You were taught correctly because a(b+c) = ab+ac It's called distribution and this is how parentheses/brackets are solved in equations. The answer is 1.
@@aliciastoaks1955 lol please Alicia. If a human brain can't use logic, how do you think calculators process data? In other words, if you want to use a calculator, use a decent one such as the Casio fx-570 which recognizes distribution when inputting equations. (I have it. Answer is 1. "Calculators don't lie") If a(b+c) = ab+ac then d/a(b+c) = d/(ab+ac) In English: you have 6 dollars and you divide them among 2 groups consisting of 1 boy and 2 girls. How many dollars does each kid get?
When I was in school, we learned the distributive property of multiplication, a(b + c) = ab + ac, thus 2(1 + 2) = 2*1 + 2*2, so 6 divided by 6 equals 1. We always simplified parenthetical operations first, which included any multiplier adjacent to the parenthesis. One other precept about the distributive property of multiplication, a(b + c) is NOT the same as a * (b + c). In this instance, the elliptical 1 is adjacent to the parenthesis, i.e., (b + c) = 1*b + 1*c. We even call it differently. 2(1 + 2) is described as 2 parentheses 1 plus 2, whereas 2*(1 + 2) is described as 2 times parentheses 1 plus 2. 2a is a single number, whereas 2 * a is not. The same with 2(1 + 2); it is treated as a single number, 2 * (1 + 2 ) is not. If written 6 divided by 2*(1 + 2), the answer is 9.
Yes, And I think the algebraic rules of mathematics applies also to the arithmetic of this problem. Otherwise, algebra and arithmetic have different rules ... and that makes no sense at all.
@@larrymotuz6600 Mathematics consists of dozens and dozens of rules that have to be memorized. I was amazed in College level introduction to mathematics how the first page consisted of about 12 different rules of solving equations. So everybody in class got the same answer as the textbook.
how about this: multiply out: 2(1+2) to get 2+4? 6 divided by 2 plus 4, 3+4 = 7? just kidding. I remember the historical rule from the 60s and i prefer writing problems down where there is no confusion. PEMDAS works just fine for me.
One other precept about the distributive property of multiplication, a(b + c) is NOT the same as a * (b + c). In this instance, the elliptical 1 is adjacent to the parenthesis, i.e., (b + c) = 1*b + 1*c. If written 6 divided by 2*(1 + 2), the answer is 9.
The answer is 1. And I’m sticking to it. SCARY how they can just inadvertently change the rules when people have been using them for ages. To all the young ones working for us adults - I’d hate to be you when there’s a wrong calculation in a life and death situation!
I Don't agree. I'm from 1961, so 2 years old now. Even I was tought to resolve this exactly the way as explained in this video. So apparently, nothing has just inadvertently changed sicne then, at least.
@MrGreensweightHist I would interpret it as 9, but the consensus amongst mathematicians is that it is ambiguous. It's a convention problem and there isn't a 100% consensus on what the convention should be.
The answer is 1. Math was never meant to be subjective; if it was, then we would've missed the moon by miles. But we live in an age where education has to be changed either because someone arrogantly thinks the way of doing a task is outdated or it hurts someone's feelings.
I'm 43 born 1980. My answer was 1 because that's how I was taught...My gripe is, I don't have a problem with changing the formula, equation, or steps because times are different, but when the actual answer totally changes, then "Houston we have a problem". Like my man said before me, that's the difference between landing on the moon and missing it by a mile
I was born in 1970 and I understand it exactly as you do. I understand that the rules have changed, but for people our age there was no publicly available information about the change of these rules. So the outcome of this equation is age dependent, because at some point the rules changed?
@@edeco9135 The rules haven't changed. You were simply taught "pemdas" which has led you to believe that multiplication takes priority over division, which has never been the case.
I'm still in the school system, an undergrad in ME... and I honestly don't like "pemdas" either. However, I think the critical problem here is the lack of specificity that comes with the general division sign. A well constructed equation should not be concerned with the direction in which it is read, and the only reason the exception exists here is *because* of the ambiguity of a sign dedicated to division operations. When it comes to other operations, people are generally in agreement: grouping terms or functions, then exponents, then multiplication operations, then addition. The sign itself is indicative of its role as a placeholder for the expression of division by a fraction, but by removing the numerator and denominator it makes it unclear where the grouping terms are for what can be expressed by a negative exponent. When dealing with "pemdas," even under its guiding rules exponents take precedent-- and when dealing with the general division sign, the exponent is what would otherwise place a term in the denominator. When written in fraction form, this exponent relation is assumed. When performing operations within negative exponent spaces, the direction of the exponent is treated as its inverse and typical operations can then apply. Even when I use a calculator, I make sure to include extra grouping terms to make it impossible to misinterpret where the group lies. In extreme cases or when taking a reciprocal of a larger expression, I often times substitute fractions or division signs with the exponent of -1. However, communicating this relationship even to students in higher level mathematics can be difficult. While I can admit the merit of having inverse operations treated as their own "things" when first teaching the concept of operations, subtraction and division are redundancies that aren't really discussed in the same manner in higher level math courses. When these redundancies are removed, the order of operations is much more seamless and sensible. While subtraction and addition are arguably interchangeable and the condition it poses is mostly negligible, division's general sign complicates what would otherwise be a fairly straightforward problem if it was given the proper space to communicate. EDIT: Also worth mentioning there is a practical application in which PEMDAS is standard, that being computing. Again, this comes down to convenience and ambiguity. There are numerous ways of saying, say, 6/2x. However, (6/2)*x is a less convenient expression and requires more context-sensitive interpretations on the part of the written software. When reading left to right, it can be easier to assume different cases that would otherwise be inferred in different ways when doing this work by hand. In a way, this is an answer to @aliciastoaks1955. Calculators read what you give them with a limited set of tools. Can they be made to interpret them without PEMDAS? Most certainly. However, I think part of the push to adopt PEMDAS beyond primary education may be associated with the rise of software development and the use of more rigid computational tools. What the calculator gives you back depends on how you've interpreted the equation... and in the case of 6/2(1+2), it again raises the barrier of communication on the part of the expression's source. However, writing the expressions in the simplest terms for lots of smaller term-by-term calculations would give PEMDAS the edge and encourage more clarity on the part of the user who chooses to reduce more complex equations. This may also explain why my favorite calculators don't just accept the general division sign, but rather prompt you to input a complete numerator and denominator. When a calculator is not built for doing quick and simple operations, the user's convenience is addressed in this way. As an undergrad in a STEM field, complex equations are just about all I care to work with-- as such, I gravitate towards the calculators which refuse the lack of clarity that the general division sign brings.
Order of operations, PEMDAS, Muiltiply comes before divide. The order of operations should be written as PEMdAS to show divide goes in the same operation as multiply.
Her mistake came when she removed the parentheses from the second step and replaced them with a multiplication sign. She correctly brought the parentheses down, but then magically disregarded their meaning and importance.The parenthetical expression was written for a reason. 2(3) is still a parenthetical expression and must be solved before doing any multiplication or division left to right.
That’s what I was thinking… regardless of the operation with inside the parentheses, now the whatever number solution inside the parentheses, must be multiplied, as the parentheses itself is demanding priority not just the action within it…
My answer was 1. Probably because I learned the more archaic method back in the 60s as a child. I appreciate you giving me the understanding of how others can arrive at a different answer. While it is true that Math is Math, it must be communicated properly under an agreed upon set of rules so that everyone involved reaches the same conclusion. In Engineering, this sort of problem can make the difference between landing on the Moon or missing it entirely.
order of operations state that when multiplication and division are both available, you go left to right. So this problem is 6÷2*3 The paranthesis only means you do what is inside the paranthesis first, it does not mean you use the answer from inside the paranthesis first.
Your answer of 1 is correct. Unfortunately, people not well tought at an early age have the same right to express an opinion as those who did get themselves an education. This is where the problem lies. And if this continues, the consequences will be catastrophic. 2(1+2) is an expression in itself and must be done first because there is no operation sign between the number 2 and the first bracket, which means that within the expression, the multiplication operation must be done irrespective of what is going on on either side of the expression.
