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.
@biloki3079
Жыл бұрын
This^
@larrymotuz6600
Жыл бұрын
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.
@DavidHalverson
Жыл бұрын
@@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.
@uliwehner
Жыл бұрын
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.
@EMPRESSGLADYS
Жыл бұрын
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.
@salt1956
Жыл бұрын
My answer was 1, based on what I was taught in high school maths in the early 70's.
@ihadtochoosethisuser
Жыл бұрын
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.
@DaveBukowski
Жыл бұрын
Same for me for high school math and college level calculus/diffEq
@ihadtochoosethisuser
Жыл бұрын
@@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?
@Bia08121975
Жыл бұрын
Same here!
@sakkysha5496
Жыл бұрын
The answer is definitely 1 6/2(1+2)= 6/2(3)= 6/6= 1
@keyo888
Жыл бұрын
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
@edeco9135
Жыл бұрын
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?
@Darksightkellar
Жыл бұрын
I'm almost 30 and I say don't worry fellas. 1 is the only correct answer. This video tosses everything sacred to mathematics out the window
@billy_411
Жыл бұрын
@@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.
@USMC6976
Жыл бұрын
There are a few countries that teach this method. It might be one of those reasons they are behind in development.
@gammaboy4568
Жыл бұрын
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.
@sappersteel532
Жыл бұрын
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.
@morganjohnson539
Жыл бұрын
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.
@PeterSedesse
Жыл бұрын
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.
@zahirkhan4576
Жыл бұрын
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.
@PeterSedesse
Жыл бұрын
@@zahirkhan4576 Google ' order of operations'. and read through the rules.
@jamilyusof1517
Жыл бұрын
9 as an answer don't make sense, imagine you have 6 boxes, how come when you divide it everyone get 9 boxes
@grandmasmalibu
Жыл бұрын
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.
@eastcastleplace6373
Жыл бұрын
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.
@4nomaIy
Жыл бұрын
Yes this is what I was thinking
@PoeLemic
Жыл бұрын
@@4nomaIy Same here.
@billy_411
Жыл бұрын
No, that's not how parentheses work lol. 2(30) is 2*30.
@YouTubeWatcher29
Жыл бұрын
Her mistake actually started at 0:01. everything else was a waste of everyones time.
@wreck-itralphreuss7075
Жыл бұрын
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…
@Purington
Жыл бұрын
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.
@sar_e_bear
Жыл бұрын
Same!
@BeyondLimits3D
Жыл бұрын
Same here. I was shocked when she said that was special use and a historical artifact only. WTF? I'm not an historical artifact!
@PropagandaFacts
Жыл бұрын
Yep.. me too.
@sharonschauer3257
Жыл бұрын
Me too! And I got A's in math!
@gorjanapetrovic5383
Жыл бұрын
I think the same as you (used to learn in the school)
@AmenMama-qe4sq
Жыл бұрын
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!
@erikvangelder6671
Жыл бұрын
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
Жыл бұрын
The correct answer has been 9 for over 500 years.
@Andrew-it7fb
11 ай бұрын
That's why parentheses are important to avoid ambiguity.
@MrGreensweightHist
11 ай бұрын
@@Andrew-it7fb there is no ambiguity. Just people who are mathematically illiterate
@Andrew-it7fb
11 ай бұрын
@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.
@dennmillsch
Жыл бұрын
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.
@gilbertmurphy5202
Жыл бұрын
For any actual application...the answer is one
@extantsanity
Жыл бұрын
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
Жыл бұрын
It's not ambiguous if you follow the order of operations.
@dennmillsch
Жыл бұрын
@@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.
@BKD70
Жыл бұрын
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". kzitem.info/news/bejne/zYJ5qpeXb5aKo3Y
@maxfrax333
Жыл бұрын
I got "1" in a few seconds - I'm happy with that.
@jx14aby
Жыл бұрын
Me too. I think the new rule is stupid.
@PhlyingPhil
Жыл бұрын
@@jx14aby It is not a new rule, it is simply bad math.
@zacksovine6923
Жыл бұрын
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.
@Sauvenil
Жыл бұрын
@@PhlyingPhil It's a bad mix of notation. Never use the inline division symbol, basically.
@mckeevb
Жыл бұрын
Yes because 1 is correct. To get 9 as the answer requires idiocy !
@silverhammer7779
Жыл бұрын
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.
@DaveBukowski
Жыл бұрын
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.
@hajkie
Жыл бұрын
@@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
@hajkie
Жыл бұрын
@@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.
@hajkie
Жыл бұрын
@@noomade TL;DR juxtaposition does not work when you only have numbers.
@DaveBukowski
Жыл бұрын
@@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.
@BillLeonard-c8s
2 ай бұрын
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
@paulwhillas6494
Жыл бұрын
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.
@mnewm21
Жыл бұрын
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
Жыл бұрын
@@mnewm21 That’s exactly how I read it. 6/2(1+2) -> 6/6 = 1
@Shepherd1OFH
Жыл бұрын
@@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.
@FranciscoRamos01
Жыл бұрын
I always thought multiplication had precedence over division, leading me to answer 1.
@nfpnone8248
Жыл бұрын
@@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
@corneliusagu2903
Жыл бұрын
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.
@southernflatland
Жыл бұрын
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)
@PsychedelicChameleon
Жыл бұрын
@@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)".
@southernflatland
Жыл бұрын
@@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.
@PsychedelicChameleon
Жыл бұрын
@@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."
@ElixerJohn
Жыл бұрын
Now, my head hurts. 🤕
@nightfall37
Жыл бұрын
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.
@krzysztofbosak7027
Жыл бұрын
"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.
@Rontero
Жыл бұрын
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.
@PhlyingPhil
Жыл бұрын
@@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.
@PhlyingPhil
Жыл бұрын
@@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.
@brainyjam
Жыл бұрын
Nothing is wrong with the expression. Only need to apply properly maths rules.
@marksolum1794
Жыл бұрын
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.
@marbymendez8021
Жыл бұрын
In sentence : Six all over Two Times Open Parenthesis One Plus Two Close Parenthesis In Figures : 6 /2(1+2) = 6 /2(3) = 6 /6 =1
@EnlighteningPeace
Жыл бұрын
Absolutely right
@PeterSedesse
Жыл бұрын
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
@TubeScavenger
Жыл бұрын
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.
@marbymendez8021
Жыл бұрын
@@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 !
@marbymendez8021
Жыл бұрын
@@TubeScavenger It's 3/3 = 1 The Equation is under Division !
