6÷2(1+2) = ? | Correct Answer Inside Finally Solved!!

6÷2(1+2) = ? | Correct Answer Inside Finally Solved!! | PEMDAS/BIDMAS is Wrong?!

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3 жыл бұрын

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This video goes into the reason why this problem has been causing so many issues. The notation, ambiguity and interpretations are discussed here and why this problem is causing so many issues.
In this video we look 6÷2(1+2) - also written as 6/2(1+2).
This is a viral maths problem which has got people discussing, arguing and debating.
The debate finishes with this video as I give the correct answer. And the answer I have given in this video is the one agreed upon with most academics.
I look at BODMAS, BIDMAS and PEMDAS.
This video also applies to 48÷2(9+3) or 48/2(9+3).
I also used examples and definitions from higher level maths to give clarity to this problem.
I also showed how many common solutions to this problem are actually not correct.
Enjoy.
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Thank you for watching.

Пікірлер: 2 800

@michaelkrailo5725 Жыл бұрын

As a programmer, this is simple. The order of operations are programmed in and you have to know how it is computed but I never leave it up to the conventions as shown. My first thought about this is that the initial question is completely ambiguous due to the missing parentheses around the right side of the division symbol (if that is what was intended). The bottom line is never leave out brackets which leaves you at the mercy of the order of operation rules. It's just a cruel ambiguity otherwise which causes the robot to explode "That does not compute, that does not compute...". I don't have a problem with multiple levels of parenthesis, that's the very thing that takes the ambiguity in our thinking out of the equation. Instead, simply break the equation down into smaller parts using variables. That's what we do in the programming world and it is much easier to read and understand. Do not rely on ambiguous conventions or induce ambiguity. Remove all ambiguity using variables or parenthesis and we will all get the same exact result. Edit: for instance, a=6, b=2, c=a/b, answer=$c*3, and 9 is the answer but this has nothing to do with any rules of operation as it is clearly defined what the intension is by using in smaller sized chunks instead of stuffing it all together and having to rely on conventions. It's almost as if, this was thrown out there just to cause controversy for the sake of stirring the pot on who knows the conventions and who doesn't. To be honest, I don't care. All that really matters is that whatever was indented is accurately interpreted by the person needing to get the correct answer.

@TheFlax33 Жыл бұрын

No doubt. My Pascal teacher in college would of threw my printout at me for ambiguous coding .

@earthstick Жыл бұрын

a la LISP, fully parenthesised prefix notation.

@insoft_uk Жыл бұрын

As a programmer • is always implied, one thing I like about TI 83 calculators they use * / and * is implied, I hate my CASIO it’s childish looking symbols the multiplication is x wtf use • it’s a graphical calculator and it uses what I call baby’s symbols

@KathrynLiz1 Жыл бұрын

Yep learned to do it that way... used to be an Assembler, Cobol, Fortran and RPG programmer back in the 60s....(Assembler mostly,,, IBM).

@snagswolf Жыл бұрын

It's only ambiguous if you don't know the rules of math.

@marcosmercado5648 Жыл бұрын

In other words, if you want an A grade in the class, you must do it the way the teacher explained it, otherwise you are screwed! 🙂

@utoothheartyeight Жыл бұрын

Ah, You got it!

@highlanderthegreat Жыл бұрын

@@utoothheartyeight or you can prove the teacher WRONG...LOLOLOL

@78tag Жыл бұрын

@@highlanderthegreat ....that would get you kicked out of school with an "F" to boot. That is how the leftist school hierarchy works now. Scientific truth is no longer allowed - only "their truth".

@78tag Жыл бұрын

This is always the case when "the teacher" is part of the current education system in the obiden regime.

@kamakiapeter7815 Жыл бұрын

😂 Do whatever you can to find out what your teacher prefers.

@TomTerrific-vm3qg Жыл бұрын

Where in your order of operations does it allow you to rewrite an equation? Your third step is invalid. That parenthetical has an integer directly correlated to lt That integer indicates that that parentheses denotes the multiplication operation. That doesn't mean you can rewrite the equation. Follow the order of operations solve the parenthetic and the answer is {1} not ambiguous.

@mikestuart7674 11 ай бұрын

Exactly

@donaldnelsonbarger2978 2 ай бұрын

We also should look back to the description of "÷", the page said {expression1} "divided by" {expression2} so, for this case we don't have {expression2} until the second parentheses.

@F-14_Jockey 17 күн бұрын

The American Institute of Physics - "never write 1/3x unless you mean 1/(3x) " [5]. This style is extremely common in many professional contexts, for instance " 1/2π " is a very common factor and it is universally understood to mean " 1/(2π) ". [S. Hargreaves] Hence the answer is '1', using an HP calculator with RPN you will always get one. Also... “Implied multiplication is where we have our next conflict. The American Mathematical Society has previously followed the convention that "multiplication indicated by juxtaposition is carried out before division" [3], and this is still implicit in the examples in its current style guide [4].

@timsmith4089 Жыл бұрын

A month or so ago, I went around and around with people on a similar Facebook post where I argued for the ambiguity of such an expression. In some cases I was accused of seeing ambiguity where none existed because of PEMDAS (or its variations) after all! But the fact that many on the post responded with differing answers demonstrated the ambiguity despite protests to the contrary. I argued, and still do, for clarity over convension as this video discusses. As a retired engineer, clear communication was important throughout my career. Such ambiguity would never be tolerated in the real world where the consequences can be catastrophic. I'm all for convension where its limits are understood and adhered to.

@RS-fg5mf Жыл бұрын

You can argue for better clarity BUT failure to understand and apply the Order of Operations and the various properties and axioms of math correctly as intended doesn't make the expression ambiguous and isn't a valid argument against the expression... On average 70% of adults incorrectly believe that 5+2×10=70 and swear they were taught that way. Does that mean 5+2×10 is ambiguous?? Absolutely NOT... Ignorance of the basic rules and principles of math does not equal ambiguity...

@timsmith4089 Жыл бұрын

@@RS-fg5mf I stand by my statement that the limits of conventions need to be understood. Even if, in your example, 25 is obvious to me, and even if only 30% (or less) of adults incorrectly calculate 5+2x10, even may be too much risk in the real world where clear communication regarding equations far more complex trumps the consequences of adhering to mere convention. Unfortunately, people cling to calculators too much these days yet even in the video the guy's calculators yielded differing answers. That was a surprise to me, and in my view, supports the point I'm trying to convey.

@RS-fg5mf Жыл бұрын

@@timsmith4089 I understand your point but your point is irrelevant as a majority of the people who get this wrong or get 5+2×10 wrong do not work in professional fields where Math is a major priority. In fields where Math is a major priority a vinculum would be used in almost every situation... Now understand my point... Failure to understand the basic rules and principles of math does not make the expression ambiguous it means too many people are ignorant (lack the knowledge) of the basic rules and principles and can't evaluate a basic 4th grade arithmetic expression correctly... You suggest giving a person a fish I suggest teaching a person how to fish... Give them a fish they eat for a day. Teach them to fish they eat for life. I teach math and I am an advocate of promoting the Order of Operations and the various properties and axioms of math correctly as intended...