Even if you follow the PEMDAS order of operations, which she correctly describes, and then does INCORRECTLY, the answer is 1. There is no "pre-1917", there is no "post-1917". PEMDAS is PEMDAS. Multiplication BEFORE division.
My answer is 1. I graduated high school in 1999, and we learned the PEMDAS method. Math was one of my strongest subjects in school. My son is going into his junior year in high school and is really struggling with math. Now, I understand; it's because the way I explain how to solve problems at home is different than what is taught at school. This is extremely frustrating and school districts should be ashamed of themselves. How in the world are parents supposed to know how to teach our children when the method of solving problems has changed? #disgustedanddisappointedparent
My dear we are in the same boat. I also graduated in 1999 and then went on to higher learning. I also got 1. Now my son says my Math is confusing, because the way and methods I give him are all wrong compared to his teachers. We do the same problems and most times our answers are different. We both confuse each other !! At times I'm even afraid to assist him for fear he will get his answers wrong as happened before !! Smh.
@@merloctave22 you both think multiplication always precedes division when it does not unless it is the first action in the left of an equation. You literally ignore 6÷2 because you think the friggin' bracket is a permanent feature, and somehow, the 2 in 2(1+2) is also contained within the paranthetical equation. It is not, nor does 2(3) (2×3, savvy?) precede 6÷2 in the order of operations. You're literally messing your own kids up. Do either of you think you know better than your kids teachers in any other areas of their educational experience ...? I ask because you've just proven conclusively that you do not.
I graduated in 2002. I also did 3.5 years of undergrad work. Math is my strong suit. So why do you do the multiplication before the division? That does not fit BODMAS/PEDMAS/PODMAS, etc.
Then either you werent't tought the PEMDAS method correctly, OR didn't pay attention. PEMDAS clearly states the precedence of operations and the order to evaluate operations. As the precedence of multiplication and devision is equal (as is with adding and subtracting), one has to evaluate operations with equal precedence from left to right. It actually is quite simple, if one just remembers the correct way to apply the PEMDAS method. I'm from 1961, and even I was tought to resolve this the way as explained in the video.
That "special rule" is how I learned to do it. The explanation was that the parentheses indicated you had to work that part as one side of the equation; otherwise, a multiplication symbol would have been used. The presence of the operational symbol, as opposed to the parentheses, was what indicated how to work the problem. No idea when that rule got thrown out, but I can't look at a problem like this and see it any other way.
Mr author you are completely wrong . 6÷2×3 is not 6÷(2×3) if you use pemdas then you , then it is 6×3÷2. You can use the rule for division. Multiply and invert. maha chootia
Bottom line is that no one should write ambiguous mathematical expressions. I have done tons of calculations in college and my engineering career and I have never seen an equation that posed any issues like this -- except when someone wants to make a hypothetical case on how to use PEMDAS.
Yeah, if this were a novel and no one could understand the sentences as written, such that everyone had different interpretations of basic facts and orders of events, you'd blame the author, not the audience. This "viral math problem" trend is nonsense clickbait. And I'm guilty because I clicked here also. And I hate that.
@@Gideon_Judges6, maybe ambiguous isn't the right term. But my point is simply that too easy for too many people to fail at PEMDAS, and this problem is one example. So maybe it's technically not ambiguous, but it results in multiple answers even with people who do quite well with algebra. So I say it's silly to write problems in such a way that some people will make mistakes. There are always better ways to write a problem to make it more clear and less likely to incur errors.
The problem is, the substandard level of education these days. The problem is NOT ambiguous if you were educated properly... which it appears, sadly, that a sizeable number of people were not, and thus come up with the bogus and incorrect answer of "9". ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-lLCDca6dYpA.html
That there is confusion over which method of interpretation is correct is in itself a convincing argument for proper use of brackets to eliminate any possible ambiguity. No mathematical operation should ever be written in such ways that the order of operations is open to interpretation.
I actually did this as a purely algebraic equation using variables (as I would if it were a computer program). The thing which is being explained here is totally wrong in the first half because of the ambiguity as you noted. y = a / b(c+d) is not the same as y = a / b * (c+d) How the problem is actually written the b is factored from (bc+bd) and how it is written would be 2 sets of (itemC AND itemD). Without the * (multiplication operator. Maybe I should do my own video, not bringing up PEMDAS as I was simply just taught order of operations. Nothing about using mnemonics to make it "easier". Knowing the concepts of what actually is presented is really the way to solve it. Especially if you want to get into higher math like Calc and DiffEQ. Or solve problems in physics or thermodynamics. As I said I solve these equations number "agnostic". Making it all variables and solving the equation as it is written and not adding in extra operators that don't exist.
@@noomade American mathematical society doesnt say you change 2/2(2+1) to (2/(2(2+1). That makes no sense lol. Multiply is inverse of divide. One inverse equals the other. Either undoes the other. Addition is inverse of subtract. One inverse equals the other. Either undoes the other. Bloody hell man. :P
@@noomade 2(X) is two X's. Hence 2 times X. I.e 2*X 6/2(X) is three X's, hence 3 times X. I.e 3*X. You keep forgetting that 6 at the beginning. If you want to use 2 first you need to write 6/(2(x)). Then you can do the 2 first, because 2 has priority over the 6, and the X has priority in the parenthesis, because it has its own parenthesis. I am swedish by the way. The reason is that multiply undoes division, and division undoes multiply. They're the same order, whatever comes left first comes first in the order. Solve the parenthesis first, then solve exponents, then solve multiply/divide, whatever is left most, then solve addition/subtraction, whatever is left most.
@@noomade I work in the .EDU sector in IT. However my intended path of a career was for meteorology before I dropped out and went into IT. But 3 years of Calc/physics/thermodynamics etc. precovod I used to sit with a bunch of faculty and deans (one of them was an associate dean in the math/sciences division) talkong about how badly the k-12 are teaching kids in math. We have classes at a college teaching fractions (3rd-4th grade math) as it is a new concept to students. Teachers in k-12 are failing the students by PASSING them when they don't know the content.
No left to right rule. Just add enough parenthesis to remove all ambiguity and work from the inside out. This problem was written incorrectly and uses an obsolete symbol the obelus, ÷, that should not be used anymore. Remember a/bc = a/(bc) not (a/b)*c.
The equation is deliberately imprecise to provoke discussion. It's why even well-educated mathematicians are disagreeing, why different calculators and tools produce different results and why there's still no clear answer even though the puzzle has been floating around for years. If you're asked to perform this calculation for anything more important than a Facebook survey, ask where the equation came from and clarify exactly what was intended. Either add parentheses, rearrange the terms, or format it such that all fractions are unambiguous numerator-over-denominator fractions.
@@Andrew-it7fb it's not ambiguous, unless 1/2x might be the same as 2/x. With expressions containing juxtaposition you have to use PEJMDAS, not PEMDAS, which is why it's astounding that a mathematician would get this wrong.
I had many of these equations growing up and it was drilled into us that operations inside brackets go first, then adjoining bracket multiplications and then left to right operations. Changing that long standing principal is insane and is the product of the dumbing down Signs, Operations and other non-numerical characters all mean something. Ignore them at the peril of being wrong in life even if the instructor believes otherwise.
Until at least 1970, university entrance maths in Australia used the latter method, giving 1 as the correct answer. It annoys me that something as critical as maths can be altered over time. As many posters here have indicated, we were taught the process which gave the answer 1, until quite modern times. Ps never had calculators back then to confuse the issue. 😇😈 We also used slide rules, and logarithmic tables, and learned quite complex mental arithmetic from an early age.
it is interesting as I believe in algebra it is still answer of 1 as the divided by is written as a fraction where 6 is a numerator and 2(1+2) is the denominator but maybe that no longer applies? We would never have written it in this form with a divided by sign like this so the problem would never have existed! 🤣
@@dat581 because you are reading 2(1+2) as [2(1+2)] as regards the numerator. If the latter were true then the answer would be 1. In the absence of the bracket, the answer becomes 9. People have gotten too used to seeing complex denominators as a single number instead of seeing the fraction as a linear equation. Applying order of operations to a linear equation as written without extra parenthesis or brackets gives you 9. You only get 1 when you try revisualize the linear equation as a fraction and presume the denominator should have those extra brackets or parenthesis that were not written ion the linear equation in the first place.