@pejbartolo2365
Жыл бұрын
9. After parenthesis, divide and multiplication same precedence.
@davek6415
Жыл бұрын
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.
@lawrencejelsma8118
Жыл бұрын
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.
@kolegakolega
Жыл бұрын
🍊 🍊 🍊 🍊 🍊 🍊 /2= 3x 🍊 /3 = 1x 🍊 6/2/3=1
@southernflatland
Жыл бұрын
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
@davek6415
Жыл бұрын
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.
@tyttarentottero
Жыл бұрын
the formulation of the problem you wrote is: 6 / [2(1+2)]. You should learn how to read and write maths better.
@actscidad
Жыл бұрын
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!! 😂😂
@steveng8251
Жыл бұрын
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.
@DaveBukowski
Жыл бұрын
@@steveng8251 why stop at binary. Let's calculate it in hex and octal :)
@larspelley8865
Жыл бұрын
I dislike when people use a comma as a decimal point.
@srjwaugh
Жыл бұрын
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
@woodiemarv
Жыл бұрын
Here on Earth 1. Division is Division. / or ÷ are the same
@jeanniecatton9168
Жыл бұрын
Thank you. Yours is the clearest explanation yet.
@TexSilverFarmer
Жыл бұрын
correct
@janinedbeergin1455
Жыл бұрын
parehas lang nman ibig sabihin nun.. 😂
@KasThinks
Жыл бұрын
Brilliant explanation! I could see that!😊
@janetdanes7945
Жыл бұрын
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.
@domojackson-grant
Жыл бұрын
Same here
@yengchoopeng9284
Жыл бұрын
Agree
@AnonUser-ex3qg
Жыл бұрын
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
@usonly101
Жыл бұрын
How is 2:40 not incorrect? Shouldn’t it be 2x3 = 6 then 6/6 = 1? How is she completely changing PEDMAS?
@Kingdom-zu6tm
Жыл бұрын
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.
@steveocken
Жыл бұрын
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)
@DHarri9977
Жыл бұрын
See Excel...
@pscully608
Жыл бұрын
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).
@JVincentBeall
Жыл бұрын
The other method seems to add parenthesis as (6/2)(1+2)
@jeffreyhutchins6527
Жыл бұрын
@@pscully608 Umm Numerator/Denominator is division.
@pscully608
Жыл бұрын
@@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).
@popcria
9 ай бұрын
6÷2 is same thing as in fraction form: 6 3 --- × --- 2 1 1+2 = 3 then make it in fraction form Multiply it because there's parentheses Suppose 3/1 had parentheses meaning you have to multiply it. Then apply the rules. 6×3 = 18 2×1 = 2 Now you get 18/2 simplify as 9
@manzerm7805
Жыл бұрын
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.
@musalubambo5878
Жыл бұрын
All we know is that the principle of arithmetic do not change hence can boldly say the wrong explanation given here by the author
@insoft_uk
Жыл бұрын
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
@manzerm7805
Жыл бұрын
@@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.
@subratabiswas2502
Жыл бұрын
@ 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.
@EricW6800
Жыл бұрын
Because a pocket calculator makes mistakes doesn't mean math needs a change
@keithcolman9868
Жыл бұрын
If you actually read the paper from 1917 it changes nothing. It in fact supports the argument for the answer being 1.
@dankelly
Ай бұрын
The correct answer is 1 because 2(3) is not the same as 2 * 3. You have to evaluate 2(3) first because the "P" in your mnemonic still applies... It's more tightly coupled than 6 ÷ 2.
@Serai3
Жыл бұрын
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.
@xeroxcopy8183
Жыл бұрын
there's an agenda to make people dumb with "common core math" what's that you say? 'Two answers are equally correct, except with cant prove it'
@harrymatabal8448
8 ай бұрын
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
@pw6048
Жыл бұрын
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.
@XRandonymnityX
Жыл бұрын
You are correct 💯
@johnathanmiller3033
Жыл бұрын
It's called the order of operations ... LOOK IT UP .
@piratesteve1
Жыл бұрын
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).
@ctanaw
Жыл бұрын
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
@merloctave22
Жыл бұрын
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.
@thehellyousay
Жыл бұрын
You graduated? Must have been an American school.
@thehellyousay
Жыл бұрын
@@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.
@mikado1555
Жыл бұрын
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.
@erikvangelder6671
Жыл бұрын
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.
@HistoHaHa
Жыл бұрын
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.
@GanonTEK
Жыл бұрын
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.
@MrGreensweightHist
Жыл бұрын
@@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.
@GanonTEK
Жыл бұрын
@@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.
@twylanaythias
Жыл бұрын
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.
@Fluke2SS
Жыл бұрын
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
@twylanaythias
Жыл бұрын
@@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.
@hajkie
Жыл бұрын
@@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.
@twylanaythias
Жыл бұрын
@@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.
@hajkie
Жыл бұрын
@@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.
@Tim.Stotelmeyer
Жыл бұрын
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.
@dgkcpa1
Жыл бұрын
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
@ranjithnimal566
Жыл бұрын
Hi, Iam from Sri Lanka, u are correct
@dgkcpa1
Жыл бұрын
@@ranjithnimal566 Many thanks for your kind words, best wishes to you and everyone in Sri Lanka.
@Sauvenil
Жыл бұрын
It's that inline division symbol that corrupts this. It's impossible to tell whether just the 2 or the whole expression is in the denominator.
@dgkcpa1
Жыл бұрын
@@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
@v-chris156
3 ай бұрын
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
@subratabiswas2502
Жыл бұрын
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.
@ritupravaadhikari1727
Жыл бұрын
Absolutely
@chriscorts3337
Жыл бұрын
Correct.
@kichigan1
Жыл бұрын
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.
@mikeef747
Жыл бұрын
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
Жыл бұрын
Think it might in a Maths exam where they are looking for one [their] correct answer! See my post!
@mikeef747
Жыл бұрын
@@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.
@DaveBukowski
Жыл бұрын
probably the best non-biased answer. All depends on that position of the math signs (and if they exist).
@the-dave-house-project
Жыл бұрын
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.
@davidjones-vx9ju
Жыл бұрын
when did you get to make the rules?
@tedunderkoffler4164
7 күн бұрын
I agree. Just like (2^3) is not the same as (2*2*2) or 2*2*2
@RyllenKriel
Жыл бұрын
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!