@snagswolf Жыл бұрын

The only ambiguity being created is from those who insist that juxtapositional multiplication takes precedence when you're dealing with non-monomial expressions. Order of Operations was put in place to remove ambiguity. You all are working against those efforts.

@RS-fg5mf Жыл бұрын

@@snagswolf EXACTLY 💯

@xnjgirl99 Жыл бұрын

If I have 6 pizzas to be divided between 2 tables, where each table seats 3, how many pizzas would each person get? Certainly not 9.

@DoseofScienceDoS 11 ай бұрын

You did math wrong lol. It would be 18 pizzas divided by two tables. How sad 😢

@xnjgirl99 11 ай бұрын

@@DoseofScienceDoS - what’s really sad is you truly believe it’s 9. Clearly, the educational system has FAILED you. 🥲

@mikestuart7674 10 ай бұрын

@@xnjgirl99 Dose doesn't really believe that. He is just trolling.

@gbhxu 6 ай бұрын

Exactly!

@sander_bouwhuis Жыл бұрын

Very useful video! It goes to show I either never encountered improper notation, or I simply didn't realize it was ambiguous.

@mikestuart7674 11 ай бұрын

There is absolutely no ambiguity see my explanation above.

@skilz8098 11 ай бұрын

It's not ambiguous! The only correct answer is 1. What's ambiguous is the lack of ability to properly interpret or evaluate said expression not just based on the order or precedence of said operators, but also based on upholding the basic properties of arithmetic or elementary algebra being, the distributive, the associative, and the commutative properties. The convention is only part of the story and most who try to argue about convention, always seem to forget about the basic properties and axioms of said mathematics.

@MrGreensweightHist 8 ай бұрын

@@skilz8098 It is not ambiguous,. but the correct answer is 9

@JoeNarbaiz 7 ай бұрын

@@mikestuart7674 You seem to think that 2(1+2) is juxtaposition and therefore you modified the original expression to include additional parentheses. 2a is juxtaposition but 2(a) definitely is not. 6÷2(1+2)=9 and 6÷(2(1+2))=1.

@mikestuart7674 4 ай бұрын

@@JoeNarbaiz If 2b is juxtapositional and b=(a), then 2b = 2(a) and either is juxtaposed

@pegasisilver6249 8 ай бұрын

Having 5/2x coming out as 5x/2 is pure idiocy, who came up with that?

@klm2558 5 ай бұрын

Nobody except the interpretation of poorly written expressions

@wadabid6165 5 ай бұрын

Well, when we commonly use / we probably see it as the fraction bar --- but tilted over, so normally we would think its 5 / (2x) since we are used to fraction bars. But the rules are the rules, and it is true that it may be misleading for thay exact example of 5/2x, but in an operation like 17/283•1939/848•27 it is helpful to just follow bodmas and forget about everything else, solving each sign (/ or ×) in the order they appear.

@perjohanaxell9862 4 ай бұрын

@@wadabid6165the thing is I didn't know of the left to right rule even tho I teach math. Her in Sweden it's not in the math books because we don't write expressions in a single line. That's simply not how it's done at any level of our skolsystem. If you do you therefore have to use paranteses to make it clear.

@lynnrathbun 4 ай бұрын

elementary arithmatic teachers.

@mybluemars 8 ай бұрын

The takeaway I get from this is: Understand how your calculator (dedicated or called) interprets mathematical expressions and use parenthesis whenever possible.

@donaldnelsonbarger2978 4 ай бұрын

Do the job on paper and let the calculator do the multiplications

@zakelwe 3 ай бұрын

The problem with calculators is that they don't have two lines to work with a a ------- or ------ * c bc b so don't get the notational clue on which to do first. Hence why ( ) are important to reduce ambiguity going from classical two line notation down to one.

@daviestj 8 ай бұрын

with your 2 calculator example, one calc was processing an extra pair of parentheses, forcing the wrong answer. Some calcs are inserting the extra parentheses when you hit the equals button.

@j7ndominica051 Жыл бұрын

We don't even use an inline division sign in high-school algebra. If you want to input the equation into a computer, you usually have to put all the parentheses in. A basic chinese scientific calculator won't even understand the implied multiplication without an operator.

@avibhagan 3 ай бұрын

6÷a(1+2) = 9 , solve for a I bet you won't get a=2.

@jmm1233 8 ай бұрын

the 2(1+2) is iteration of a function of n(x) so it should be wrapped up in brackets like a parcel as in 6/{2(1+2)} , which works well in python and c++ interpretation

@MrGreensweightHist 7 ай бұрын

"the 2(1+2) is iteration of a function of n(x)" no it isn't "so it should be wrapped up in brackets like a parcel as in 6/{2(1+2)} " Except you just changed the problem because you assumed 2(+1+2) was grouped when it clearly isn't. If they had meant 6/{2(1+2)}, they would have typed 6/{2(1+2)}, and not 6/2(1+2) Work the problem as it is, not as you want it to be

@KyleTremblayTitularKtrey 4 ай бұрын

@@MrGreensweightHist Except people write 2x and know its (2x) If I write 4/2x it means 4/(2x). If I write 4^xy every single math textbook interprets 4^(xy). Juxtaposition combines without needing brackets.

@ejrupp9555 6 ай бұрын

x = (1)x ... you could do that to every number to change 2 ÷ 2 = 1, to 2 ÷ (1)2 = 4, if you do the division before the parenthetic ... therefore, it is obvious that the parenthesis when used without the multiplication sign takes precedent.

@thierrypauwels 11 ай бұрын

When I was at secondary school, we were taught that multiplication had a higher precedence than devision, not only when it is juxtaposition, but even when explicitly written with 'x'. Then I started to programme in Fortran, and suddenly multiplication and division had the same precedence. I really had to be very careful when programming a formula like (a+b)(c+d)/(e+f)(g+h).

@culwin 11 ай бұрын

You were taught wrong then.

@thierrypauwels 11 ай бұрын

@@culwin It is not wrong. It is just a different convention. Conventions are not part of the mathematical concept and are not dogms. There is not such a thing as a right convention or a wrong convention. Same with driving on the left or on the right. It is just a convention. And Britain has chosen a different convention then the US. That does not mean that one of them is wrong. And if you go to another country, you should know which convention they use before hiring a car...

@culwin 11 ай бұрын

@@thierrypauwels You're wrong.

@DoseofScienceDoS 11 ай бұрын

I agree, you weren’t taught right and you are still wrong. There is only one answer and solving your example equation is ridiculously easy

@BrianG61UK 10 ай бұрын

@@thierrypauwels But conventions are supposed to be ideas that most people use. Does your country only use calculators made locally and only program computers in locally designed programming languages?