@@Shepherd1OFH you don’t need a bracket around 2(1 + 2) because it is a parenthetical statement with a implied operator which only works on the parentheses. This comes directly form factoring, and factoring must give the same answer forward and reverse so 2(1 + 2) = (2 + 4) = 2(1 + 2) = 6
""MATH IS MATH! YOU CAN'T CHANGE MATH!!"" And yet here you are doing the math wrong. When you were born is irrelevant,. The answer has been 16 for over 500 years. P.S. I was born in '73 so no, you don't get to hide behind "iN mY dAy". You're just wrong.
@@MrGreensweightHist if what you say is correct, then everything I was taught about factoring no longer applies. Because if you factor the 2 into the 1+2 that is inside the parentheses you end up with 6÷6 or 1. If this had an exponent in it, the expression 2(1+x) factors into 2+2x to get rid of the parentheses. If you plug the first 6 back in it would read 6÷2+2x=? once the 2 is factored into the parentheses. Go off of order of operations at that point and you get 3+2x. Knowing that the x is actually a 2 in the original equation you get 3+4 which is 7. That method is ridiculous as 7 is not even the same answer as the "9" that this video is defending as I assume you are even though you somehow came up with the correct answer being 16 for the last 500 years. Taking factoring into account as a tool or rule in math it proves that this method does not work without inconsistent results. The fact that the original problem is written out as 2(1+2) is stating that 2 is multiplied by whatever is in the parentheses. Otherwise it would have been written as (6÷2)(1+2). You are wrong. This method is flawed. And you are in outer space if you actually did somehow came up with 16. (I'm assuming that was a typo)
@@MrGreensweightHist and I assume you are hiding behind some form of "I have a higher education than you do, so stop thinking, and take my superior word for it"
@@MrGreensweightHist Watch the following linked video and you will see where this flawed interpretation of mathematical expressions came from and why it is wrong. ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-4x-BcYCiKCk.htmlfeature=shared
I'm a math / stats major and currently an Actuary. In my humble opinion, all of this doesn't help the situation. It just helps people who are doing it incorrectly not feel bad for doing it incorrectly based on a precedent most of us were not here to see. We need to hammer into people that it's multiplication or division and addition or subtraction which ever comes first left to right. Or even better, that division is multiplication and subtraction is addition and then we can drop 2 letters from PEMDAS (aka "please excuse my aunt," sorry "Dear Sally"). For the historical precedent, that confusion is the same phenomenon of misusing a comma. The interpretation of the person reading it can easily be confused. If we all just agreed as a community to write it this way (6)÷(2)×(1+2) = 9 and (6)÷(2×(1+2)) = 1 we would never have to talk about this again. However, as any math person will tell you, we only write in short hand (except when coding because computers were personally built to shit on our ambiguity 😝). Thus people 100 years from now will still be debating how to multiply, instead of learning about all of the much cooler / yet to be discovered math topics because we lost them a long time ago, lol. Side note speaking of commas I probably misused or didn't use several. I'm a math guy, what do you want from me!! 😂😂
The point is, it was not written that way.. It was written, such that the resultant should be one.. 9 in a real world application, outside of binary conversion math, would result in err.
A viral math problem, like almost all viral math problems, comes down to poorly written or expressed problems. Having to rely so heavily on order of operations to make headway with a problem only tells me the problem could be written more clearly.
"like almost all viral math problems, comes down to poorly written or expressed problems" Exactly. Those are for people who look for problems like 0/0 as if it would be the core and reason of existence of mathematics.
Bingo! This is not a math problem. This is an arithmetic convention problem. PEMDAS is merely a convention that allows for shortening expressions by removing unnecessary brackets. This expression needs at least one more set of brackets to have a "correct" answer and really needs better use of symbols overall. It tells me the person writing it doesn't really understand math and only has a basic understanding of arithmetic conventions.
@@forbidden-cyrillic-handle "So basically ill defined problem. I.e. it has no value as the expression is invalid." I disagree. The expression is quite valid. The issue is that the parenthisis needs to be fully evaluated, which includes any operation on the parenthesis. Only then are you to move on to the next step in the order of operations.
@@forbidden-cyrillic-handle no. the implied multiplication is on the content of the parenthesis. That is, an operation of multiplication on the content within the parenthesis. This needs to be evaluated to fully remove the parenthetical component of the order of operations.
The P and the B represent the (). Removing the () requires performing the representative operation. Therefore in this equation, clearing the brackets 2(1+2)= (2+4)=6 or 2(3)=6 Simply performing the addition within does not complete nor clear the (). The operation dictated by the brackets must be accomplished before proceeding with the next priority. If you agree that 6=6 then let’s do some factoring 6=2(3), or 6=2(1+2), or(3+3)=6[1],or 24/4=3(18)/9=54/9=6 They all = 6 employing algebraic rules and or pemdas. Therefore6/6=1
You should note that 2 outside the parenthesis is a common factor of 1 and 2 inside the parenthesis. To understand the problem better, first you have to multiply the group of the numbers inside the parenthesis by the common factor outside while retaining the brackets to maintain the group, giving 6÷(2+4) Next, collect like terms of different groups: 2 and 4 are like terms and their sum gives 6, resulting in 6÷6 Finally, 6÷6 = 6/6 = 1. My dear nothing to be confused about with this simple problem. We must first understand a problem before thinking of any rule written by a group of individuals. Parenthesis is used to group terms that could be treated alike, meaning that before it is removed, the terms must be evaluated into a single product. Remember any expression outside a parenthesis without an operator is a common factor of all terms inside the parenthesis.
You're forgetting that although you're supposed to do the math inside the parentheses first, that doesn't change the left to right order with division and multiplication. Once you've done (1 + 2) = (3), then the problem becomes 6 / 2 * 3. Process that left to right. 6 / 2 = 3, 3 * 3 = 9. The confusion with this sort of math problem is in the nature of the implicit multiplication rule when a number directly precedes an open parenthesis. Whenever you see a number in front of a parenthesis, you should first go ahead and insert the implied multiplication so things make more sense... 6 / 2 * (1 + 2)
@@southernflatland Mathematical symbols and their usage have _meaning_ beyond the simple rules of pemdas. 6 / 2(1+2) does NOT mean the same thing as 6 / 2 * (1+2), otherwise it would have been written that way. The implied multiplication is there, but more is implied than just multiplication: when the author of the mathematical expression deliberately omits writing the multiplication symbol between the "2" and "(1+2)", the author is stating that there are two of the quantity within the parenthesis. If you follow the pemdas rules explicitly, you are not allowing the intention of the author to be represented by the expression, and the expression must instead be written in some very cumbersome way that confuses its meaning, such as "6 / [2*(1+2)]", or even worse "[2*(1+2)/6]^(-1)".
@@PsychedelicChameleon This is the difference between formal written mathematics and modern day programming. In formal written mathematics, *inside* the parentheses should be processed first, but outside of the parentheses should be treated as an implied multiplication, to be processed left to right. In programming though, it's much more common to treat every X(Y+Z) or similar syntax as a function and completely eliminate the parentheses first.