@73kevdoc
Жыл бұрын
Excellent penmanship except for the r looking like a Y
@manueladevilliers5301
Жыл бұрын
i agree
@manueladevilliers5301
Жыл бұрын
If 6 is the numerator and 2(3) is the denominator.... well
@ChasOnErie
Жыл бұрын
Wrong wrong…
@manueladevilliers5301
Жыл бұрын
@@ChasOnErie what answer is wrong? 😂
@air-edge
Жыл бұрын
I'm 46. Born in 1977. The answer is 1. Like Mr. Incredible says "MATH IS MATH! YOU CAN'T CHANGE MATH!!"
@MrGreensweightHist
Жыл бұрын
""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.
@air-edge
Жыл бұрын
@@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)
@air-edge
Жыл бұрын
@@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"
@air-edge
Жыл бұрын
@@MrGreensweightHist Watch the following linked video and you will see where this flawed interpretation of mathematical expressions came from and why it is wrong. kzitem.info/news/bejne/la5jqJePfJt8dqAfeature=shared
@leogrande9977
Жыл бұрын
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).
@GanonTEK
Жыл бұрын
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.
@MrGreensweightHist
Жыл бұрын
"If the rules have been changed from the historical way of processing the operations" They have been the same for over 500 years. The answer is 9
@leogrande9977
Жыл бұрын
@@MrGreensweightHist So you don’t understand the rule of juxtaposition.
@MrGreensweightHist
Жыл бұрын
@@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.
@MrGreensweightHist
Жыл бұрын
@@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.
@X00000370
Жыл бұрын
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...
@Eight69
5 ай бұрын
Bro is onto absolutely nothing.
@mcmoore02
Жыл бұрын
6/2(1+2) is different to 6/2*(1+2) for BODMAS. 1 and 9 are the respective answers. You can confirm with a calculator or computer.
@geralds361
Жыл бұрын
Yes, you are right, and this should settle the matter. The only correct answer is 1, and the answer presented in the video is just plain wrong.
@keefersmotherland1308
Жыл бұрын
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.
@mcmoore02
Жыл бұрын
@@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.
@keefersmotherland1308
Жыл бұрын
@@mcmoore02 Google it !
@vueloimaginario
Ай бұрын
@@mcmoore02 Con calculadora científica "Hiper" el ejemplo tal cual está, ofrece 9 como respuesta, pero al cambiar el signo divisor (obelus) por diagonal / el resultado cambia a 1.
@j.r.arnolli9734
Жыл бұрын
Math is, also, about agreement. ( Where I live, we learned that multiply has priority over divide. That changed about 40 years ago)
@MrGreensweightHist
Жыл бұрын
"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.
@thesoundsmith
Жыл бұрын
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.
@MrGreensweightHist
Жыл бұрын
You were taught wrong.
@M1837
Жыл бұрын
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!
@Axiomatic75
Жыл бұрын
I'm astounded that a mathematician would not only get this wrong but make a video about it
@Amen.22
Жыл бұрын
This is the correct answer I was looking for.
@Andrew-it7fb
11 ай бұрын
It's not wrong, it's just ambiguous, which is what any mathematician should recognize.
@Eight69
11 ай бұрын
The mathematician is not wrong. You are wrong. The answer is 9.
@zakelwe
7 ай бұрын
Yep, spot on. Both answers are right
@shaunpatrick8345
4 ай бұрын
@@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.
@MuhammadHussain-lu4xs
Жыл бұрын
2x ÷2x = 1 But according to you X square
@ChrisLee-yr7tz
Жыл бұрын
Best explanation of why saying 9 is just ridiculous.
@HerryNovri
Жыл бұрын
Spot on 😂
@donmacqueen
Жыл бұрын
But the original expression does not have 2x in it. It has 2(3), which is different.
@ChrisLee-yr7tz
Жыл бұрын
@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.
@Froghair75
4 ай бұрын
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
@l0g1cb0mb
Жыл бұрын
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... .
@John-McAfee
Жыл бұрын
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.
@Bojanarules
Жыл бұрын
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
Жыл бұрын
Exactly. Each step in PEMDAS happens separately from left to right in order.
@chestermarcol3831
Жыл бұрын
@@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.
@LegoGirl1990
Жыл бұрын
American here. I graduated in 2007 and the answer is 1. They're probably teaching this wrong deliberately. Our schools are so beyond f*cked.
@jensboffin7225
Жыл бұрын
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.
@PeterSedesse
Жыл бұрын
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
@jensboffin7225
Жыл бұрын
@@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''.
@PeterSedesse
Жыл бұрын
@@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.
@DaveBukowski
Жыл бұрын
@@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.
@drziggyabdelmalak1439
Жыл бұрын
@@PeterSedesse Not so clear in real-life situations though, is it Peter? See my post!
@mlefter
Жыл бұрын
The fact is that between algebra and arithmetic there is a difference in the order of operations: Procedure: In algebra, the procedure is the same as in arithmetic, but there is an exception: in algebra, the multiplication sign connects the components of the action more strongly than the division sign, so the multiplication sign is omitted. For example, a:bxc = a: (bxc). To eliminate misunderstandings, V. L. Goncharov points out that it is preferable to use a bar as a division sign or put brackets [87]. P. S. Alexandrov and A. N. Kolmogorov [59] suggested changing the order of operations in arithmetic and solving, for example, as follows: 80:20x2 = 80:40 = 2, instead of the usual: 80:20x2=4x2=8. However, this proposal did not find support. In algebra, the first rule does not apply in the case of dividing a number by a product, for example: a:bcd. If multiplication signs were written in the divisor, then we would have to write: a:(b x c x d). So the expression a:bcd should have been written like this: a:(bcd). However, the following practice has been established in the spelling of algebraic expressions: when dividing a number by a product in which the multiplication signs are omitted, you can not enclose the divisor in brackets, that is, write: a:bcd. Procedure: In algebra, the same procedure as in arithmetic, but there is the same order an exception: in algebra, the multiplication sign connects the components of the action more strongly than the division sign, so the multiplication sign is omitted. For example: In ALGEBRA!!!! a:bc = a:(b x c). That is the theory! but: If you want IN ARITHMETICS the result to be 1 use the bar or put brackets. If you want to be 9 don't confuse the people (that was the idea of that example to provoke the people) use the multiplication sign.