@virtualDon Жыл бұрын

Your calculators are correct: The one on the left had 6/2(1+2)=9 and the one on the right had 6/(2(1+2))=0. The extra brackets on the right calculator do in fact make it equal to 1. Also, your analogy of 1/2x is not the same as 1/2*x

@teknul89 Жыл бұрын

That’s because the one that give 1 was an outdated way to calculate it from 1917 but it’s outdated Historically the symbol ÷ was used to mean you should divide by the entire product on the right of the symbol. But the correct answer is 9 since we do order of operation aka pemdas Since there is a hidden multiplication before parenthesis It’s easier to understand it if you say (6/2) * (1+2) = 9

@GanonTEK Жыл бұрын

Depends on the scientific calculator but here are some that give one or the other if you type it exactly as in the video: These give 1: Casio FX 83GTX, Casio FX 85GT Plus, Casio 991ES Plus, Casio 991MS, Casio FX 570MS, Casio 9860GII, Sharp EL-546X, Sharp EL-520X, TI 82, TI 85 These give 9: Casio FX 50FH, Casio FX 82ES, Casio FX 83ES, Casio 991ES, Casio 570ES, TI 86, TI 83 Plus, TI 84 Plus, TI 30X, TI 89. Online calculators don't agree either. Microsoft Math gives both answers on screen. The notation is ambiguous. There is no agreed upon convention on whether multiplication by juxtaposition implies grouping or not. Half of calculators use the academic way (Sharps, most Casios and some TIs) and half use the more programming/literal way (Some Casios and most TIs). Both equally valid. The expression itself is the problem and is not valid.

@romerypb13 Жыл бұрын

@@GanonTEK nice speech

@etzjunior_ Жыл бұрын

So explain why 0:26 , The calculator on the far right and the one in the middle still say 1? No extra brackets

@tonitalas1757 Жыл бұрын

The one on the right gives 1, not 0. There is no correct simplified answer to this expressio!

@royg123 8 ай бұрын

Great video. I've always considered these sorts of questions less ambiguous, and more malformed. Division via the quotient symbol is part of one notational system, whereas implied multiplications part of a different notational system. If you are using implied multiplication, you would always use fraction notation for division, and you would never have ambiguities as a result. PEMDAS really applies specifically to the notational system that uses explicit multiplication and quotient symbol for division.

@perjohanaxell9862 8 ай бұрын

Yes it's all that one line notation that makes it ambiguous. It's all so much clearer when using two lines so you can write the divisions properly.

@pompejio 8 ай бұрын

@@perjohanaxell9862 As a tutor I teach my students right from the beginning to use a fraction line instead of the division sign. At first they don't like it, then they love it. Not only because you can see how to reduce fractions way earlier... It's the same with negative powers, just put them down the escalator (denominator).

@MrGreensweightHist 7 ай бұрын

Uh, no. This is a straight forward problem. the only possible answer is 9 You are misapplying the term implicit multiplication

@zakelwe 3 ай бұрын

@@perjohanaxell9862 Spot on, techically you should even use the parenthesis on the two line notation but as it is so obvious what is intended there is no need. In the old days of course this would never have even popped up, as all handwritten on two lines, but as we move to one line notation it is causing issues. People are starting throwing MD or DM or left to right at it depending on their fancy, none of which actually apply to two line notation very well ! Instead if on line use parenthesis to indicate which of the two line ones you are representing. Simple. Hence why that is the suggested convention and not MD or DM or left to right .

@MichelSLAGMULDER 6 ай бұрын

The problem is very simple. The symbol ÷ is illegal. That all. I 've made maths studies in france and during this period I have never used this symbol. No teacher used it. We have other solutions.

@MuffinsAPlenty 6 ай бұрын

Eliminating the obelus (÷) wouldn't resolve the ambiguity. Because then people would write 6/2(1+2) and still have a debate over whether 1 or 9 is the correct value. And I know this because lots of people talk about the problem with the solidus (/) too, and all the same confusion/disagreements pop up. The issue is inline notation where implicit multiplication directly follows division. And this problem is unlikely to ever go away, because inline notation will likely always be used by people somewhere, and the differences of opinion on whether implicit multiplication gets special precedence or not are "natural" on both sides of the debate.

@doughendrie5468 6 ай бұрын

This is a simple term divided by a term consisting of 2 factors. The 2 and the (1+2).

@Billicyhot 2 жыл бұрын

This is some calculators will return an invalid expression error until the implied multiplication is explicitly written and replaced with the "boatload of brackets"

@williamjackson2089 7 ай бұрын

If 6/2(1+2)=9 if calculating from left to right and 6/(1+2)2=4 calculating from left to right and 6/2(1+2)=1 if using juxtapostion multiplication convention and 6/(1+2)2=1 again using juxtaposition multiplication. Since 2(1+2) and (1+2)2 both =6.Also 6/(2(1+2)) and 6/((1+2)2) both =1

@harrymatabal8448 21 күн бұрын

6÷2×3 = 3×3=9. 3÷2=3/2 ×6=9 6×3=18÷2=9. Simple grade 5 maths

@AmerigoGadsden 2 ай бұрын

Excel says: "We found a typo in your formula and tried to correct it to: =6/2*(1+2)" It gives the answer as 9. It doesn't like the input.

@highlanderthegreat Жыл бұрын

another way it should be written is 6 divided by (2(1+2 ))= you do what is inside the parentheses first. then you divide

@joenarbaiz1640 Жыл бұрын

So, you agree with me that it should be written that way if you want to emulate multiplication by juxtaposition. Your distributive property example has been discredited.. Thank you. 😊

@highlanderthegreat Жыл бұрын

@@joenarbaiz1640 nope not the way i was taught back in late 50s and early 60s..i still say the answer is 1

@joenarbaiz1640 Жыл бұрын

@@highlanderthegreat And I was taught that the answer is 9 for that expression. I don't give a damn what YOU were taught. You did exactly what I said that you have to do to emulate the function of a vinculum. 6÷2(1+2)=9. 6÷(2(1+2))=1. It is blatantly obvious that you don't know the difference between an obelus and a vinculum. An obelus and a solidus have the same functionality as opposed to a vinculum. Have a good one. 👍 This conversation is over. Adios! 😆🤣😂😹

@highlanderthegreat Жыл бұрын

@@joenarbaiz1640 in the vids i sent you my juxtapositions of the problem have been affirmed as the correct way...