@@southernflatland Thanks Brian. In your explanation of both "formal written mathematics" and programming, what is inside the parentheses gets treated and reduced to a single expression first. I think that what you are saying is that in programming, immediately after processing "Y+Z", say into "W", then the function X(W) is processed next before the division takes place. What I'm saying is that PEMDAS is a short-hand set of rules to attempt to standardize and formalize the order of operations in educational settings, but that it does not correctly account for every situation that arises in math, particularly when the author of an expression is trying to state something that doesn't get a specific symbol. So in the given example, the "formal written mathematics" is incompatible with PEMDAS, since the author of the expression is clearly stating that there are TWO (Y+Z) values, and is not stating that 6 should be divided by 2. In this example, the written expression is specifically written this way so that the computation should be done the same way as how you are describing it would be done in programming. This is part of the difference between how math expressions are actually used to represent situations, and how math is taught. This difference is well known to many mathematicians, physicists, chemists, and I presume to many programmers as well. In the wikipedia article about order operations, the "special cases" and the programming languages sections take up about a third of the article, specifically because they don't perfectly match the PEMDAS rules. Here are a couple excepts: "Mixed division and multiplication: In some of the academic literature, multiplication denoted by juxtaposition (also known as implied multiplication) is interpreted as having higher precedence than division, so that 1 ÷ 2n equals 1 ÷ (2n), not (1 ÷ 2)n." and "This ambiguity is often exploited in internet memes such as "8÷2(2+2)", for which there are two conflicting interpretations: 8÷[2(2+2)] = 1 and [8÷2](2+2) = 16."
I began with multiplication as you do the operation in brackets first. So 1+2=3, then multiplication before division so 2x3 =6 and finally 6/6=1. I learned PEMDAS (Parentheses, Exponents, Multiplication Division, Addition and then Subtraction) at school.
Then you learned PEMDAS incorrectly. PEMDAS has always been a way of helping children learn the basics but if you want to see how it should be written it would be more like PE(M/D)(A/S) because, like was explained in the video, if you are doing multiplication/ division or addition/ subtraction it is done in the order it is written. Those steps are simultaneous, PEMDAS is just as accurate as saying PEDMSA. So: Parentheses Exponents Multiplication and Division Addition and Subtraction
After adding 2+1 inside the parentheses you get 3. 3 is the only number left inside the parentheses. The parentheses has been solved. Only thing that is left is division and multiplication. Since the entire rest of the equation is division and multiplication you solve from left to right which means 9 is the correct answer.
If the rules have been changed from the historical way of processing the operations, then the math expression should also be written in accordance with the new rules to avoid ambiguity. In this example, an explicit multiplication sign shall be inserted between 2 and (1+2).
Appropriate brackets would resolve the issue also (6/2)(1+2) for 9 6/(2(1+2)) for 1 This is in line with modern international standards like ISO-80000-1 then which addresses one line division.
@@leogrande9977 yes I do. YOU don't understand it. Juxtaposition literally means "side by side" It is used for a coefficient and variable combination, which are treated as one term, such as 2x. Do you see a coefficient and a variable in this problem? I sure don't.
@@leogrande9977 allow me to demonstrate... We have two problems 20/2(x) = and 20/2x = We cannot solve these ebcause we do not know what x is. Then we are told, let x-5 Now we are cooking. We plug x into the first problem. 20/2(x) 20/2(5) 10(5) 50 We are done. Yes, this is the correct answer. this problem did not have juxtaposition. The other problem, however, does. 20/2x = If we just plug the 5 in for x it would look like 20/25, but that is completely wrong. This is where Juxtaposition comes in. Because the 2 is DIRECTLY attached tot he x, we put the 5 in by doing multiplication by juxtaposition. 2*5 is 10 We now replace the entire 2x with 10 20/10 2 This is the correct answer for the second problem, and the correct way to use multiplication by juxtaposition.
wrong. order of operations state that by rule when there is division and multiplication available, you go left to right. 6÷2*3 You do what is inside the paranthesis first, but then the other rule kicks in
In Figures and Sentence: 6/2(1+2) Parentheses first = 6/2(3). No exponents. Division appears first from left to right = 3(3). Multiplication is all that's left = 9.
@@TubeScavenger Symbols of Multiplication : Dot, X , Bracket, Parenthesis and Exponent ! .... On Order of Multiplication : Parenthesis /Bracket then Exponent with Simple Dot/ X or Words - Multiplied By follows . In our days it's just simply My Dear Aunt Sally !
The inadequacies of the people programming modern calculators should not be allowed to influence the way basic mathematics is taught. If you have 6 oranges, and you wish to divide them between 2 groups, and each group consists of 1 boy and 2 girls, how many oranges does each child get? According to your 'correct' answer, the children would get 9 oranges each. They don't. If you follow the order of operations correctly, you have not fully resolved the parentheses until after you have completed the multiplication of whatever is inside them by the external number attached to them. Therefore... 6 / 2(1+2) = 6 / 2(3) = 6/6 = 1.
Debugging a programming line of more than one arithmetic process requires a programmer to teach the computer from it's left to right "PEMDAS" calculations. So then if the programmer finds out an evaluated "9" results in a debugging line then the programmer corrects it by adding the parentheses now not so redundant: = 6 / (2 . (1 + 2)) line instead of = 6 / 2 . (1 + 2) in error of your instruction coding to left to right computer calculations.
Just because you process the math inside the parentheses first doesn't change the left to right order. The number outside the parentheses acts as an implied multiplication. Rewrite the problem first to explicitly express the implied multiplication so it makes more sense, then follow left to right PEMDAS... 6 / 2 * (1 + 2) 6 / 2 * 3 3 * 3 9
Would you say you have resolved an exponent in any given equation while it is still there? No. In order to fully resolve it, you need to remove it from the equation. The same applies to parentheses. In order to fully resolve them, you need to remove them from the equation. In this instance, that means you need to apply the multiplicand. Then you can move on to the next step of PEMDAS. Changing the equation by adding an extra multiplication sign naturally changes the outcome.
f÷f = 1 All variables have coefficients. This actually means 1f÷1f = 1, we just don't write the 1's. By your logic, if f=3 1(3)÷1(3) = 3÷1(3) = 3÷1*3 = 3*3 = 9 but f÷f = 1 f÷f can't be interpreted as f*f
The answer is 1. NOT because of some special rule from 1917, but because you can't "convert 2(3) into 2x3" like you said. They are NOT equivalent and interchangible things. The parenthesis exist in the expression for the sole purpose of telling us that they must be dealt with first, and you're just replacing them with multiplication so that you can do the equation in whatever order you like. Wrong. The ONLY way to remove the parenthesis, when there is an associative factor (the 2 in this case) is to multiply that factor. It's called the Law of Distribution. 6/2(1+2) =6/(2x1+2x2) =6/(2+4) =6/6 =1 Even if you add the (1+2) first you wind up with 6/2(3). You still have parenthesis and you can still ONLY remove them by using the Law of Distribution, by multiplying by the 2. You can NOT convert it to 6/2x3. Forgive the use of the /. I haven't found the division symbol on this keyboard yet. Before anyone says anything about me 'inventing parenthesis', I didn't. The Law of Distribution states that, when there is an associative factor, it is treated as if it were inside the parenthesis. Consequently, calculators that recognize distribution give the correct answer of 1. Those that don't give 9.
The critical mistake in this demonstration comes from her rewriting the problem from 6 / 2(3) to 6 / 2 x 3. She even says that everything under the division, in this case the product of the denominator which should be (2x3), yet fails to demonstrate it in her steps. So the problem really should be 6/(2x3) or 6/2(3) if you prefer as a rewrite. In either case PEMDAS is not violated because the paren evaluation comes first. So her rewrite changes the order of operations and 9 is the wrong answer as the (2x3) or 2(3) would need to be evaluated first. Ultimately everything on the right falls under one set of brackets like so 6 / [2(1+2)]. Since there is nothing on the left to evaluate, the right side is fully evaluated before applying the division. The answer is 1.