@gavinlamp
Жыл бұрын
Someone explain to me how I got a physics degree and study acoustics and use complex math every day and got the answer 1 and not 9. Someone explain to me how I can find the fundamental resonate freq of an object but can't understand why the answer would be 9? SOMEONE EXPLAIN TO ME HOW I AM DOING AN ENTIRE CAREER WITH "THE WRONG WAY OF MATH" and still am finding success in my field?
@ErniJuliaKok
Жыл бұрын
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.
@Gwydion_Wolf
Жыл бұрын
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
Жыл бұрын
So a computer would do All operations left to right? : 6/2(1+2)= 6/2=3 so 3/(1+2) (1+2)=3 .. therefore 3/3 =1 ??
@Gwydion_Wolf
Жыл бұрын
@@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.
@Gwydion_Wolf
Жыл бұрын
@@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
@thegorillaguide
Жыл бұрын
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.
@Gwydion_Wolf
Жыл бұрын
@@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.
@easy_s3351
Жыл бұрын
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.
@seymourbuttes3194
Жыл бұрын
It would help to see an example without explicit numbers, I think. How would one go about simplifying x/y(z+y)? To clarify, do you factor x/y as a whole into (z+y), or do you factor y into (z+y) and then divide x by the result?
@edwardfitzgerald3877
Жыл бұрын
Clearly, you factor x/y as a whole into (z+y). But really, to simplify things, all you do is follow the order of operations: you solve x/y then multiply the quotient by (z+y).
@DaveBukowski
Жыл бұрын
If you want to know how this works I did it but I'll retype it here for your answer. I did use this exact thing by using a b c and d, as we don't know that the 2 outside and inside the parenthesis is the same value. You could have 2 for both, but they could be 2 different variables at this point. ; denotes comments like in DNS zone file. I usually would use // or # but those could be interpreted in mathematics of people think #TOPIC has a hashtag instead of comments like in shell scripting (BASH, CSH, Python, PERL, etc) y = a ÷ b(c+d) y = a ÷ (bc + bd) ; distributing to the parenthesis value this could also be written as below ; or y = a ÷ ((c+d)+...) ; the number of times that b is, but since b is a variable here its easier to express it as the above ; here we solve inside the parenthesis still first (applying what was outside of them DIRECTLY associated with them, without any arithmetic operator like ×) ; NOW the problem with how the problem is written it is not using a × between the 2 and the (1+2) in our case b and the (c+d). ; IF there actually were a × or * symbol then the parenthesis does not have a number to distribute (actually there is, but its the implied number 1 and any number multiplied by 1 is the number). ; So IF the equation were written as y = a ÷ b × (c+d). ; In this case it would be evaluated from left to right. Again the implied 1 in front of the (c+d) so 1(c+d). ; Using the 2 equations and substituting the numbers y = 6 ÷ 2(1+2) y = 6 ÷ 2(3) OR y = 6 ÷ (2+4) ; both are the same y = 1 ; If the problem were y = 6 ÷ 2 × (1+2) y = 6 ÷ 2 × (3) ; evaluated left to right at this point y = 3 × (3) y = 9 ;;;;;;;;;;;;;;;;; Key point here is does the 2(1+2) have the presence of the × symbol or not. If it does then its a separate operand. Since there is no ×, we distribute the value outside the parenthesis with what is inside. Since there is no variables it could be done either way as both ways come up with the same answer (bc+bd) = b*(c+d). If c were "x" then you would have to distribute the first way (bc+bd). such as in this problems instance the place of c is actually the variable 'x' y = 6 ÷ 2(x+2) ; would be evaluated as y = 6 ÷ (2x+4)
@EMPRESSGLADYS
Жыл бұрын
As you wrote it, y(z + y) is the divisor. This is x divided by (yz + y²).
@DaveBukowski
Жыл бұрын
@@EMPRESSGLADYS like I mentioned in my post. don't make the 2 being y for both instances. In this case it just happens to be. What is it was 2(1+3) instead of 2(1+2). It's better to use it as 3 different variables instead of just 2 ;-) so not y² but a ay. Both a and y can be 2, but that is not always the case. Best to stick with not ASSUMING that the expression will be x = a / y(z+y) but instead x = a / y(z+b). JUST in case your values are slightly different. :) Unless you are absolutely sure that the 'y' in your example which is 2 is the same product. Making it a word example: there are a total of 2 dogs and 4 cats. = (2 dogs + 4 cats) = 2(1 dogs + 2 cats). The 2 outside the parenthesis does not always represent the values inside, but is a factorization of them.
@MrGreensweightHist
Жыл бұрын
@@EMPRESSGLADYS "As you wrote it, y(z + y) is the divisor." That is false. y alone is the divisor.
@g1bC
Жыл бұрын
We were never taught order of operations at school. Including up to year 12. I did pure math and applied math and physics. Year 12 final exams determined which Uni and which course we were able to do. Maybe all the exam questions were written in an unambiguous way. I do admit that I always assumed that 2a meant (2*a). I don’t recall using ➗or X symbols after primary school. Maybe the only intuitive operator is addition. Minus is removing an addition. Times is adding same number over and over. Division is taking away addition lots of times. Exponent is adding groups of added same number lots of times. Maybe the best question to ask is how did “order of operations rules “ come about, and what was the reasoning behind the “rules”?
@biloki3079
Жыл бұрын
They should be thought of as guidelines instead of rules. They don't always apply.
@larrymotuz6600
Жыл бұрын
@@biloki3079 Unfortunately, they are taught as 'rules' not guidelines. But if this was an algebra problem, then 1 would be the correct answer.: 6/2(a +2) = 3/(a+2) and if a =1 then the solution is 1 also. There is a failure of logic in the new rule for it implies that the answer is 3(a+2) which if a =1 means the answer is none. This 'new' rule needlessly complicates basic operations to get at what are wrong answers algebraically.
@larrymotuz6600
Жыл бұрын
...means the answer is 'nine' NOT none.
@biloki3079
Жыл бұрын
I turned it into a word problem to make it easier for people to understand. We have 6 oranges and want to divide them evenly between 2 groups. Each group has 1 boy and 2 girls. Between the 2 groups, we have 6 children(2 boys and 4 girls), and we want to distribute them out evenly, so that means each kid gets 1.
@robertwilliamson922
Жыл бұрын
School has changed over the years. Back in the 1950’s we were taught the order of operations in elementary school. Long before we got to high school. We were also taught history and geography in elementary school. Times have changed. They teach woke stuff now and Marxism.
@be643
Жыл бұрын
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.