@joenarbaiz1640 Жыл бұрын

@@highlanderthegreat What videos? Why I said you agree with me is because you added another set of parentheses to the expression. 6÷(2(1+2)) is how you represent a vinculum in inline text. You do what is inside each set of parentheses first before you divide and obtain an answer of 1. You just illustrated the proper way to indicate juxtaposition but it doesn't match the original expression. 😕 The original expression is merely multiplication. The obelus (÷) and the solidus (/) are functionally different from a vinculum or horizontal fraction bar. 😆🤣😂😹

@Vinraymi 8 ай бұрын

in school, I leaned that multiplications and divisions, as well as additions and substractions don't have a specific order, as long as you do P E (M/D) (A/S) Edit: forgot to mention that you have to do it from left to right in cases with multiple M/D or A/S

@danquaylesitsspeltpotatoe8307 8 ай бұрын

LEARN TO MATHS its grade 6 you derps!

@dorothymacritchie 8 ай бұрын

if pemdas to my knowledge the anwser is 9

@tobesgamer3976 7 ай бұрын

@@dorothymacritchie any version of pemdas like bemdas and bodmas always get 9 because multiplication and division is equal to you do from left to right

@zakelwe 3 ай бұрын

There is a left to right rule for addition and subtraction but not one for M and D, this is a common misconception. The reason why none for D and M , even though it has been suggested in the past, is because originally this format of a/b*c was written over 2 lines and the notation indicated what was required to give the two possible answers. Doing left to right always means you get (a/b) * c whereas the person writing it might have wanted you to actually do a/ (b*c). The two line version are obvious without the brackets. For one line you need the brackets to tell you which way to pick, D first or M.

@samael338 Жыл бұрын

So the solution to this dilemma is to stop writing, in lower level maths, ambiguous math equations if you honestly expect an unambiguous solution. It is pure laziness or incompetence to complain about using extra brackets or parentheses. It is like complaining about using vowels in words.

@GanonTEK Жыл бұрын

100%

@MrGreensweightHist 8 ай бұрын

9 is the only correct answer. the problem is not ambiguous. People who think it is ambiguous simply don't understand how to read a math problem correctly.

@samael338 8 ай бұрын

At least we know how to read English.@@MrGreensweightHist

@MrGreensweightHist 8 ай бұрын

@@samael338 I doubt it. but by all means, continue with the insults instead of addressing the facts. 🙄 This problem is NOT ambiguous. 6÷2(1+2) 6÷2(3) 6÷2X3 3(3) 9 Is the ONLY way to read it

@samael338 8 ай бұрын

Hey, it will be ok. I know words can be hard sometimes. Stay strong brother!

@steveross8364 6 ай бұрын

What's to debate? It's 1. Because you complete the calculations on each side of the inital operator first, then solve the equation.

@edmondgautier8301 9 ай бұрын

As the expression is ill formed ( non compliant with ISO 80000-2), there is no answer possible.

@GanonTEK 9 ай бұрын

Non-compliant with ISO-80000-1 also.

@natetheg379 Жыл бұрын

3:30 What he was talking about here, I say that if there is an invisible 1 before variables without a coefficient, then there's invisible parenthesis around the coefficient and its variable or two multiplied variables before divided ones that just causes an exception to the order of operations.

@mikestuart7674 11 ай бұрын

There is no exception needed. Just do the parenthesis first and remember the integer in front of the parenthesis is the common factor of the parenthesis and is part of the parenthesis. It is not a separate term. 2(1+2) = (2+4) = (6) = 6

@MrGreensweightHist 7 ай бұрын

@@mikestuart7674 Wrong, as usual

@MrGreensweightHist 7 ай бұрын

"then there's invisible parenthesis around the coefficient and its variable or two multiplied variables" That is true, but in... 6/2(1+2) There is no variable. There is no coefficient

@J-kd2qc 5 ай бұрын

@@mikestuart7674 You can't just separate the 2 from the 6, you multiply what's outside the parentheses with what's inside the parentheses. 6/2(1+2) 6/2 * 1 + 6/2 * 2 3*1 + 3*2 3 + 6 9. Think of it this way, one half of 20 is 1/2(20) = 10, not 1/40th.

@mikestuart7674 5 ай бұрын

@@J-kd2qc The 2 is separated from the 6 by a division sign. Numbers do not attach to divisions. They do however attach to parenthesis. Go ask your high school math teacher if you do not believe me.

@hurktang Жыл бұрын

No! Multiplication by juxtaposition have priority! That's it. You know it, you saw it clearly in your research. People who use PEMDAS in grade 2 are not told about juxtaposition so they will not write that formula. Clearly PEMDAS cannot solve juxtapositions right. So it's okay if you say "error I don't know", but I'll tell you. This answer is 1.

@jamesalexander7540 8 ай бұрын

I was taught PEDMA and Inside Out. Therefore I come out with the answer of 1.

@goldenrainbow745 3 жыл бұрын

Which as level maths is easy Cambridge or Edexcel?

@Steve-re9md Жыл бұрын

I had a lot of problems with maths at school. Basically I did not know my tables and being asked a question relating to them frightened me to death! I often found myself thinking 'why am I learning this rubbish' In any event I decided on a career at sea and found out that I needed virtually everything I had studiously rejected! Somehow I bodged my way through all the exams and ended up as Captain of a High Speed Passenger Catamaran running from Gibraltar to North Africa. The moral of my story? well I had to turbo charge my self confidence when I went for a job, I became very good at first impressions and gaining the upper hand in interviews but oh how much easier if I had been told why I needed all those maths things in the first place.

@dannygjk Жыл бұрын

Sounds like you cheated your way thru.

@pulsar22 Жыл бұрын

Even a street vendor need math. Even a farmer in some 3rd world country needs math. It really is the onus on teachers to make practical use of math apparent right from the start so that students will be more motivated.

@skilz8098 11 ай бұрын

@@dannygjk I wouldn't say cheated, but I could joke at the point of saying: faking his way through with a big charming smile lol...

@mikestuart7674 10 ай бұрын

If you had gone to my school this would not have been a problem. When we learned our times tables, until you could recite your times tables to 12 x 12 you could not go out for recess. A good incentive to learn.

@charlesdarwin5185 9 ай бұрын

You should have done koomon😂

@larryhutchens7593 Жыл бұрын

After much number crunching with my pocket calculator and using a flat earth based geometric system which negates the forces of gravity I came up with 42 as the correct answer.

@confusious7433 Жыл бұрын

😜

@donmacqueen Жыл бұрын

Congratulations! You have now been granted membership in the Secret Society of Special Symbols.

@larryhutchens7593 Жыл бұрын

@@donmacqueen Oooooh, I like secret things.

@drziggyabdelmalak1439 Жыл бұрын

😂Brilliant!

@blokkadeleider Жыл бұрын

🤣 Gold!

@turtlerockfire3664 4 ай бұрын

To help sole the problem, write it as a fraction. 6/ 2(1+2). In math, you can write this as a fraction. The answer is 1.

@kychoi2653 8 ай бұрын

Implied multiplication or ratio - has implied parentheses around it, so 'ab' means (aXb). If we code it in a program, we should add ( ...) to it. 48÷2(9+3) is 48÷(2(9+3) ).