Not one thing you just typed was correct. LOL I particularly like how you arbitrarily and fundamentally changed the entire problem when you placed the 2 x 3 in parentheses. Or that there is one wit of difference between 6/2(3) and 6/2 X 3 They're the exact same thing. (which is still 9, no matter how badly some of you all want it to be, you know. ONE LOL
@@chestermarcol3831 lmao you clearly dont know what your talking about. 2(3) isnt that same as 2x3. having the 3 in parentheses changes the order of operation. remember Pemdas? its explained in the video lol
@Don MacQueen It's not even the point. Just because there is a rule 'BODMAS', the question is ambiguous, and nobody would ever write 6÷2(2+1) meaning 6÷2 × (2+1). Somebody who's not very good with maths could write it meaning 6/(2(2+1)) Anyone who does maths beyond primary school, who's done algebra, would assume that the implied multiplication comes first. People who just think BODMAS must always be strictly applied just don't have any common sense. Nobody is arguing about how to strictly interpret BODMAS.
The answer is 1. The main reason people claim 9 is because they are taught basic math not Math.. It is the way the equation is written that causes the issue. In math they dropped outer parentheses to make equations easier and cleaner to read. When you have 2(2+1) is assumed in real math that that is the same as (2(2+1)). Since their is no multiplication sign, it is assumed as one expression. Not two separate equations. Thus 6 is divided by the product of 2(2+1) not of 2. If you wanted 6 to be divided by 2, you would right (6/2)*(2+1). That is not what is written. What is written is 6/(2(2+1)). because 2 is part of the expression of (2+1) not of 6/..
The answer should be 1. 2(3) is part of the parentheses action and should be executed before the division. Implicit multiplication is not the same as multiplication in terms of operational timing. As an action, do the following formulas in the way that feels correct and see which returns the appropriate x of 1. 6 ÷ 2(X + 2) = 1 6 ÷ 2(X + 2) = 9
I think the confusing part is the use of the parenthesis without the explicit * sign, so the problem is not 6÷2*(1+2) which would unambiguously be 9, given BODMAS and L to R execution. To examine further, , let us put (1+2) as x, so the expression is 6÷2x which is not the same as 6÷2*x. Although we normally think of 2x as 2*x but in the context of 6÷2x, 2x would mean 6 and the answer would be 1. I do think the expression is ambiguous and the author must rewrite it as (6÷2)(1+2) if he wants 9 to be the answer.
6/(2(1+2)) = 1 is what CASIO comes up with because it’s ambiguous. Prime gives 9🙂, why as a programmer I prefer the HP Prime it’s thinks like I do, and * is multiply none of that CASIO crap x, seriously • or * but x, r you serious CASIO, even my old TI-83 knows it’s 9
@@insoft_uk You have fully parenthesized the denominator so the answer should unambiguously be 1. I haven't used casio lately but the old calculators did not let you enter something like 2(1+2) without putting an operator before the parenthesis. If you remove the outer parenthesis and enter 6/2*(1+2) then the answer would be 9. There were some calculators which used to use reverse polish notation and that was a bit confusing.
@ Manzerm Answer 9 is wrong. Actual answer is 1. Because, in case of simplification, dot product should be done before division. 6÷2(3). In this case 2(3) is dot product i,e 2.3; so ,2.3=6 and 6÷6=1. In the case of cross product (×), the answer will be 9. when 6÷2×3 then answer will be 9. Mind it that, there are two types of Multiplication in Mathematics namely cross product (×) and dot product(.) and as per rule of Mathematics, cross product(×) and dot product (.) are not same. There are difference between cross product (×) and dot product in Mathematics.
You dont need to solve anything IN parenteses you need to solve THE parentheses. And those are not (1+2) but 2(1+2) which is one entity that can be writen as (2x1)+(2x2) and that becomes 6. And only at that moment you have solved THE parentheses and can you move to the division.
This is correct. The order of operations requires not only that the value in the parentheses be evaluated but that the operand must be evaluated in order to remove the parentheses. Therefore 6 ÷ 2(1+2) is not the same as 6 ÷ 2 x (1+2). You could also evaluate this equation by multiplying both sides of the equal sign by 2(1+2) which would result in 6 = 2(1+2).
Answer is 1 It's just simple arithmetic problem where we have to give first preference to bracket a÷b(c+d) = a÷(bc+cd) So, 6÷2(1+2) = 6÷2(3) =6÷6=1 Mathematicians always write like this
Sorry to disagree, but 2(3) = (2x3). Factor the 2 out of (2x3) and you get 2(3) Distribitue the 2 in 2(3) and you get (2x3) When adding a muliplication sign between two or more factors, ALWAYS enclose the factors involved in parentheses. For example, if 2x3=6, and 6÷6 = 1, does 6÷6 = 6÷2x3 or 6÷(2x3)??? Conclusion: 2(3) = (2x3); and 6÷2(3) = 6÷(2x3) or 1
@@Sauvenil It's easy. 6÷2 x (1+2) 2 is the divisor. 6÷2(1+2) 2(1+2) is the divisor Division by a product =division by its factors. 2(1+2) is a product, so we divide 6 by both the 2 and (1+2). Answer=1
This is just a guess: The change is related to the advent of computer code such as Fortran. Long ago, people wrote expressions with parentheses around every operation. But that was clumsy if you had to type punched-cards with code. So an attempt was made to reduce the number of parentheses by adopting order of operations. Also note that the computer keyboard does not feature a divide sign, so the above problem would be typed as 6/2(1+2)
The problem is shitty quality control and lack of oversight into the manufacture of mathematics textbooks over the years. ÷ and / should never have been treated as the same operation. One is simple division while the other >implies< a numerator / denominator relationship, which is entirely different (solving the fraction turns the denominator into an implicit nested parenthetical expression).
@@jeffreyhutchins6527 Division of expressions, not values. The difference between 6 ÷ 2 (1 + 2) and 6 / 2 (1 + 2) where / is representing what modern textbooks show the middle line between the numerator and denominator Is the difference between 6 ÷ 2 (1 + 2) and (6) ÷ (2 (1 + 2)) The distinction is important and referring to it as a simple division operation combined with lazy textbook manufacturers who don't distinguish between the two is a large contributing factor to the confusion behind this problem. Essentially ÷ should have been treated as simple division between left and right value, and / should have been treated as divide the expression on the left by the expression on the right, at least if there was consistency between textbooks that often use / to denote simple fractions (easier and faster than playing with the formatting to get a proper fraction in text).
This is why I wouldn't say I liked algebra in primary school. Children don't make rules, they needed to to be told and follow suit. As an adult and not a mathematician in what so ever aspect, my logic instantly gave me 9 as the answer.
For a little more confusion, what about using the Commutative property of multiplication or ab = ba. Then 2(3) = (3)2 = 3*2 then PEMDAS would have us first divide 6 by 3 = 2 and then multiply 2*2 = 4. Now we have three answers...
The answer is 1, I did maths at school, then at technical college, then Mathematic For Electrical Engineers at University. The way we were taught in all places was to work out the parenthesis which is 2 X 3, so the righthand side is 6, so the equation is 6 ÷ 6 = 1, How can the whole basis of the way mathematics was taught for my entire education be altered to give 9 as an answer? Just as crazy as biological men claiming to be women, and just as hard to work out.
These teachers want to force kids to follow the PEMDAS/BODMAS rule blindly so they don't teach distribution as part of the process to solve parentheses/brackets. a(b+c) = ab+ac The answer is indeed 1.
The problem, as I see it, is in the divisor sign '÷'. This is not the same as the divide sign '/'. If the problem was written as 6/2(1+2) then the answer is 9. However, the divisor sign, ÷ has a different meaning to the divide sign. The divisor sign has a 'top dot-horizontal line-bottom dot' format. This implies that the top dot is a numerator expression and the bottom dot is a denominator expression. In this problem the numerator is 6 and the denominator resolves to 6. Numerator divided by denominator = 1
I've been asking for years, what other math formula(s) have changed? Area a a regular shape, Pythagorean theorem, value of pi, Golden mean? And if pemdas says deal with parentheses first, why doesn't new math do that? I was taught, a long time ago: inside (), connected to (), left to right
No mam! When you got 9 for the first equation, you lost my attention. I struggled for years learning PEMDAS in school…so NO!!! at 37 I will not be learning a new method!