@ihadtochoosethisuser
Жыл бұрын
Correct. Distribution. a(b+c) = ab+ac 👍
@loizosnikolaou2864
Жыл бұрын
Correct. You cannot just disregard the distributive property. The answer is 1 for me as well.
@Eight69
11 ай бұрын
Incorrect. The answer is 9. While using distributive property, you must distribute 6/2 as a whole. 6/2 as a whole is attached to the brackets
@be643
11 ай бұрын
@@Eight69 the division is not connected to the bracket.. if you want it to be, you must put the 6/2 in a bracket.
@Eight69
11 ай бұрын
@@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.
@petergershkovich
Жыл бұрын
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.
@johnnymnemonic8487
Жыл бұрын
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.
@jeannesery9936
11 ай бұрын
The question has two awnsers thats the fuss
@mattpellico5255
Жыл бұрын
The confusion is all in the symbol ÷ . This is a symbol used to denote a fraction (notice the the top dot represents a numerator and the bottom dot represents a denominator). The symbol was designed to represent the two levels of a fraction on a single line of type (think typewriter). If you represent the problem as 6 x (1 + 2) 2 versus 6 2 x (1 + 2) Writing as an actual fraction (two levels, with only horizontal dividing lines) eliminates the confusion. Also diagonal (and sometimes vertical) dividing lines have forever confused students with unit analysis - a pet peeve of this old physics teacher.
@padraicbrown6718
Жыл бұрын
That symbol (the obelus) doesn't have anything to do with typewriters or fractions per se. Typewriters always have several common fraction keys. Good typewriters might have a dozen fractions available. Fractions are always written with horizontal lines or a solidus separating the numerator and denominator. The problem as written in the example is simply poorly laid out.
@DaveBukowski
Жыл бұрын
as an old physics teacher, tell me where you get the × in the 2 × (1+2). Remember distribution is part of the parenthesis and is handled at that priority. Say you have (1+2) is actually the variables you plugged in and you have from a derivative The derivative of (1+2) ^ 2 = 2(1+2). Remember in physics you work with variables and anything "tied" to that variable is actually grouped as (2(1+2)). There is no × between the 2(1+2). 2(1+2) and 2 × (1+2) MAY have the same answer, but they are not the same equation. b×(c+d) vs b(c+d) 2 different equations. ;-)
@mattpellico5255
Жыл бұрын
@@DaveBukowski Seriously? I think I know the difference between implied multiplication and placing the symbol "x" to mean multiplication. I merely used the "x" here because the text capabilities did't allow me to use the underlie feature for showing a dividing line.
@DaveBukowski
Жыл бұрын
@@mattpellico5255 The problem is adding the '×' changes the equation. 2 × (1+2) is different than 2(1+2). As it stands as numbers in place it is the same answer, but the equations are very different equations. Especially with the fact its actually a small subset of the larger equation. That is part of the problem with having the equation written as it is. Despite the fact of the OOO isn't being followed correcty when using the first "solution". That is my pet peeve, adding operators that don't exist. :)
@TimeStream-el4te
Жыл бұрын
Indeed. I agree because I myself have taken Linear Algebra and Differential Equations. One of the most advanced mathematical classes to be offered in math for any college level student, and I can tell you right away that the division symbol (also known as an "obelus") is never seen either on a printed sheet or on an evaluated problem. A line known as a "fraction line" is used instead to separate between the numerator and denominator.
@harveyharon3335
Жыл бұрын
I don't agree 2(1+2) This shows that it is 2(3) Bracket comes before division
@drmanny1957
Жыл бұрын
Okay. So then make it an algebra problem: Substitute x for (1+2)...which means x=3. 6 divided by 2x to get 6/2x = 3/x. Replace x with 3 and you get 3/3 which = 1.
@hajkie
Жыл бұрын
Yes, that is true... if parenthesis is X. But parenthesis is not X. Only if parenthesis was X from the beginning can you solve it that way, juxtaposition for multiplication is only done when you have letters. If its only numbers you cant use it since it breaks the formula. 6/2(1+2)=9 9/(1+2)*2=6
@johncipolletti5611
Жыл бұрын
This result can also affect programming in AI. One judgemental error in thinking can cause a complete change in what goes on. That is why, before something important is undertaken, there should be a review of what one thinks when doing a complex program!
@cyberswept
Жыл бұрын
AI evaluates the answer as 1
@johncipolletti5611
Жыл бұрын
@@cyberswept So did I!
@holleey
Жыл бұрын
not really as there's no common programming language where something like 2(3) is valid syntax
@johncipolletti5611
Жыл бұрын
@Holly Are you kidding me? You are talking to a 50 year programmer. Once that program is converted "internally" to binary, one mistake in a zero or one can cause a major problem. I experienced this back in 1968!
@robertmaxwell3220
Жыл бұрын
@@johncipolletti5611 ok you're a bot!😅
@laurentwatteau8835
Жыл бұрын
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... 😉
@phyar7194
Жыл бұрын
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
@Eight69
5 ай бұрын
2(3) is not part of the parentheses, it's normal multiplication. Division comes first.
@darkmistvoicemtv5439
Жыл бұрын
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.
@axle.australian.patriot
Жыл бұрын
This often comes down to a problem of the context of the notation. Different disciplines will place different meaning on to the notation and some of this is historical legacy as you say. Work between physics notation and computer programming notation and you will encounter this repeatedly :)
@axle.australian.patriot
Жыл бұрын
P.S. The implicit notation is as above 6/2(1+2) which translates to the explicit 6/2⋅(1+2) and 6/2*(1+2) and 6/2 x (1+2). The implicit Y = (1+2); result = 6/2y can resolve to explicit 6 / 2 ⋅ y or 6/(2y) depending upon the discipline (context) in which it is used. The later is typically written with the horizontal fraction line ----- with 6 above and 2y below. Unfortunately common text often forces us to abbreviate to using / instead of ----. although ÷, / and ---- are all divide symbols each has a different resolution depending upon context. Resolving an expression containing ½ and an expression containing 1/2 is not always the same. Put simply it is implicit, meaning ambiguous, without the context of the discipline in which it has been used.
@DavidHalverson
Жыл бұрын
Probably why Sheldon being a theoretical physicist got 9 for his answer and Kuptapauli got 1 being only an engineering scientist, sorta like the rest of us born after 1960 to 1973, who also got 1 for the answer. 1973 was when the 'NEW' math came out, I was 10 years old in grade 5, totally threw my mind out the window when I learned the answer is supposed to be 9. Oh any btw, 2+2 does equal 5.