@MrGreensweightHist 8 ай бұрын

@J-kd2qc 5 ай бұрын

No it doesn't. Implied multiplication is only where the multiplication is implied. Adding parentheses changes the expression. Look at this: 10 - 5 + 2 should be 7 right? Adding parentheses to 5 and 2, 10 - (5 + 2), this now equals 3. Implicit multiplication is so that you can write letters next to each other without having to explicitly have a multiplication symbol. A * B * C * D = ABCD. That's all implicit multiplication means. In this case, 6/2(1+2) is the same as 6/2 * (1+2). All you need to do is multiply what's outside the parentheses with what's inside the parentheses. 6/2(1+2) 6/2 * 1 + 6/2 * 2 3*1 + 3*2 3 + 6 9. Think of it this way, one half of 20 is 1/2(20) = 10, not 1/40th.

@lawrenceandrews4367 3 ай бұрын

@@J-kd2qcwrong

@is7728 8 ай бұрын

Problems of Dividing by a(b) always causes arguments 😮‍💨

@nomis4913 Жыл бұрын

I just tried this using a Casio fx-991MS calculator. If I enter 6/2(1+2)= it gives 1 If I enter 6/2x(1+2)= it gives 9 (where / is actually the division symbol in both cases) Two different answers from the same calculator depending on whether the multiplication is implicit or explicit. Go figure. For what it's worth, if I were presented with this in an exam I would have written down 1.

@donmacqueen Жыл бұрын

There are two ways to interpret the expression 6/2(1+2). When you enter 6/2(1+2) the calculator chooses one of the two ways. (some other calculators choose differently) When you enter 6/2*(1+2) you are telling it which of the two ways you want. There is lots of disagreement over which of the two ways is correct, with adherents on both sides adamantly insisting they are right and the other is wrong. As best I can tell, there is no universal authority to settle the matter. The ISO has two relevant documents, ISO 80000-1 and ISO 80000-2, and they do not settle the matter.

@abbyz5388 Жыл бұрын

Yeah when I see a number next to the parenthesis I carry it over I don’t just add a multiplication symbol between them.. it’s so weird my brain hurts 🗿

@utoothheartyeight Жыл бұрын

Does a cow give milk? NO, you have to take it.

@p.thomas7843 Жыл бұрын

Great calculator uses BODMAS!!

@bartsky1945 9 ай бұрын

and 1 is only correct answer to equation that is written this way

@SpiralDiving Жыл бұрын

You can say 2(x) is "2 lots of x" and then you will be in accord with most scientists....

@MisterTutor2010 8 ай бұрын

The only problem is ambiguous notation. This is why I don't use ÷ when writing an equation. The horizontal version of / makes the intended order of operations clearer.

@herbie_the_hillbillie_goat 8 ай бұрын

No, it's pretty clear. Follow the established order of operations and you unambiguously get 9.

@MrGreensweightHist 7 ай бұрын

÷ and / mean the same thing, and if you write it with a /, the people getting the wrong answer or 1 are still going to tell you the wrong answer of 1. The sign is not the problem

@syncradar 5 ай бұрын

I think that ÷ and / should be differentiated. 6÷2(1+2)=9 While 6/2(1+2)=1

@MrGreensweightHist 5 ай бұрын

@@syncradar ÷ and / are the same thing. There is no difference and no reason there should be.

@syncradar 5 ай бұрын

@@MrGreensweightHist Its for my own convenience.

@rockymarciano6750 11 ай бұрын

If you set this problem, you could use brackets to prevent ambiguity.

@MrGreensweightHist 8 ай бұрын

The fact a second set of brackets is not used means it is not ambiguous. The answer is 9

@zakelwe 3 ай бұрын

@@MrGreensweightHist Or 1 depending if you do the multiplication first. With format a/ b * c there is ambiguity without brackets on whether to do the division or multiplication first, there being no convention actually for DM or MD or left to right .

@MrGreensweightHist 3 ай бұрын

@@zakelwe " there being no convention actually for DM or MD or left to right ." Yes, there is. Multiplication and Division share priority. When operations share priority they are done left to right. That is the convention Basic orders of operations. 6th grade math

@soilomasbello1156 Жыл бұрын

That's why I use RPN calculators so I'm in control of operations order if the order is incorrect is because of me not inadvertently the calculator.

@RichM3000 11 ай бұрын

Same. Even on my iPhone I use an RPN calculator app.

@williamjackson2089 7 ай бұрын

Is there a practical exercise with say bricks to try to prove which is right?

@fcey337 7 ай бұрын

Thank you so much for your excellent explanation.

@BAMozzy69 Жыл бұрын

Its intentionally ambiguous and isn't written the 'best' way to communicate the intended Answer. To me, the way its laid out, it could be written as 6 / 2(1+2) more like a Fraction - therefore the Answer is 1 If the person setting this problem intended us to get the answer 9, It should have been written (6÷2)(2+1) - but that's not how this is written so its the fault of the person setting this question and not communicating clearly.

@thierrypauwels 11 ай бұрын

We could swith to RPN (reversed Polish notation). No more ambiguities ! ;-) 6 2 1 2 + x : or 6 2 : 1 2 + x

@1-0-8 7 ай бұрын

Thanks for this explanation . I was never taught PEMDAS/BIDMAS as a child . I did GCE O and A level Maths and Physics in the 1970's so my answer was 1 (and not 9 )

@davetooes6179 8 ай бұрын

I'm 75 this is the first time my head exploded!! My maths learnt in the UK and Australia was BODMAS similar to the two you show. I ALWAYS thought people who got those math problems you see being posted WRONG were just not properly schooled in the way of doing those problems. Similarly seeing two electronic calculators getting differing answers just made it worse.

@tatspatsoor6096 8 ай бұрын

@davetooes6179 His 2 calculators are showing a different formula with an extra ( so no wonder it shows a different result.

@davetooes6179 8 ай бұрын

@@tatspatsoor6096 mate I missed that. bastard played with the data to get the results he wanted to show. Interestingly neither of those two formulas is acceptable in Excel without additional operands. I see previous replies esp. from engineers have the answer as 1. I'm the wrong one out my answer would have been 9 due to the maths I had been taught. But I never went passed year 10 Maths so there is that.

@danica899 8 ай бұрын

My Math in Canada utilized BEMDAS for order of operation: brackets, exponents, multiplication, division, addition, subtraction. It has been years ago since learning this and have never forgotten it. lol

@davetooes6179 8 ай бұрын

@@danica899 and using that your answer was 1 ??? My BODMAS gave it as 9

@cliffordschaffer5289 7 ай бұрын

@@davetooes6179 As a computer programmer I would fire anyone who didn't put parentheses in to make it clear. Nobody should be guessing what someone meant. Cheaper and easier to put a parentheses in than to deal with mistaken results later one.

