differ.

[@felicjandulski4986]

Omitting the multiplication operator in arithmetic operations is not allowed. This causes incorrect solutions to the task. Unfortunately, some calculators use such a notation (without the multiplication sign before the bracket) are treated as covered by an additional bracket. Therefore, 6/(2*(1+2)) equals 1.

[@gavindeane3670]

It is allowed! It is completely normal. Indeed it's ubiquitous. However, it's only supposed to be done when no misunderstanding is possible.

[@tomtke7351]

parentheses first 6÷2×(3) alternately 6×(1/2)×3 9 6×3×(1/2) 9 (1/2)×3×6 9

[@joseluiscartesvaliente5924]

(6 : 2)x3 = 3x3 = 9 6 : 2x3 = 6 . 3x2 = 6 : 6 = 1 El divisor es el producto, no uno solo de los factores.

[@Eturoel]

Distributive postulate for multiplication with respect to addition.

[@catmandubh]

I got 1. My scientific calculator also got 1.

[@gavindeane3670]

Other scientific calculators will give 9. Some implement both conventions and provide a configuration setting so the user can switch between them. Ultimately, putting this into a calculator doesn't tell you anything except which convention the designer of that particular calculator has chosen to implement.

[@gregpoehlein6654]

One of the biggest problems with this equation is that too many people think that the implied multiplication - 2(1+2) - takes precedence over division because of the parentheses. Their mistake is not that they think multiplication goes before division but that the parenthetical multiplication does. I suggest that this be specifically addressed in a future video.

[@prestwig1]

That is because in Science and Engineering ( people who actually use math) it does. In science and engineering multiplication by juxtaposition takes priority. T=pv➗nr ( the number of moles and the gas constant are multiplied together before dividing)

[@paulfrank8738]

@@prestwig1 That's not a completely true statement. There is disagreement in the Math world about where multiplication by juxtaposition should exist in the order of operations. Just like the Mathematicians, the Scientists and Engineers have not come to an agreement either.

[@pvlietstra]

Which is correct: 1) 4a÷2a=2 2) 4a÷2a=2a^2 I believe the answer is quite obvious, based on juxtaposition multiplication.

[@RusselRezaie]

That is true, and it needs to be discussed.

[@paulfrank8738]

@@pvlietstraI'm an Electrical Engineer. The only calculators approved for use on the PE (Professional Engineer) license exam *do not* use a higher precedence for juxtaposition multiplication. So, I'm going to go with the professional Engineering licensing authority's interpretation and say that the 2nd answer is correct. But like I said before, there is disagreement. Some are using and teaching the other interpretation.

[@shearermemories1963]

Hi John, I learnt the order of operations back in the early 60’s, but forgot about grouping the multiplication and division also + -. So in a previous video I got the wrong answer. This video I had learnt my lesson from that experience and happy now I wont repeat this basic error. Thanks to you, I’m thinking about relearning all my maths again to keep my brain sharp! Regarding a lot of the negative comments you get in some of your videos imo unjust from jealousy. People never change🙏I’ll pray for them.

[@billraty14]

The mere fact that a majority of people will get this wrong indicates that the mneumonic PEMDAS doesn't work, because it doesn't provide any clues that Multiply and Divide are to be treated as equivalent in precedent and AS are also to be treated as equivalent precedent. In fact, I know the meaning of this has changed over the decades (yes, I'm that old), and the way that it is treated in this video differs from how I was taught, when the precedence was in order. Multiply, then divide as the second and third steps respectively. Those of us that used RPN calculators had to reformulate the equation, and the result would come out as 1, not 9! At the very least this will make it problematic for literate adults to teach children how to approach the problem since the *meaning* of PEMDAS has drifted. It will also make kids distrustful of their parents and grandparents. Seems to me that academia needs to come up with a better mneumonic.

[@bulldog6925]

What do you do when the instructor does not follow PEMDAS and does division before multiplication?

[@jald910]

PEMDAS has multiplication and division equal precedence. Then addition and subtraction equal to each other but after multiplication and division.