@axle.australian.patriot
Жыл бұрын
@@DavidHalverson Yeah I got both answers, but held 9 as the correct. I just not long did a heap of conversions of Einsteins equations to C language functions and encountered a lot of ambiguity. I had to rely on examples where solutions were shown to test if I was converting them correctly. Even then I encountered different interpretations :)
@DaveBukowski
Жыл бұрын
In my experience doing both computer programming and physics. In my particular case it was thermodynamics (hypsometric equation) solving (and output) the altitudes were given the values of a temperature and pressure of weather balloon data. This was a meteorology class so of course the application was involving weather examples LOL. We were given data in pressure, temperature, and a few other variables which were inconsequential. The only variables we needed to work with was Tv (temp in C but had to convert to Kelvin) and the pressure. Had to do the integration by hand to create the formula used by the program. We had the option of using C or Fortran (a lot of applications for meteorology still use Fortran libraries). This was back in 1998. Nowadays, Python is a very popular language that can do a lot of this, I still use my good ole C for a lot of things. I don't program for a profession. I do server and network administration along with InfoSec, but still have my love for weather as that was my intended career path until I switched over into IT directly with a job after 3 years of study in meteorology. It still is fun to dive into physics/calculus to keep the mind refreshed even though I have no purpose. My next thing to learn more on Python and doing it in C and also C++ and then go along to JS is write the same program over all the languages, is to make a simulation that will simulate queues at the grocery store (my first actual job was working at a grocery store as a cashier). Would have it run over the course of a business day and given a file with different inputs like different cashiers at different times of day (based on a schedule) and different cashiers with different checkout speeds. My IPM (Items Per Minute) averaged around 43. It was close to 50 with cash and CC/checks took longer which dropped down to 40. But use that, add some randomization into each item (probably make it more advanced later that things like fruit have to type in the PLU# instead of simply scanning it. (PLU# + Scale + tare weight + ENTER). Also simulate that a certain % of items will come across a price check that will increase scanning time because well, it needs to be manually checked. It would be a fun simulation to write and have it log all the results through the day of each "customer" experience also log all the variables like how many times a price check occurred, how many customers wrote checks (will use a random value but with a weighted random value). In 1994-1998, I came across I'd say 35% cash, 30% checks, 30% CC. (CC would be both EFT and EBT like food stamps). There also was the 5% of foodstamps (old paper version until they moved to EBT) and WIC. WIC was probably the hardest because as the cashier we had to verify that each item on the WIC order was being scanned. Had to be certain items, and no substitutions allowed. It was always the dreaded thing to come through when it was busy. Not so much when it was a quieter time of night. Anyways back on programming notation with physics/statistics notation, it is in a way the same, but really when you work with it a lot.
@axle.australian.patriot
Жыл бұрын
@@DaveBukowski Cheers :) On Programming I write in C, FreeBASIC and Python 3 side by side. In essence the same "Programmatic Flow" in a Procedural context so that the 3 source codes read like a "Rosetta Stone" Or Rosetta code. I actually find the syntax working between the 3 languages very similar and I can pretty much write up a function or routines in one language, debug it and then transcribe to one of the other 2, or both, and the application will compile/run without error. I find BASIC is closer to Python syntax, but Python is heavily wrapped in C semantics. All 3 languages fit together well so I am writing some beginner to intermediate guides/books using all 3 languages side by side for the examples. > I wrote up a basic analog clock using the new Graphics.h (Old Borland BGI) based upon SDL2 and I will do the same in raylib as one of the graphic library examples. I got a bit side tracked and decided to do a quartz like constant motion of the second hand, instead of the ticks, at 30 and 60 FPS which came up good :P I then got side tracked again and extended the mathematical dimensions of the clock so that the radius would be 2862807095.5421653553357478091848m making the tip of second hand travel at the speed of light. I then mapped the accumulated time dilation for the velocity of the second hand at 500 equal divisions along the second hand and graphed the time dilation of the second hand. So I ended up with a clock that shows real time as well as accumulated time dilation at the same time and it's dynamic and in motion. That's what watching too many online physics videos does to ya lol At some point I will add more of general relativity (mass, acceleration, G, g etc.) to the clock. See if I can't turn my clock into a mathematical black hole :P
@johnagbor638
Жыл бұрын
I think you are wrong. You didn't resolve the parentheses first as required by PEMDAS/BODMAS. You simply converted it to multiplication. There's a link between a constant preceding parentheses
@dibyaprakashmarndi8744
Жыл бұрын
Yes, you are right
@danielamaro4656
Жыл бұрын
I also remember reading a rule sometime ago that is no longer taught that states a fraction (such as 7/8) was considered it's own separate number rather than a division in terms of order of operations. To me, that made much more sense. Funny how the confusion seems to always stems from what basically amount to verbiage being changed than incompetency.
@Xingularity
Жыл бұрын
a fraction IS a division. In order of it to represent its own value, you would place it inside parenthesis in an equation. i.e. (7/8) as in (7/8) * 4. Once inside, it takes precedence using PEMDAS.
@DaveBukowski
Жыл бұрын
@@Xingularity that is if you want to solve the actual decimal value for it. Now if it contained variables. 5/x ; x ≠ 0 or x/5 Just like in the calculation for CF or km to mi. Its easier to work in the "fraction" form when convertijg between systems even when combining decimals in place. Such as converting inches to m for example: Find how many m is 500 inches (500 inches/1) * (2.54 cm/1 inch) * (1 m/ 100cm). Doing this quickly in my head I can move . over 2 spaces (500/100 = 5). So 2.54 * 5 ~ 12.5m (not even pulling the calculator up or writing it down) 2.54 × 5 -------- 12.70 12.70 actually doing here longhand, which was close to the mental calculation just quickly looking at it. But back to the fractional form is sometimes best to keep it in that form through a calculation until the very end, especially when dealing with comversions. Allows you to make sure you are using proper identities of units. Keeping the variable in place though might be best also to keep in fraction form as well until the end. So the final solution would look like meters(inches) = (2.54x/100) ; x=inches if you wanted it in a fairly easy to read format. Could compute it out more as .0254 in/m but this is an example where we work with a system with a number divisible by 10. Gets different when working with for example F/C conversions where your ratio is 5/9 or 9/5 depending on which way you are converting.
@thomasmaughan4798
Жыл бұрын
@@Xingularity "a fraction IS a division" No, it is a value; it has a point on a number line. A division is two points on a number line.