@brybb3775 Жыл бұрын

Best to just follow the ISO 80000-2 standard for mathematical notation and do away with the ÷ sign altogether. I don't recall seeing that symbol being used beyond lower elementary arithmetic anyway. In cases where teachers choose to use it, they should clearly define what it means... whether or not ÷ is equal to / or if ÷ means that the upper dot represents the value to the left and the lower dot the values to its right. Still, I prefer they do away with it from the start as it may cause confusion for their students later on.

@cryofpaine 11 ай бұрын

The problem isn't the ÷. You would have the same problem if you used / as well. In fact, it would be more ambiguous because it wouldn't be clear whether you meant 6 - (1+2) 2 or 6 ----------- 2(1+2) But with the ÷, it's clear that the six is divided by the rest of the term, not that there is a fraction coefficient on the term in the parenthesis. The only ambiguity is people not understanding that multiplication by juxtaposition is not the same as multiplication, and comes higher in order of operations.

@MrGreensweightHist 7 ай бұрын

@@cryofpaine "But with the ÷, it's clear that the six is divided by the rest of the term," That is wrong.

@MrGreensweightHist 7 ай бұрын

÷ and / mean the exact same thing. Either way, you get... 6÷2(1+2) 6÷2(3) 3(3) 9

@brybb3775 7 ай бұрын

@@MrGreensweightHist, when no distinction is made between X over Y (X/Y in this case as I could not express the formula s intended in this thread) and X ÷ Y, one can get confused over the order of operations. In higher level maths (e.g. Physics), I don't recall seeing the ÷ symbol being used... which I think is due to this ambiguity (hence the ISO standard referenced). I am inclined to think that symbol was used due to the limitations in printing technology but nowadays, anyone can print out the actual unambiguous expressions nowadays making this symbol unnecessary for anyone past the lower elementary grades.

@MrGreensweightHist 7 ай бұрын

@@brybb3775 "one can get confused over the order of operations" Only if one does not understand the orders of operations. "I don't recall seeing the ÷ symbol being used." Understandable as it is not commonly used, but it means the exact same thing as / so once you know that, it should not matter. "which I think is due to this ambiguity " There is no ambiguity. To think the problem is written ambiguous, due to use of a seldom used symbol, even though the symbol has clear meaning, is akin to claiming a book is ambiguous because it uses a word you haven't learned yet. It is not a fault in the writing of the book. It is merely a gap in your knowledge. A gap that, once filled, makes the book crystal clear. "making this symbol unnecessary for anyone past the lower elementary grades." Until it pops up somewhere you didn't expect, like an internet brain teaser, and you find yourself lacking the knowledge to solve it. Not knowing something is never a fault. Not learning when the opportunity arises is. Whether it is written 6÷2(1+2) or 6/2(1+2) or 6 --(1+2) 2 It remains the same problem

@craigward4868 6 ай бұрын

The equation isn't mathematics. The question is a description of mathematics, i.e. a language. As with any language, if it is used poorly, it can be ambiguous. This equation is ambiguous. Some of that ambiguity can be removed by observing that division is a form of multiplication. Rewrite the statement as 6 x 0.5(1 + 2) process the parentheses first and get 6 x 0.5 x 3 No matter which way you process the operators, the answer is 9. If the author of the statement wanted the divisor to be the product of everything after the division operator, she should have added more parentheses or used other symbols available to arithmetic as a language. The two calculators in the video were given different equations so it is not unexpected that they would give different results. It just illustrates how ambiguity can be written in any language.

@ap3xmath123 7 ай бұрын

Thank you very much!!!! This was interesting! Definetely will guve another watvh and challenge my lecturers wow math is truly amazing

@MrMousley 8 ай бұрын

I would do it like this .. 6 / 2(1 + 2) = 6 / 2(3) = 6 / 6 = 1 I'd do the 2(3) before the divide because it's 2(3) and not 2 x 3 If it was 2 x 3 I'd do the divide first .. working left to right

@syncradar 5 ай бұрын

6/2•(1+2) 6/2•3 6/6 1 6÷2•(1+2) 3•(1+2) 3•3 9 I used ÷ and / differently.

@J-kd2qc 5 ай бұрын

All you need to do is multiply what's outside the parentheses with what's inside the parentheses. 6/2(1+2) 6/2 * 1 + 6/2 * 2 3*1 + 3*2 3 + 6 9. Think of it this way, one half of 20 is 1/2(20) = 10, not 1/40th.

@tigershark94 16 күн бұрын

@@J-kd2qcnope. One half of 20 would be expressed as 1 --(20) 2 Or, better yet, as 20 -- 2 What you wrote was 1 1 --- = --- 2(20) 40

@J-kd2qc 16 күн бұрын

@@tigershark94 HAHAHAHA, wow, you're so bad at math dude. Go back to second grade and learn the order of operations.

@user-jt1qc8vp9f 11 ай бұрын

Thanks for posting this need for clarity of presentation in mathematics. It also reminded me that some of the calculators that give different answers when the data was entered with the division sign can give the same answer of 1 when the data is entered as a fraction where the 2(1+2) is completely in the denominator.

@detroittigersandotherbaseb7220 9 ай бұрын

The only rules involved here is the commutative and distributive principles. Why are people doing 6/2*3? Multiplication and addition are commutative so the numbers can be swapped. And using distributive principle you have the answer of 1 It should be 6 6 ----- --------- 2(2+1) or 4+2

@emresahin94 8 ай бұрын

question is not 6/(2(2+1) so you cannot convert the question to a fractional number.@@detroittigersandotherbaseb7220

@MrGreensweightHist 8 ай бұрын

"2(1+2) is completely in the denominator." And that is a fault of the calculator because if you change to division to a fraction, the denominator is the 2 alone, not the (1+2)

@detroittigersandotherbaseb7220 8 ай бұрын

@@MrGreensweightHist One does not use calculators in this. All division is a fraction. In division there is the dividend / divisor = quotient. The dividend is the numerator and the divisor is the denominator.

@degrass5408 8 ай бұрын

The input into the second calculator is completely different than the first calculator since he put in 6+(2(1+2)), which means that 2(1+2) is done first because it's in parentheses. While the first calculator doesn't have parentheses around 2(1+2), thus 6+2(1+2) doesn't equal 6+(2(1+2)).