[@markhoelscher4477]

They are of equal importance yes but it's from left to right

[@TheAlienPoison]

Test it yourself.

[@paulfrank8738]

I'd tell my instructor in private that they made a mistake, and hand them a printout of one of the many charts you can find online that summarize PEMDAS.

[@pippodeclown]

10 lashes for insubordination

[@dionysos6838]

So that means that representing it as a fraction with 6 as the denominator and 2(2+1) as the divisor is fundamentally wrong? Because then the result would be 1. I'm really surprised... What prohibits representing it as a fraction, because in term conversion you would never get the result

[@csc8697]

Do you do that with + & - too?

[@Joe_Narbaiz]

Yes.

[@Larrym-rz5bk]

Sadly operator presedence is taught differently by different teachers and different computer compilers handle it differently. Everyone and every compiler do agree that expressions inside of inner parentheses are evaluated first. So the solution is to use parentheses in a way to make the evaluation unambiguous. So either write it 6/(2(1+2)) or (6/2)(1+2) depending or what you mean.

[@ron6607]

I've been taught, a long time ago, to first solve the expression, in this case 2(1+2) = (2x1) + (2x2) = 6 So the final answer would be 1

[@rockcat5000]

Back in the good old days...we were taught that the multiplication associated with the parenthesis happened first, then the division. Then someone tried to "standardize" things with the pemdas way of thinking. This was arround the time that "new math" was introduced to schools. I got both answers as right, noting to myself, that the implied brackets linking the multiplication to the parenthesis was not valid by what is taught today. Go figure. That's why I no longer enjoy math. You are now wrong no matter how you think.

[@gavindeane3670]

It has never been the case that a multiplication gets precedence just because one of the terms happens to be in parentheses. Such a rule would lead to absurd results and inconsistencies. What is common though is to give implied multiplication higher precedence than division - that is, multiplication where two terms are written next to each other without an explicit multiplication operator between them. If you're following that convention then it applies to ALL implied multiplication, not just cases that happen to involve parentheses.

[@supmojo]

if you look at old math books, the mathematical operations were separated by parenthesis. the PEMDAS method is confusing to a lot of people hence these kinds of simple problem will yield wrong answers.

[@pippodeclown]

who is defining the order or sequences in general arithmatic?

[@oscarfernandez7386]

What people get wrong in PEMDAS is that in the “M” for multiplication or D for divide. In the pemdas it multiplication and or divide. So if you know that multiply didn’t work you can switch to division and then go multiply.

[@prestwig1]

@TabletClass John, So in your world 4a/4a=a^2 ?

[@Simrealism]

Back before school was about feels, this question would have been a trivia question for a free pack of fries in a McDonald's contest.

[@jerrylegion]

This is wrong. 2(1+2) counts as an entire bracket to be solved first. So 1 is the only correct answer. Otherwise you will have 6 / 2*1 + 2*2 and that equals 7. The equation does not say 6 / 2*(1+2). Your answer is based on this equation: (6/2)(1+2) and that is 9. But that's not what you ask. I've had multiple discussions with my math teachers about writing down the correct question.

[@gavindeane3670]

2(1+2) is not "an entire bracket to be solved first". That sentence doesn't even mean anything.

[@jerrylegion]

@gavindeane3670 Wrong. The correct notation of that problem should be 6/(2(1+2)). The second line of brackets though are never written down because redundant.

[@oscarfernandez7386]

It’s from left to right. My teacher would say m or d when she taught us the PEMDAS. SO IT CAN BE MULTIPLICATION AND OR DIVISION FIRST

[@gstan471]

Let me re-write your problem: 6/2(1+2) This clarifies the equation with 6 in the numerator and 2(1+2) as the denominator. Shouldn’t one simplify the denominator before considering the numerator?

[@gavindeane3670]

Credit for replacing the obelus with the proper division symbol, but you haven't clarified anything. 6/2(1+2) is exactly the same ambiguity.

[@imagseer]

PEMDAS works from Left to Right, hence 6/2*(3)=9

[@AgentFriday]

> 90% will get it wrong by thinking there is a correct answer.