@MrGreensweightHist
Жыл бұрын
"a fraction (such as 7/8) was considered it's own separate number rather than a division in terms of order of operations." That has never been the case. "Funny how the confusion seems to always stems from what basically amount to verbiage being changed than incompetency." No, it is incompetency. Whoever told you that "rule" was incipient. The fraction 1/4 is literally saying 1 divided by 4 That's what fractions are. Even the symbol use in the original question is telling you "This is a fraction" Look at it. ÷ It is literally a fraction bar with a dot on top for numerator and a dot on bottom for denominator.
@Hi-DE3021
Жыл бұрын
My answer is as follows: 6 ÷(2 x 3) = 6÷6 = 1 Always do the parentheses first 2(1+2) then the multiplication step is next 2×3. This is then followed by the division step, 6÷6 making 1 the correct answer as I was taught in the 1970's also. 6:18
@prestwig1
Жыл бұрын
This is not ambiguous. Most mathematicians consider multiplication by “juxtaposition” to being executed first. The thinking being that the absence of an operation Sign merges the implied operation with the parenthesis. Also is the problem was written vertically there would be no question about the answer
@jmas2312
Жыл бұрын
Ok guys, I got 1 at first too. However, strictly following the order of operations, it is 9. My mistake was letting my brain work thru the problem as if it was an equation with an unknown present such as 6=2x(1+2). A common practice example that many of us went over a million times. Makes you want to get rid of the parentheses to solve the EQUATION which leads you to 1. lol. Cool.
@etm567
Жыл бұрын
No, they have changed the rules.
@Pancajayna
Жыл бұрын
@@noomadecorrect... Algebra goes to shit if we try to work it out to get 9
@TheTweetybird1122
Жыл бұрын
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
@thegorillaguide
Жыл бұрын
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.
@MrGreensweightHist
Жыл бұрын
You were taught incorrectly. There is no "special rule"
@MrGreensweightHist
Жыл бұрын
@@thegorillaguide "I am also confident " your confidence in misplaced. It is 9 in ANY language and ANY culture.
@jozenthejozarian2564
Жыл бұрын
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.
@Eight69
11 ай бұрын
You are wrong.
@jozenthejozarian2564
11 ай бұрын
@@Eight69 then prove it
@Eight69
11 ай бұрын
@@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.
@mamadoubagate5363
Жыл бұрын
It's 9. 1 plus 2 equals three 6 divided by 2 equals three 3 times 3 equals 9 how is that viral
@Ghredle
Жыл бұрын
In PEMDAS the P stands for Parenthesis. So the () is always first and the answer is still 1
@GJAkuo
Жыл бұрын
🤡 Put the equation in a calculator. It comes out to 9. The fuckin parenthesis waa solved ALREADY when the damn 1+2 was solved. After that it became (3) not (2x3). How tf r u getting that ?
@RichardAmesMusic
Жыл бұрын
Nobody who actually does math uses that "divided by" symbol.
@vukkulvar9769
11 ай бұрын
PEMDAS is taught to young children. Every advanced book and publication in maths, chemistry, physics, engineering will have juxtaposition (implied multiplication) have a higher priority than division. 1/2x is not the same as x/2
@cliffordschaffer5289
11 ай бұрын
Every place that programs it into computers will tell you to include parentheses so there is no doubt.
@vukkulvar9769
11 ай бұрын
@@cliffordschaffer5289 Computer do not have juxtaposition because juxtaposition does not have a character to represent it in the code and it would probably be a hassle for the compiler to understand when there is juxtaposition and when there is a syntax error. But we're talking about maths notation, not programming. You can write "sin x" in maths but in a computer it would have to be "sin(x)". You can write "e²" in maths, but it would be "exp(2)" in a computer.
@paulafournier8934
Жыл бұрын
I came up with 9 but, I did it a little differently . I always do parentheses first, than follow the rule. In this case I happened to get the same answer🤷♀️ Example (2+1) 3 6/2 = 3 Now I laid it out 3 (3) parentheses indicates multiplication 3*3 so, 6/2 (2+1) =9
@steveklemetti8035
Жыл бұрын
The 6 is not divided by two. In division always think of dividing by people. You can't just move number around when there are people.
@Eight69
11 ай бұрын
@@steveklemetti8035 What do you mean dividing by people?
@steveklemetti8035
11 ай бұрын
@@Eight69 If you have 6 cookies and you divide those among 2 groups of 3 people, how many does each get?
@steveklemetti8035
11 ай бұрын
I got one as I distributed the 2 among the 1 +2 for (2+4) then added them to get 6. 6/6
@Eight69
11 ай бұрын
@@steveklemetti8035 This is arithmetic, not a word problem.
@mackdenn
Жыл бұрын
As a computer programmer, you need hard and fast rules to get accurate calculations each and every time so the first method is what we were taught and how the computer interprets the equations. The correct and only answer is 9.
@goofygirl1311
Жыл бұрын
I got 9, too, using PEMDAS.
@drziggyabdelmalak1439
Жыл бұрын
See my original post! What's the computer's answer to how many cakes each person would get, then? 9?
@ElixerJohn
Жыл бұрын
To correct this, we should avoid ourselves putting parentheses when only two operations involved. This is a headache for all of us.😅
@dennmillsch
Жыл бұрын
Or maybe rewrite the problem using / for divide rather than the division symbol. It actually is more intuitive to me when the / is used.
@Sauvenil
Жыл бұрын
@@dennmillsch the actual vinculum instead of trying to write the problem with annoying inline notation, so it's obvious what's being asked.
@dennmillsch
Жыл бұрын
@@Sauvenil, yeah, my point is that a wise person would write a problem or expression in such a way that there is no ambiguity and that 99.9% of people will apply PEMDAS correctly, rather than make them think too hard about notation. Personally, I never even think of PEMDAS when I do math. I just understand what to do, so maybe PEMDAS is just subconscious or intuitive to me. If you do enough problems, soon it's second nature.
@johnathanmiller3033
Жыл бұрын
Only for the people that didn't pay attention in their 6th grade math class !
@dennmillsch
Жыл бұрын
@@johnathanmiller3033, unfortunately a lot of people don't really understand math deep down and thus get easily confused. However there are ways to write equations where people make fewer mistakes. I know PEMDAS inside and out so well that I don't even think about it. In fact I don't recall ever learning that sequence of letters to help me remember. I quickly understood how math works and didn't need it. And all the subsequent calculations in college and an engineering career just came natural and without error. Nevertheless I do not want equations that make me pull out PEMDAS to guide me through a maze of symbols when the problem could have easily been written with greater clarity.