@DavidLee-qe3rd 5 ай бұрын

How calculators respond to implied multiplication varies depending where they are being sold and is based on canvassing the opinions of local maths teachers and examination boards (not professional mathematicians in general) for marketing purposes. The order of operations is always stated in the calculator manual - but of course almost nobody ever reads these! Likewise in publishers' style guides for printed mathematics in books and journals. Interestingly international Sharp calculators have always correctly and consistently interpreted implied multiplication and return different values with and without the "×" operator. eg my Sharp EL-531returns: 6 ÷ 2 × (1+ 2) = 9 but: 6 ÷ 2(1+ 2) = 1 Also interesting to note that, whilst log x² is ambiguous, the ambiguity is eliminated by convention in trigonometric functions. eg sin θ² = sin (θ²) whereas sin² θ = (sin (θ))²

@dennismood7476 10 ай бұрын

Interestingly, the (1+2) is never in question and is always 3. However, 2(3) = 2 X 3.= 3 x 2. therefor: 6 division sign 2(1+2) COULD BE (1 +2) =(3), so, 2 x 3 =6 divided by 6 = 1 OR 6 divided by 2 =3(3) =9 or since 2 x 3= 3 x 2, then it could be 6 divided by 3=2(3)= 6. The presentation is what the problem is NOT the math.

@jeremyhorne5252 Жыл бұрын

In logic, we call this a "well-formed formula problem". This is an interesting problem you present here. I am not sure if there are any parallels in logic, where precedence of operators always is critical.

@alext8828 Жыл бұрын

Why is the 2, just outside the parentheses not included in the parentheses operation. That would clear up the entire issue.

@joenarbaiz1640 Жыл бұрын

@@alext8828 Parentheses only include the contents WITHIN the parentheses. 2(1+2) is implicit multiplication. 2*(1+2) is explicit multiplication (2(1+2)) is juxtaposition.

@doughendrie5468 10 ай бұрын

2(1+2) is a parenthetical expression. The factor 2 is connected to the parentheses by juxtaposition. The expression is the factorisation of 6, and to simplify the 2(1+2) back to 6, the factor to must be distributed back into the parentheses, either by the Distributive Law or Order of Operations. 2(1+2) distribute the 2 (2*1+2*2) simplify (2+4) simplify 6 parentheses removed. Or by O of Ops 2(1+2) inside parentheses first 2(3) inside to outside next 6 parentheses removed The term 6 that is to be divided has no connection to the factor 2, due to 6/2 is a fraction, and factors must be whole numbers. “p22 Elements of Algebra Chapter IV - Of the Nature of whole Numbers, or Integers, with respect to their Factors p38. If, therefore, we consider all whole numbers as products of two or more numbers multiplied together, “ NOTE - Whole Numbers

@degrass5408 8 ай бұрын

@@joenarbaiz1640this is true if there is no other × or ÷, but the way it's written in the calculator it's clear that 6÷2(1+2) doesn't equal 6÷(2(1+2)) because (2(1+2)) is done first since it's all in parentheses: 6÷(2(1+2))=6÷(2(3))=6÷(6)=1. While the quantity 2(1+2) is not in parentheses, thus we get 6÷2(3)=6÷3×3=9. He may have a point, but his examples (or at least this example) doesn't say anything beyond that PEMDAS is an arbitrary convention that is accepted.

@MrGreensweightHist 8 ай бұрын

@@joenarbaiz1640 "2(1+2) is implicit multiplication. 2*(1+2) is explicit multiplication" Wrong. 2(1+2) is explicit multiplication. 2*(1+2) is explicit multiplication 2x is implicit multiplication. Implicit multiplication ONLY applies to a coefficient's relationship to its attached variable. It does not apply to parentheses, which are, in their own right, and explicit sign

@grumpyolddude439 Жыл бұрын

ab/xy is different than a*b divided by x * y. ab written as such, is a singular value. Like 13. 13x7, despite 13 = 10+3 and 7 = 5+2; does not work when written 10+3 x 5 + 2. Likewise ab while when isolated IS the same as a*b; when in an expression, may NOT be as simple as a*b.

@JackieSkellington 8 ай бұрын

brackets first, so what is done with it after the division?

@sarahcarpentervascik4515 8 ай бұрын

Forget the alphabet soup, in English, the problem says 6 divided by (over) 2 times the quantity 1+2. Distribute the 2 over the quantity 1+2 and you wind up with 6! I shouldn' t have to tell you the next step.

@plektosgaming 8 ай бұрын

The originator of the symbol intended it to be shorthand for a fraction. So it reads, as you said, "X (over) Y". The mistake is lazy people who want to say that multiplication and division have the same priority. They do not. Never have, either, because of this. Fractions are their own special hell in math. lol.

@lucientjinasjoe1578 Жыл бұрын

Let's materialize it, I have 6 divisions of armed vehicles and divided them to two which contains blue and yellow and sub divided one with black armband and two with white armband and the outcome is 9 on paper and 1 on the ground , funny isn't it 😊

@Eewec 9 ай бұрын

Sad that North America removed juxtaposition from the order of operations in their educational system. It's in their early text books teaching PEMDAS but it seems that somewhere along the way, lazy students who never went passed the first page that listed the rules, never went through the examples that show things like (a/c)*(b/d)=ab/cd. Then those same students became the teachers and never taught what they never bothered learning. Even the calculator companies put it back in after it was pointed out that only North America removed juxtaposition. Now it seems that NA is trying to foist their dumbed down ruleset on the rest of the world. I believe Casio had a period where they removed implied multiplication, then to my understanding they re-introduced it.

@doughendrie5468 9 ай бұрын

Casio fx-570EX calculator. • If you execute a calculation that includes both division and multiplication operations in which a multiplication sign has been omitted, parentheses will be inserted automatically as shown in the examples below. - When a multiplication sign is omitted immediately before an open parenthesis or after a closed parenthesis. Example: 6 ÷ 2(1 + 2) - 6 ÷ (2(1 + 2)) Calculation Priority Sequence 7 Multiplication where the multiplication sign is omitted 8 Permutation (nPr), combination (Cr), complex number polar coordinate symbol (2) 9 Dot product (•) 10 Multiplication (x), division (+)

@jensschroder8214 9 ай бұрын

6/2(1+2)=x 6/2*3=x Division is not a legal operation. I rearrange the equation. 6=2*3*x 6=2*3*1 ; x=1

@len2524 8 ай бұрын

In higher level math you will always have units associated with the numbers and the units will dictate the order of operations. The archaic division symbol is never used in Engineering.

@MrGreensweightHist 7 ай бұрын

That is a lie

@highlanderthegreat Жыл бұрын

you do what is inside the () parentheses first and since the 2 is outside of the parentheses you do that next so that is 2 x 3 =6 then you divide so its 6 divided by 6 the answer is 1...at least from the way i was taught back in the 50s

@joenarbaiz1640 Жыл бұрын

You don't understand that implied multiplication and explicit multiplication are still multiplication and fall under the rules of multiplication with respect to the Order of Operations. 😆🤣😂😹

@highlanderthegreat Жыл бұрын

@@joenarbaiz1640 i will go so far as to say this good sir,,, both answers can be correct and both answers can be wrong, all depends on how and when you learned, i learned in the late 50s early 60s, my answer is 1, with the so called calculator the answer is both 1 and 9....so in my old fashioned way the answer is 1 in the modern day after the year 2000 i guess the answer is 9 so can we just flip a coin,,, heads i win tails you lose...lololol aint that fair??????