I went to an American Midwest public charter school early 200s that was really strict. Highschool was a joke compared to my k-8. I was taught the special rule. I got 1. I love your explanations
I went to a British school and (set faces to stun) the answer is 1 here also. I am also confident that the answer is 1 in any language, any culture, any time and any place.
I don't understand the confusion this is basic algebra. The answer is 9 and if you got 1 then you didn't pay attention in math class back in middle school.
The problem is that implied multiplication is being given the same order of precedence as explicit multiplication when it should be given a higher order. So PEDMAS should be PEIDMAS with the order being Parentheses then Exponents then Implied Multiplication then Division and explicit Multiplication then Addition and Subtraction.
The correct answer is 1 If you follow PEMDAS rule not from left to right. Remember in seventh grade when you were discussing the order of operations in math class and the teacher told you the catchy acronym, “PEMDAS” (parenthesis, exponents, multiplication, division, addition, subtraction) to help you remember? Memorable acronyms aren't the only way to memorize concepts. You do first the multiplication then divide.
The correct answer is that there are two correct answers and that therefore the problem is written in an ambiguous way. In math you're supposed to write problems in such a way that they are not ambiguous and so the author of this problem is in the wrong. He/she should have written 6/(2(1+2)) if the answer is supposed to be 1 and (6/2)(1+2) if the answer is supposed to be 9. However, a/bc is used to describe a divided by b*c and not a divided by b and then multiplied by c. Otherwise it would have been written as ac/b. So the answer of 1 is more likely than the answer of 9.
We know to multiply because of the way 2 and (1 + 2) are grouped. 2(1 + 2) is shown to be a group. It remains seen a group as 2(3). Writing it as 2 × 3 doesn't show that it is a group. Writing it as (2 × 3) does show it as a group. 6 is divided by this group.
Went to elementary during the 90’s. The correct answer is 1. The creator is wrong. They should have multiplied 2(3) to get 6 accirding to PEMDAS. It was in parentheses before and therefore should have made the equation 6/6. They ignored that and got 9. The second way on the right of the screen is the correct way.
Answer 9 is wrong. Actual answer is 1. Because, in case of simplification, dot product should be done before division. 6÷2(3). In this case 2(3) is dot product i,e 2.3; so ,2.3=6 and 6÷6=1. In the case of cross product (×), the answer will be 9. when 6÷2×3 then answer will be 9. Mind it that, there are two types of Multiplication in Mathematics namely cross product (×) and dot product(.) and as per rule of Mathematics, cross product(×) and dot product (.) are not same. There are difference between cross product (×) and dot product in Mathematics.
This isnt an outdated method or something, its people getting dumber. In both cases the correct answer from machine point of view is 9. Cause for machine to get your logic it should be this way: 6:(2*(1+2)) For normal well educated human its obvious, that the answer is 1. Because there is a certain order and a certain grouping, not only machine-like "left-to-right". Once more: 6:2(1+2) doesn't equal to 6:2*(2+1)! That''s the most evident example of how "smart" our current tik tok generation is. Sadly.
I learned, brackets 1st: (1+2)=3, next step multiply 2(3)=6, then division: 6/6=1, therefore answer would be 1 But if you learned, brackets 1st, then do outside functions, you end up with 3(3)=9 So question is, do you do math functions in order of the rules? Left to right? I learned all multiplication then division then add or subtract, but brackets are always done first, most inner to outer
I enjoy how "modern" maths when explained vs "historical" shows a deprication date of early 70's when the "historical" manner of solving maths has been so until the advent of YT and more precisely a few years ago when such "problems" came about. Have had freeway off ramps not match-up only to find out the the "Engineer" used new maths as it is often called vs. the traditional or "historical" maths that were used//employed in the plans for the original freeway for with the new ramps are attaching. The result, a major and costly screw up. Had it been a rocket or something critical, lives likely would have been lost. And this change in doing a thing is the result of new Academics putting there spin on it because L->R is easier to remember than the correct\\historical order of operations - which you will find the world was built on, not that modern nonsense. It's a new school vs the old school "puzzler," not one in which those that got 1 did it wrong, but one in which those that got 9 are using a different system and by dint of being fresher from schooling on the subjects claim to be right. But look at any Engineering plans and try to come up with the right values to make it work, you will find the modern way in error. But I ain't one to gossip... .
Something so simple can get so complicated. I actually prefer the = 1 for a couple of reasons: • aside the L-R rule, w/ PEMDAS where the M is before the D thus, you mulitply out before you divide • x/2y explanation also makes a lot of sense as far as anything after the ÷ should be a denominator • you COULD argue that when you turn (1+2) into (3) that the 3 is still _technically_ in parentheses and needs to be pried out of those first by multiplying by 2, which gets you 6÷6
she just dropped the parenthesis without solving the quantity. That's how we ended up here. if we were using physical objects to express this 6 divided by 2 times the contents of a box that contains 1 +2 objects the answer is 1
It's not getting complicated. People's brains are too lazy and unexercised and they go into meltdown after 30 seconds of use and it just appears to be more complicated. A symptom of "mental obesity". Common in the USA. Thier brains are as fat and out of condition as their bodies are. Just watch the infamous RU-vid street questions with dumb Americans as an example LOL
Ur wrong on so many levels. Idk wtf yall learning in school. After an equation in parenthesis has been solved, it becomes a multiplication problem. For example 2(1+2) would be the same as 2(3). Since the parenthesis was solved, u trear the damn remaining equation as a 2x3. She didnt randomly drop the parenthesis. Thats literally what is taught and dictated by math rules. A(B) is the fucking same as AxB. Idk where the hell yall coming up with 1 from.
I agree especially on the point about the 3 remaining in parenthesis and therefore to clear the parenthesis the 3 needs to be multiplied by the 2 before moving on to the next step. Even with using PEMDAS, the first step is to take care of the parenthesis by solving what is inside and then multiplying by the number on the outside reducing everything to one simple number before moving on to the rest of PEMDAS (exponents, multiplication, division, addition, subtraction). If the rules in math have changed this drastically where there is ambiguity that it could leave an answer of either 1 or 9, there is a huge problem. I didn't get the worldwide notification that anything has changed, therefore I am comfortable with the answer of 1 for this math problem until further notice and explanation that makes sense. 😊
@@dianad3080 in pedmas you go left to right. Were d and m can be switched and a and s can too. Not specifically 1.P 2 E. 3.D 4. M 5.A 6.S SO 6/2*3 = 9 ITS not where you have to distribute the 2. It's not 6 / (2(1+2)) = 1
This is incorrect. The actual rule has nothing to do with division or the symbol used. Multiplication by juxtaposition such as ab, or a(b) takes priority over normal multiplication and division operations. Normally multiplication and division have equal priority and are solved left to right. It isn't historical or outdated to treat juxtaposed terms this way, and this is used in higher level math notation today. When dealing with juxtaposed terms, there are implicit parentheses around the terms which cannot be discarded. a*b is not the same as ab or a(b), even though they have the same product. This confusion could be cleared up if we added an extra term to PEMDAS that accounted for juxtaposition, such as PJEDMAS. Or more accurately, we can identify juxtaposition as being synonymous with parentheses.
The only difference in this type of equation is simply depending on which method you were taught. The one that does Division first, or Multiplication when they are side-by-side. Cant remember exactly why there is a difference in the two, but i want to say one of the reasons for the difference is due to how Computer Program's are hard-coded in Machine-code to process the Math (or any input for that matter) from left-to-right So it will always hit the Division prior to hitting the Multiplication step (in problems written such as this) if there is not a parenthesis or other type of "divider" giving it explicit instructions on which to do first. Human brains can go with the "Please Excuse My Dear Aunt Sally" Method because we have the ability to 'backtrack' through a problem written such as this, where a Computer reading line-by line, strictly left-to-right, cannot.