[@gavindeane3670]

Judging by the comments whenever this gets posted, it's a lot more than 90%.

[@chrisdissanayake6979]

Answer: 9 ----------- 6 ➗ 2(1+2) PEMDAS 6 ➗ 2 x 3 3 x 3 =9

[@tinchin6328]

Wrong

[@georgecattani7199]

= 6 / 2( 3) . =6 / 6 = 1

[@cstout1634]

The problem with PEMDAS is that it can’t be taken at face value. Because you have to then add the rule of M and D.

[@filmtvbiz]

It really depends on the method one approaches the problem with. While at University (Boston/Engineering), I was asked by a professor to show the class how I solved the equation. End result, you could follow the text book or perform my method. As a society, people are now realizing, there are always alternative solutions, various way, and many times, “correct” is somewhat dependent on the solution one seeks. This diversity in problem-solving reflects the broader recognition that innovation often comes from thinking outside traditional methods. In engineering, as in many fields, the willingness to explore alternative solutions can lead to breakthroughs or more efficient processes. This principle applies beyond academia into everyday life and societal issues, encouraging a culture where different perspectives are valued and integrated for better outcomes. ✨♾️

[@thenetsurferboy]

Alternative solutions and alternative answers are two different things Alternative solutions means alternative methods There is only one answer to this 1 You never gave your answer

[@NEMTOMZkr]

@@thenetsurferboy wrong. It’s 9.

[@flagmichael]

@@thenetsurferboy The only rigorous method for this one is to make the meaning clear with nested parentheses and/or brackets as necessary. PEMDAS means nothing to 80% of the people in the world who do not speak English. It should have been dumped a century ago in favor of properly rigorous conventions.

[@TheAlienPoison]

​@@NEMTOMZkr Proved its 1 through algebra, replacing the 1+2 as X. If it was 9, 1+2 would equal 27, which is incorrect.

[@NEMTOMZkr]

@@TheAlienPoison😂 wtf are you talking about!? Replacing 1+2 with X? So 6/2X=9? Right, it’s equal 3X=9 which makes X=3 and 1+2 is 3🤷‍♂️🤦‍♂️😆😆😆

[@plainswell]

So I got 1 as the answer. So did the calculator on my iPad. If you really want the answer to be 9, the person who created the question should have been sensible enough to phrase it as... (6/2)(1+2)=? (edited again by me to correct my own typo) ...and prevented a lot of smugness generating errors. You say PEMDAS, but you then interpret it as PEDMAS, because super-secret reasons, not presented in the 'helpful' acronym. Makes perfect sense. Maybe PEMDAS should be PE(MD*)(AS*)... *perform operators L->R as encountered, ignoring this acronym order (you're welcome). Not confusing at all...

[@eric4709]

(6/2)(1+3) = 12? Think you meant. (6/2)(1+2) Actually ... what is interesting here is what the "divide by" symbol actually means If the question was written as: 6 ----- 2(1+2) Then that suggests you evaluate the bracket and multiply by 2 BEFORE passing "up" through the divisor line to divide into 6, which gives 1 Totally different from 6 : 2(1+2) Imo the use of the divide symbol should be avoided. Its not difficult to write expressions ( as you suggested in this case) that are unambiguous which removes any real need for pemdas. Its quite clear to anyone that parenthensis and exponents need to be evaluated first! The rest can be easily priroritised by sensible structure.

[@gavindeane3670]

If you really want the answer to be 9 you should write it as (6/2)(1+2) and if you really want the answer to be 1 you should write it as 6/(2(1+2)). Your calculator gave the answer 1. Other calculators will say 6/2(1+2) is 9. Putting this in a calculator doesn't tell you anything except which convention the designer of that calculator chose to follow for implied multiplication. The PEMDAS answer is 9. The answer 1 is PEJMDAS.

[@Bob-ts2tu]

I totally agree. As a computer programmer for a job since the 70's i learned the importance many times over of putting things down simply without the chance of any ambiguity, else you are setting a trap that either you, or someone else will fall into sooner or later, even if it means that simpler happens to be more verbose. more often it's seeing the picture as a whole and not be caught out by minor details, and that goes for anything i suppose. GL

[@louisd95714]

Strange, I got the answer 9 on my iPhone, which is very close to the iPad in functionality.