@sinchenna1
Жыл бұрын
Changing the way the math is done shouldn’t change the outcome of the answer. The math ain’t mathing.
@iblesbosuok
Жыл бұрын
I have never been lazy to add parentheses when writing mathematical equations to make it clear, even though my ways are often laughed at.
@zahirkhan4576
Жыл бұрын
Absolutely wrong. Correct answer is 1. When you have a bracket next to a number, there is a hidden multiplication sign between the number and the bracket. This takes a higher order than the normal multiplication/division sign, so the operation within the brackets must be done first, then the multiplication operation must be done with the number immediately outside the bracket. If you enter 6÷2(1+2) in a calculator, you will get the answer as 1. If however, you remove the higher order of multiplication between a number followed by a bracket, by inserting a normal multiplication sign x, then 6÷2x(1+2) will give the answer as 9. Check it in a calculator. This is how it was tought to me, my dad, and grandad. This has been the convention. Why are you new people messing things up? Please go back to primary school. Seriously, the maker of this video cannot possibly be a mathematician. You don't even know basic mathematics. Good grief!!!
@yantzee0014
Жыл бұрын
The way people get there is pretty simple. If you will recall division of fractions, you solve those by flipping the divisor, for example (5/2)÷(1/2) = (5/2)*(2/1)=(5*2)/(1*2)=5/1. Now, we can do something similar with 6÷2, which is (6/1)÷(2/1)=(6/1)*(1/2)... In other words, 6÷2 can be easily expressed as 6*(1/2). This leads to 6÷2(1+2) actually being 6*(1/2)*(1+2), and I'm sure you can resolve that yourself. What I'm trying to say here is that division is actually multiplication by the inverse of the divisor. so you do division and multiplication from left to right, unless brackets say otherwise. If you want to get 1, then you write 6÷(2*(1+2)), as in we're dividing 6 by both 2 and (1+2). I was typing this on my phone so forgive me for computation error, but I hope that you can see why people say 9 instead of 1.
@TubeScavenger
Жыл бұрын
Wolfram Alpha says the answer is 9 which is correct.
@Sauvenil
Жыл бұрын
@@yantzee0014 The division symbol is the screwy part. Half of people read it as "everything after this is the denominator" and half of people don't.
@daroganwr421
Жыл бұрын
My calculator also gives 9
@allta5
Жыл бұрын
6÷2(3)=only 1. 6÷2×3= 9. though 2(3) is 2×3 meaning, we can not apply to 2(3) to 2×3. Therefore 2(3)=only 6, because 2(3) can not be divided 2×3
@slc504
Жыл бұрын
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/..
@christopheharvey8910
Жыл бұрын
I was educated in the 60's BODMAS Worked perfectly. WHY was it changed???
@deysworld314
Жыл бұрын
I too am amazed to see this, and curious to know why it changed or it's just a hoax
@christopheharvey8910
Жыл бұрын
@@deysworld314 I think it is real. They have twisted everything. Base 2 (0,1) is no longer called base two. We had Natural numbers (1- infinity) and whole numbers (0 - infinity), They call them intergers now. Intergers are only positive numbers now. Multiplication and division are done in away that they do not need to know times table. It looks weird and indirect but it is not physically working the numbers.
@Sauvenil
Жыл бұрын
@@christopheharvey8910 Integers are just non-fractional "whole" numbers. Not sure where you got the idea that there aren't negative integers, but "integer" doesn't care about positive or negative.
@christopheharvey8910
Жыл бұрын
@@Sauvenil Back in the 60's we were taught that Natural Numbers were the European short comings and had no Zero. Then when the Far East made us aware of our missing essential we called the more fuller set Whole Numbers. Integers are Whole Numbers and their inverse or negative. Zero was the mirror making numbers the inverse order of Natural Numbers. Fractional Numbers is a portion of a number or group or unit. It exists zero/nothing and 1/a whole/unit/group/ set. It can be attached to an integer as improper fraction E.g. a set or whole divided 7 and one portion is 1/7. Improper Fraction e.g. 3 whole units plus 1/7 of a unit = 3 1/7 or 22/7. Natural Numbers are all positive Integers are Natural Numbers and their negative inverse plus Zero. ZERO is neutral Absolute numbers is the reference to its location to zero. It is written as a number between vertical lines. Then I watched a long equation solving and it was stated that X was an integer and therefore positive. That is when I became confused as when Natural Numbers and Integers Numbers were the same. vid
@nwj03a
Жыл бұрын
I heard some professor explain equations like this one as being similar to saying, “I saw a man with a telescope.” Did you see a man while you were using a telescope? Or Did you see a man in possession of a telescope? Either can be correct.
@l.w.paradis2108
Жыл бұрын
Super! Exactly right.
@capsumithfirst5345
Жыл бұрын
6÷2(1+2) is the question but Writing as 6÷2×3 is incorrect 😂
@mysteriousjz
9 ай бұрын
I believe the parenthesis are always solved first. 2(3) is basically one quantity that you need to solve first. Look at it as spouses, one can not be without the other, so its ONE couple. Therefore, just as (2+1), the parenthesis solved first, you must also get rid of the parenthesis but this time it is multiplication. So, its 6. After that, you would follow the order (PEMDAS) rule. So, answer is 1. (Note: if there was no parenthesis, lets say, 6÷2×3, then it would have been 9). So, the rule of thumb is to solve inside of parenthesis, and then rid of parenthesis asap.
@summerrose8110
Жыл бұрын
0:00- The answer is 1, I'm not great at mental math. I need to write it down, use PEMDAS and my calculator. 3:35- So you divided first and that's how you got to 3. With PEMDAS multiplication comes BEFORE division. You went backwards towards the end.
@hajkie
Жыл бұрын
You calculator will not give the answer 1.
@prasannayt1881
Жыл бұрын
1 Is The Correct answer.
@HHplayground
Жыл бұрын
Did you not watch the video?
@prasannayt1881
Жыл бұрын
@@HHplayground.. what video.. .. whats your answer bythe way?
@bryndelmano6134
Жыл бұрын
I got 9 immediately and assumed I was likely incorrect, given there's more than one video on this equation and I was an art major.
@zakiya1635
Жыл бұрын
Your answer is correct.
@dannymlimosnero3353
Жыл бұрын
9 is the answer
@pulsar22
Жыл бұрын
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.
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