@@restey5979 Where's the 'division' after the 3 come from? once you get that first 3, the 'division' is nolonger there, as the computer has already 'processed' that division.
@@restey5979 What the computer would do is 'see' 6/3 followed by a ( which to a computer is considered a divider. It would then stop, prosses the 6/3 then store that value. As there is no symbol between the value it now has and that ( , it will consider that to be multiplication (due to the way the 'math' function in computer code is set up). So it will hold onto that value of 3, solve what is inside the ( ), then imediatlly multiply that 3 to whatever number it comes up with within the ()'s
There is only one methiodology and only one solution. If there were two answers we could forget about getting rockets to the moon because arithmatic would no longer be universal. Reinterpreting the brackets as a multiplication symbol is just so wrong. The answer is 1.
@@thegorillaguide *facepalms* What i meant is that a computer's "math" function is literally told to treat the following: 4(3) as 4*3 The 'bracket' itself is not treated as multiplication, the lack of any other instruction between a number and a bracketed object is considered multiplication. Which is the same as it is when you hand-solve math. The problem comes in that computers cannot back-track like the human mind automatically does.
1 is never the answer. You aren't following the order of operations correctly if you get 1. At the point where you get to "MD" ... they are treated the same and done left to right. You are going backwards, choosing to do right to left by doing the multiplication first. The division is clearly on the left and is done first. And because you ignore order of operations, you get the wrong answer.
@@keefersmotherland1308 2(1+2) is a bracket (B) expression and evaluated first. It is not a multiplication (M) expression as in 2*(1+2). To clarify 6/2(1+2) = 6/(2(1+2)). If it was written out properly on paper, the 6 would be the numerator and 2(1+2) the denominator. 6/2*(1+2) = 6 * (1+2) / 2 where 6 *(1+2) is the numerator and 2 is the denominator. Different expressions with different answers 1 and 9. Verify using a scientific calculator or computer.
When checking the answer on a calc, make sure that it allows you to write the whole expression before it gives you a full answer. Otherwise, it will assume that each step is independent and will not consider the Order of Operations and in this case Left to Right when Equal Precedent issues arise. Google Calculator does it right.
I got both the correct answers --- because that problem, as it's written, is ambiguous and has no actual solution. Write the problems correctly and you get the correct answers of 1 and 9! There is really no need to invoke some "special rule" of historical usage, though in reviewing your video, I think I understand where it might have come from! I also noticed that you made an error in evaluating the problem that even with PEMDAS you would get the right answer if we actually follow the rules! The only real issue with all of these viral problems is that they are written in such a confusing manner that we can't help but get two answers. That CAN NOT happen in arithmetic. If it does, then there is something wrong with the initial problem as it's written. 1st, write the problem clearly: 6 / 2(1+2) Stop using the obelus. It just confuses matters. Use the division bar or vinculum in stead. I think this might be where the "special rule" you quoted hearkens back to. When we think about logically, L ÷ R = L / R. Keep in mind that the division bar is a grouping symbol (like brackets, parens, roots). (Logically speaking, the obelus should thus be treated as a grouping symbol as well.) I'm thinking that the "special rule" might have come about simply to avoid the confusion that the obelus otherwise causes. Who knew that mathematicians in 1917 could foresee the internet meltdown a simple little mathematical symbol, improperly placed, could cause! Anyway: 6 / 2(1+2) = 6 / (2x1) + (2x2) = 6 / (2) + (4) = 6 / 6 = 1 If you want the answer to be 9, you still have to write the problem clearly! (6 / 2) x (2+1) = (3) x (3) = 9 Clarity! That's the first Order of Operations! Now, I noticed that you made a mistake with PEMDAS that still should have given you the right answer, even with the confusing matter of the obelus. 6 ÷ 2(2+1) = 6 ÷ 2(3) You still have to evaluate the parentheses before you go back to do anything else! Never get rid of those until you are totally finished with them! Doing the implied multiplication will get you: 6 ÷ 2(3) = 6 ÷ 6 = 1
Using the algebraic analogy, the first method would be equivalent to 6 / 2 x Y which would be 3Y. But the extension to PEMDAS is that *implicit* operations are performed before *explicit* operations - as on the right, 2(1+2) = 2(3) = 6 *before* the division is carried out.
And this is wrong, because of what the order of operation is. Brackets and Parenthesis first, then you move outside of them. And yes you learn this when you get into Algebraic and Geometric Equations. It also helps to know what a Bracket & Parenthesis means in mathematics. Whatever is inside a bracket or parenthesis gets multiplied by everything outside of the bracket or parenthesis. And yes you can have multiple layers of this deep as you get into more advanced Algebra, Geometry, and Trig/Calc. 6 / 2 (1+2) = X Simplify Parenthesis first: 1+2 = 3 (Left to right when brackets and parenthesis are no longer present) 6 / 2 x 3 = X 6/2 = 3 3 x 3 = 9 9 = X
@@Fluke2SS As some have pointed out, the leftmost 2 of 2(1+2) is part of the parenthetical; treated the same way as one would treat 2Y (Y, in this case, being 1+2). 2 * (1+2) is two values; 2(1+2) is a single value.
@@twylanaythias By that analogy the left most 6 is also part of parenthesis. Hence you still need to start with 6. As the formula goes, P or B first, parenthesis or brackets. the only number we have in parenthesis is 1+2. Nothing else.
@@hajkie Except for the math function separating the terms. 6 is one term and 2(1+2) is the other term. The given expression wasn't 6 / 2 x (1+2), which would have been 9.
@@twylanaythias Where do you get that 2(1+2) is a term? From which rules do you come to this conclusion. No matter if we use pejmdas or pedmas or bomdas or whatever you want to use, it always says to solve parenthesis and brackets first. 2 is not part/in/inclusive of the parenthesis, its clearly outside the parenthesis no matter how we try to argue this. We have a problem in parenthesis that needs to be solved. The parenthesis problem is 1+2. 1+2 equals 3. Parenthesis equals 3. You now have (3). You no longer need to write parenthesis. What do you have left? 6/2 3 So what does that mean? You have six divided by two three's. Think of it like this. Three three three three three three. Thats the first six three's. Remove half the three's. We're left with three, three, three. Thats 3 threes.
If you use different order of operations (or rules) that produce a different result, technically they are two completely different math problems, because the only thing that is the same is the visual positioning of the numbers and math signs. But, that doesn't mean it's wrong to use a different system, it just means it's not the same math problem.
@@drziggyabdelmalak1439 Well in a math exam, you would know which order of operations are being used in that country (or school). No one being taught at a university in one country is going to take their exam in a different country that uses a different order of operations. If you want to get super technical by pointing out some rare case that this would occur in, that is an anomaly not the norm.
We are in the age of confusing and it clearly shows in our struggle to go to the moon in this age when we landed on the moon in 69 with BODMAS. My answer is 1.
Bodmas, bedmas, pemdas, etc. are all ridiculous acronyms that don't accurately reflect order of operations. Multiplication and division don't take priority over each other, they are equal therefore you do them in the order presented.
"Where I live, we learned that multiply has priority over divide" You were taught wrong from the beginning. The rules did not change. They have been the same for over 500 years.
Only young kids use ÷ anyway so who cares? Anyone who sees 2(1+2) knows that the first 2 is a common factor of what's in the parenthesis. It's not really the same as 2 x (1+2). These problems are just stupid.
Actually, here in school, we are taught to use the order of operations but indeed, we are allowed to distribute into the parantheses first as part on how to calculate the parentheses. I assume regardless of old rules, it's the unclear appointment because distribution should have had a place in the order of operations for people to not get confused... I don't think it's the question if people can count it, but more rather the inability to have a worldwide consensus.
there is a clear rule defined in the order of operations. When both division and multiplication are available, you go left to right. 6÷2*3 so by rule, you do the division first
@@PeterSedesse that may be correct but we aren't supposed to ignore the parentheses, thus the distribution of the parentheses... a(b+c)=ab+ac ... At least that was taught to me in school... So it becomes 6÷(2+4) = 6÷6... Calculation is never the problem for most of us... It's just about ''what are the appointments''.