[@plainswell]

@@eric4709 Yes, sorry, my own typo to add to the confusion...

[@kathleenkumiega1092]

Got it right away!

[@kathybray2838]

1! So happy I got this one right! I’ve forgotten a lot at 78!

[@dollywilson3395]

I was taught BEDMAS! When did this change?

[@Joe_Narbaiz]

It didn't change. Just using a different acronym. The concept is the same.

[@xaiyab6892]

@@Joe_Narbaiz exactly.

[@gavindeane3670]

It didn't. PEMDAS, BEDMAS, BODMAS, GEMDAS, BIDMAS, PEMA, BIPS, BOPS, GEMS, etc... There are lots of variations of the acronym. They all mean the same thing.

[@jolantakrata1297]

6 : 2(1+2) 6 : (2*1+2*2). Li 2(3) 6 : (. 2 + 4) 6 : 6 = 1 RESULT 1 × 6 = 6 :

[@russelllomando8460]

got 9 in 1 second 3 X 3 = 9 PEMDAS rules. thanks for the fun

[@laurencebudd489]

Maybe you should have taken 2 seconds and got the correct answer which is 1

[@russelllomando8460]

@@laurencebudd489sorry, it's 9 PEMDAS in order watch the video 6 / 2 = 3 X 3 = 9

[@xaiyab6892]

There must be a lot of middle school level (or lower) educated people commenting on these videos OR there are a LOT of trolls.

[@shadowstar68]

9 remembering BODMAS - Brackets Of Division Multiplication Addition Subtraction

[@joseluiscartesvaliente5924]

Disculpe, está usted en un error. 6 : 2x3 = ? Según las tablas de multiplicar, 6 = 2x3 = 3x2 De modo que cualquier número que se divida por 6, por 2x3 Ó por 3x2, dará el mismo resultado. 6 : 2x3 = 1 6 : 3x2 = 1 6 : 6 = 1 ESA PEMDAS no está contemplada en la Aritmética, es ABSURDA. Un saludo.

[@shadowstar68]

@@joseluiscartesvaliente5924 As explained by TabletClassMath you Add the brackets first So equation becomes 6 divided by 2 times (2+1) or 6 divided by 2 times 3 So 6/2 = 3 then multiply by the 3 from solving the brackets and you get 9 PEMDAS is used so that everyone solves the sum in the same order.

[@danielbejarano2734]

9

[@357Amun]

Do parenthesis 1st, then multiplication, OR division from left to right. 9

[@ravindranponnusamy9075]

X and Y buy go to mango shop. each eat 1 mango first . After some time they eat two mangos each from the same kind. Total spend is 6 dollars. What is price of each mango? When you look at this problem you understand the folly of the explanation given in this post

[@gavindeane3670]

You've got that backwards. This video shows the folly of representing your mango story with the mathematical expression 6/2(1+2). The expression you want for your story is 6/(2(1+2)).

[@Nadia-rf8kp]

I wish you were my teacher, Bravo, Thank You.

[@Mo_Klonus]

I got 9, but no happy face at the end...

[@osgubben]

This is just silly. There is no global agreement on how to solve this. Therefore just avoid creating math more difficult than necessary. The solution is simple: use paréntesis. So: (6:2)(1+2). That gives 3x3=9

[@flagmichael]

That is my enduring complaint. If we need PEMDAS we are consigning ourselves to methods without mathematical rigor. There is no excuse for this.

[@timothysteadham331]

There is global agreement by those that know. The answer is 9. The people that are not in agreement (and therefore the reason there isn’t global agreement) are just wrong. Plain wrong. In fact, they are idiots.

[@HazratAlli-fe6kh]

9 is wrong. The answer is 1. Shocking.

[@gunfet]

If he is correct, then the expression is very poorly written. PEEDMAS is not math. It is only an agreement by American school teachers. Problems like this are never encountered in the wild.

[@sammymcclelland1071]

The answer is 1.

[@Larrym-rz5bk]

The only thing wrong here is to state an ambiguous problem. The fact is operator presidence

[@Surreal_Wizard]

Hmm... this looks exactly like one of those "Viral Math Problems" on Presh Towelwalker's "Mind Your Decisions" channel. Might even have been this exact one. Basically, according to the current standards of math, the correct answer should be nine. However- and Presh Towelwalker does talk about this a little bit on his channel- many people were taught that the expression 2(1+2) is always evaluated as a single expression grouped together, so the whole problem would be evaluated as "Six divided by...the product of two times three," or in other words, one. That was how I was taught (and apparently 90 percent were as well?) That is not technically correct.

[@gavindeane3670]

Presh has done this exact expression, and several similar videos covering other forms of the same expression like 8/2(2+2) and 48/2(9+3). In them he explains the PEMDAS interpretation but doesn't discuss the PEJMDAS interpretation. Both interpretations are as correct as each other. That is the entire point of this meme.

[@kb5elv]

Please excuse my dear aunt Sally says that the answer is 1.

[@gavindeane3670]

No, PEMDAS says it's 9. PEJMDAS says it's 1.

[@flagmichael]

If many will get it wrong, it is written very poorly indeed. Ditch that silly PEMDAS and BOMDAS; use parentheses and brackets, nested as necessary. More than 80% of the world does not speak English and wonders what "PEMDAS" means.

[@DominicPandolfino-xu5ud]

I’m a genius.,also I really like this lecturer,his delivery and his wry sense of humour!!

[@unknownname-t8z]

6/2(1+2) Brackets = 6/2(3) Indices Division = 6/2(3) = 3(3) Multiplication = 3(3) =9 Addition Subtraction

[@unknownname-t8z]

if working with brackets confusing do like this. 6/2(1+2) 6/2 *3 3*3 9

[@travershipkiss]

Using that divide symbol is the real issue.

[@kb5elv]

...And that's why I never got past high school algebra.

[@AbdulKhan-gu1gk]

Can be 1 or 9. Depends if you follow bodmas or bima

[@gavindeane3670]

BODMAS and BIMA are the same thing. It depends whether you follow PEMDAS (which is the same as BODMAS and BIMA) or PEJMDAS.

[@flagmichael]

@@gavindeane3670 All mathematical heresy; 80% of the world's population does not speak English and would have no idea what the acronyms mean.

[@gavindeane3670]

​@@flagmichaelSo what? What I wrote is accurate and does not presume that everyone in the world speaks English or uses these acronyms.

[@GenaroCasugbo]

1 answer

[@motrebal]

Thank you I have learnt something at 63

[@kb5elv]

Oh crap. I got it wrong. I forgot that yes, you do parentheses, and multiply and divide before you add and subtract, but multiply and divide work left to right. Crap on toast.

[@debbieholoquist2059]

LOL! You startled me with that happy face on the =1. You being cute!!

[@danimass6067]

I thought multiplication is before division. So wouldn't that mean solving 2(3) first then dividing that by 6 to get 1?

[@gavindeane3670]

In the video he's evaluating it according to PEMDAS, which gives multiplication and division equal priority and simply evaluates them left to right. That means division first in this case.

[@kraken9234]

I disagree! The answer should be 1 When a number is adjacent to the parentheses, it is multiplied into the parentheses before other calculations. The same as 2(x+1). The 2 has been factored out of the expression in the parentheses.

[@xaiyab6892]

no, it is not. PEMDAS. Parentheses is ALWAYS FIRST (meaning what is INSIDE the parentheses only. factoring does NOT take precedence). Then Exponent, Multiplication/Division (left to right), Addition/Subtraction (left to right).

[@gavindeane3670]

There's no reason to assume that just because a number is being multiplied by a bracketed sum, that number must have been factored out of the brackets. It MIGHT have been factored out, but to assume that it MUST have been is completely baseless and completely silly. And anyway, even if you are going to assume that here, how do you decide whether the number that has been factored out is 2 or 6/2?