@@jensboffin7225 but it is basic order of operations. Do the calculation inside the parenthesis first. You are starting out doing the multiplication first when you do the distribution. Read the rules for the order of operations carefully. It does not say you deal with the parenthesis first, it says you do the operations inside the parenthesis first. You are starting your process using a number that is not inside the parethesis.
@@PeterSedesse wrong. Parenthesis takes higher precedence and 2(1+2) is all the same group. You cannot just forget the parenthesis exists. 2(3) is actually higher precedence than the division is. As I mentioned in my own comment. the 2(A+B) is like a covalent bond in chemistry. The value 2 (which we shall call C as in CONSTANT) is actually part of that "bonded" value. C(A+B) becomes (CA+CB). Start thinking abstractly and without using numbers but using the variables to represent those numbers. So if you want to follow the OOO, parenthesis comes first and C is distributed as a GROUP of that parenthesis. @jensboffin7225 is right here. The parenthesis do not just disappear, they are still part of the equation and get resolved before the division even occurs. You multiply to solve/simply parenthesis, but the order of operations remains that the multiplication of that value goes first (not in L->R order) AND its its own value, not a value split into 2 values at the same level as the rest of the equation.
P/B: Parentheses or Brackets first E/I: Exponents or Indices (i.e., powers and square roots) MD: Multiplication and Division (from left to right) AS: Addition and Subtraction (from left to right) Applying these rules to the expression: 6/2(1+2) = 6/2 * (1+2) (Step 1: No parentheses, move to next step) = 3 * (1+2) (Step 2: Division 6/2) = 3 * 3 (Step 3: Addition 1+2) = 9 (Step 4: Multiplication 3 * 3) So, the result of the expression 6/2(1+2) is 9.
The issue is your order doesn't take implict notation into account. It needs to be all replaced with explicit notation first. Academically, multiplication by juxtaposition implies grouping so 6/2(1+2) is 6/(2×(1+2)) Which gives 1. Literally/programming-wise, multiplication by juxtaposition implies only multiplication so 6/2(1+2) is 6/2×(1+2) Which gives 9. It's just a really poorly written expression written like that on purpose to be misleading and go viral. It's a trick.
@@GanonTEK "The issue is your order doesn't take implict notation into account." This problem has no implicit multiplication. YOUR problem is you don't know what that term means. "It's just a really poorly written expression" No , it isn't.
@@MrGreensweightHist There is no explicit multiplication symbol in 2(1+2). Hence, implicit. 2*(1+2), 2×(1+2) or 2•(1+2) are all explicit multiplication as a multiplication symbol is present. Hope you understand what the term means now.
I quickly solved the problem with the answer of 9. A few seconds in however I started looking for other answers and came up with 1 as the only other possible outcome. Having dyslexia in my family is a blessing and a curse in many circumstances so moving left to right could be confusing during long equations when I was young. Yet I was taught that parentheses always take order of importance first and foremost in equations. This rule really helps people like myself! Excellent penmanship by the way. This deserves a like!
I was taught (1950s, that's pretty _hysterical_ historical) that the answer is 1 because of the parens being resolved first and the div symbol putting everything to the right under it.. But ultimately, it should be written more clearly, IMHO. if the goal is to BE clear, rather than to teach proper usage.
It really becomes clearer if you convert this into a word problem: Is it "six halves times the quantity one plus two" or "six divided by two of the quantity one plus two"? To me it is the latter since 2 is an integral part of the the quantity one plus two. Had it been written as 6 ÷ 2 (space) (1+2) then it is clear that you divide 6 by 2 first since then there is a space that separates the two from the (1+2). However as written without spaces, 2 becomes grouped with (1+2) implicitely.
This is ridiculous!. The answer is "1". The problem should not change because you substitute the division sign (obelus) with the slash. The numerator and denominator remain the same. The answer is the same. The order of operations does not change. Math is not subjective. There is no squinting your eye and turning your head 270 degrees here. It's not that complicated.
Why do you substitute the division sign? What mathematic rule says you need to do this? If you have a problem, solve the problem. 1+2=3. 6/2 equals 3 3 times 3 equals 9. That is the order of operators.
This is a simple task thought in primary school in my country and the answer is 1. Multiplication we always did first as someone said you first have to solve that problem before division. Well I went to school during 90's and I don't think math has changed that much since then. At least thats my opinion.
@@betsysingh-anand3228 LOL It's actually PE(MD, left to right)(AS left to right) When you get to algebra, dealing with variables it becomes PEJ(uxtaposition)(MD, left to right)(AS left to right) This is not an algebraic equation. PEJMDAS is more common outside of the US, but once I got past College Algebra II, none of my TA's associate professors etc. were FROM America. LOL My first semester of Calc, the AP was from India, barely spoke English, and had a quite debilitating stutter. That was fun. (study group essential course) LOL Guy could not have been nicer though. He realized it was added difficulty on us, and went out of his way to help outside of class. He was so far above us that it must have felt like teaching children to tie their shoes.
Well, the problem is ill defined. Change that expression into a fraction 6*1/2(1+2) and you get one. You have to solve the denominator first. You can write it differently 6/2*(1+2) and then you get 9. Two different expressions. Don't confuse people.
if you have an expression in the form of A / BC, then you can not arbitrarily change it to AC / B, which is what you did on the left. A / BC DOES NOT EQUAL A / B * C. It is A / (B * C) I could write this as A / D, where D = BC. Which makes it pretty clear what the operation should be. If this expression was instead 6 / (1+2)^2, then I could write this as 6 / (1+2)(1+2) or 6 / (3)(3). Your method gives 6. The correct answer should be 6/9 or 2/3 YX = (Y * X) or in plain English, Y value of X. Y is a dependent multiple of X and not a discreet operation.
@@jozenthejozarian2564 A/BC does equal to A/B*C. I plugged this into Wolfram Alpha and Microsoft Math Solver and they agree. You said you can plug A/D where D=BC. You can also plug DC where D=A/B. If the question was 6/(3)^2, You cannot write it as 6/ (3)(3). You need to use brackets to clarify that (3)(3) should be solved first. So that would be 6/(3*3). This does give the correct answer of 2/3. The logic used here is correct.
The 2 beside the bracket isn't just multiplication, it's the distributive property and you can't separate it from the bracket. Also, you must solve that bracket first because it is the first part of BEDMAS. the answer is 1.
@@be643 6/2 can be written as a fraction with 6 over 2. This is multiplied by (1+2). You cant put (1+2) in the denominator. It must be multiplied by the numerator (6). This gives 9.
The answer is one. Nobody uses the division sign after about 6th grade because it leads to this kind of confusion. Division and a fraction should be the same and you can't evaluate the fraction without solving the multiplication first. Also, the entire parenthetical expression must be solved. You can't just pick it apart as you please. x(y+z) = (xy+xz). In this example 2(1+2) equals (2+4)=6. Also, multiplication by juxtaposition implies brackets. I never heard PEMDAS when I took algebra. It's a stupid acronym that some JR high teacher came up with.
Some historical order of operations Physical Review Style and Notation Guide, The American Physical Society; First Edition July 1983; Revised February 1993; Minor Revision June 2005; Minor Revision June 2011: (e) When slashing fractions, respect the following conventions. In mathematical formulas this is the accepted order of operations: (1) raising to a power, (2) multiplication, (3) division, (4) addition and subtraction.
Thanks for this video. My comment is a little off topic, but it shows that one should never write this kind of mathematical expression, and be perfectly clear about the intention, even if it is necessary to resort to superfluous parentheses with regard to the rules of precedence. My personal answer was "1" by the way... 😉
6 ------------ Because of the parentheses, this is how it looks. 2(1+2) Suddenly replacing the parentheses for the X symbol changes the interpretation. So the answer is 1.