[@nowaynotthatway3487]

Order of operations.

[@MatthewKessler-u7b]

The answer is 9. Use PEMDAS METHOD. solve the bracket first (1+2)=3. Then do division over multiplication from left to right. 6÷2=3 then 3×3 =9

[@JeremyTibbitts-w5v]

6 divided by 2(1 + 2)= 6 devided by 2 = 3(times 2= 6

[@mikeanndavis]

Must be one!

[@Joe_Narbaiz]

No it doesn't.

[@brucew845]

Yes, it is 1. This is A/BC; where A=6, B=2, C=(1+2). I've recently heard the word "juxtoposition" to refer to BC, but I learned it as a given.

[@Joe_Narbaiz]

@@brucew845 The solidus (/) or the obelus (÷) do not have the grouping properties of the vinculum (---). So 6 is not the numerator and 2(1+2) is not the denominator.

[@Joe_Narbaiz]

@@brucew845 Juxtaposition is a math concept not an actual math operation so it doesn't apply to the Order of Operations.

[@jimcameron7846]

math gymnastics. the real situation is the problem statement is missing. seldom do these jumbles of operations have purpose. problems have an order of operations specific to a situation. and that order is whatever the numbers represent and the solution definition. not PEMDAS.

[@supmojo]

90% will get it wrong but not if they use the old rule with parenthesis.

[@arnebendixen9917]

It's 9 by my math.

[@ianjacoby7280]

obvious the answer is 1

[@Eldooodarino]

Snore. Just don't write ambiguous expressions and everything will be fine.

[@darlene675]

9 order of operations

[@dawnradel9008]

1 I fell into the trap. LOL Should be 9

[@theeardrafter]

then the PEMDAS law should be scrapped This answer is 1 in my world

[@xaiyab6892]

If ignorance is bliss, you must be VERY happy.

[@paulfrank8738]

What I heard is, I don't know the order of operations rules well enough to get the right answer, so the world should throw away a well established Math convention that is used by millions of people daily.

[@brucew845]

Yes, this is A divided by BC where A equals 6, B equals 2, and C equals 1+2. If B and C are not reliant on each other than there would be a times symbol.

[@paulfrank8738]

@@brucew845 Except the order of operations does *not* distinguish between multiplication with or without the symbol. "AB", "A*B" and A(B) are exactly the same as far as the order of operations are concerned. You (or someone who taught you) has added interpretations of those different methods that didn't exist before. I personally "blame" computers. Prior to computers we would have written A ---- B C or A ---- C B When we move it to one line, too many people started writing both of those expressions as: A/BC The first one should be A/(BC).

[@gavindeane3670]

Not scrapped. Just extended. What you've done is PEJMDAS.

[@ObserverDingue]

i'm going with 9, now let's see...

[@zurinakasim2918]

BODMAS ( ) ÷ x + - 6÷2(1+2) step 1: 6÷2(3) ( ) step 2: 3(3) ÷ step 3: 9. x

[@Bob-ts2tu]

the acronym is pretty useless really, it gives an order to do stuff, but too easy to misinterpret if you don't know or appreciate the additional rule which is what the question is all about. when i was at skool over 50 years ago it was called BODMAS, but although in this case sticking to BODMAS would yield the right answer, that too falls over in different circumstances. anyhoo, thanks for the explanation haha.

[@gavindeane3670]

It's still called BODMAS. And PEMDAS. And BIDMAS, BEDMAS, GEMDAS, PEMA, BOPS, BIPS, GEMS... There are lots of varieties of the acronym. They all mean the same thing.

[@tomasnicholas1881]

The problem should be rewritten using parenthesis....as....(6/2)(1+2)......NO confusion...please respond

[@emmanuelmwesigye6519]

Is the answer 1? 3*2=6 6/6=1

[@margaretflowers5722]

(MD) (AS)

[@advancedautomotivemachine4791]

9 got it in 15 seconds :)

[@nowaynotthatway3487]

Brackets first.

[@billmclaurin6959]

9 via BODMAS