@joenarbaiz1640 Жыл бұрын

@@highlanderthegreat It is interesting that CASIO calculator models can provide different answers to the same expression. Actually, the historical interpretation ended in 1917. Again; you are ignoring the multiplicative inverse property and the proper interpretation of the distributive property. Thanks for admitting that you live in the past. Your comment about coin flipping is at the least ludicrous. 😆🤣😂😹

@highlanderthegreat Жыл бұрын

@@joenarbaiz1640 awwww joe, i thought the coin flip was sorta funny,,, no way i could lose that way...lololol yes i am using shall i say, somewhat old method,,, and no i dont live in the past, although the way the problem is written does lead to the 2 different answers from the way i was taught so you could also say you can not solve the problem the way it is written, thats why i say coin flip to solve it...

@davidbrattain1446 Жыл бұрын

This is right and what I have been arguing in comments on these posts. This is a problem of syntax that plagues mathematics as much as it does the English language where the use of homonyms and synonyms as well as various punctuations can produce sentences with very different meanings. We must provide all at our disposal to clarify problems and not leave it to the student to make assumptions. This is the kind of thing that creates unnecessary noise in a subject that the majority of people already find challenging. Good work! ☺

@DoseofScienceDoS 11 ай бұрын

What?? This is an easy equation to answer. There is no confusion, the answer is nine

@peterzawadowski6947 7 ай бұрын

This is typical issue of common sense. It is obvious that you need to divide whole "thing" on the left BY the whole "thing" on the right. Therefore, make order with the elements on the right which is 6. Then proceed by dividing left side by right AND you'll get 1. But tell to contemporary "confused" minds. I must say that my proposal is applied in current computer programming utizing SUBROUTINES. So here you are. To make issue simple, we have short brained minds which would apply strictly left to right order. In this case it's just screwball. Perer Zawadowski. 02nd of November, 2023.

@humbledb4jesus 7 ай бұрын

i assumed the 2(1+2) was a higher operation than 2x(1+2) in the bedmas... why?

@TheYaddayadda Жыл бұрын

"Who would want to write out a boat-load of brackets like that every time?" Programmers: >.>

@Mesa_Mike Жыл бұрын

LISP programmers!

@J-kd2qc 5 ай бұрын

Set a = 6/2; set b = 1+2; set c = a*b; Done, no brackets at all. c = 9.

@DrDaveW 8 ай бұрын

This is a great analysis - yes you have to be explicit when writing equations, but also use the minimum amount of notation that removes ambiguity. However, I would say that this is not ambiguous. Ther problem arises when 2(3) is expanded to 2 x 3. It shouldn't be. It should take precedence and be calculated as 6. By expanding it, you are removing the precedence that the parenthesis imply. Don't convert a non-ambiguous expression into an ambiguous one.

@MrGreensweightHist 7 ай бұрын

"Ther problem arises when 2(3) is expanded to 2 x 3. It shouldn't be" Yes, it should. " It should take precedence and be calculated as 6." There is no rule in math stating any such thing. " By expanding it, you are removing the precedence that the parenthesis imply." Parentheses only give precedence to what is INSIDE the parentheses. Never to what is outside them

@J-kd2qc 5 ай бұрын

You only need to multiply what's in the parentheses with what's outside the parentheses. 6/2(1+2) 6/2 * 1 + 6/2 * 2 3*1 + 3*2 3 + 6 9. Think of it this way, one half of 20 is 1/2(20) = 10, not 1/40th.

@KyleTremblayTitularKtrey 4 ай бұрын

@@MrGreensweightHist2(3) should not be expanded to 2x3 if they wanted to expand it to 2x3 he would have written 2x3. Its literally less symbols. 2(3) is 4 symbols, 2×3 is 3 symbols. Why are we using an extra symbol? Because we are actually writing (2x3) with LESS symbols. 4 instead of 5. You dont make a shorthand thats longer than the original notation, you'd just use the original.

@MrGreensweightHist 4 ай бұрын

@@KyleTremblayTitularKtrey "2(3) should not be expanded to 2x3" All existing rules of mathematics disagree with you

@PrashantKumar22222 7 ай бұрын

I have a diff ans of this question which goes like this 6 divided by 2(1+2) take 2 common from whole then it will be 2(3 divided by (1+2)=2(3 divided by 3 )=2(1)=2 is it correct ?

@GanonTEK 7 ай бұрын

No, it's not, it's mostly right but you just made an error on the last line. Here is what you meant: 6 / 2(1+2) 2(3) / 2(3) 2 / 2 1 Not just 2. You get 1 if you give multiplication by juxtaposition higher priority and 9 if you don't.

@mikestuart7674 7 ай бұрын

@@GanonTEK Actually I believe the intent here was to divide the numerator and denominator both by 2, then you get... 3 / (1+2) = 3 / 3 = 1 And this is the best approach I've seen to this problem... Kudos Legend !!!

@doughendrie5468 6 ай бұрын

We could factorise the term 6, then cancel common factors from both sides. 2(1+2)/2(1+2) = 1

@ivanblakely903 8 ай бұрын

excel requires an operator in front of the bracket before accepting the formula, but once inserted =6/2*(1+2) gives 9. =6/(2*(1+2)) gives a 1

@johnyeates2156 8 ай бұрын

As a long retired engineer that's done a lot of maths, I can't recall using this ÷ sign to denote division. In my era, we always used a horizontal line with the numerator above the line and the denominator below the line.

@chutalotr 8 ай бұрын

Obviously from the UK where we study Maths rather than Math.

@nicholasjh1 8 ай бұрын

But the slash gives precedence to the numerator and denominator so it is incorrect to use in a line unless you intend a fraction

@helenamcginty4920 8 ай бұрын

Well im 75 and English. im sure we used a division sign before we started algebra in senior school. But can only visualise doing long divisions which we wrote differently. Nb in Spain where I now live the 1st set of accounts I read had the total at the top. And kids at least write long division backwards compared with how I was taught. Plus full stops are used where we use commas and the decimal point is a comma. Eg. 550.234,00 not 550,234.00. What is the system in other countries?

@josephpoley4805 7 ай бұрын

The division sign is just a placeholder for correct notation which would be 6 / 2(1+2) = 1. 6 numerator; 2(1+2) denominator. Left to right is BS. Also the brackets/ parentheses aren’t cleared until the multiplication is completed and =6.

@MrGreensweightHist 7 ай бұрын

@@josephpoley4805 that is incorrect.

@jamesdlightfoot Жыл бұрын

This is an elegant explanation that is well suited for a pre-algebra student.

@mikestuart7674 11 ай бұрын

It is a load of horse manure. See my comment above for an explanation. There is no ambiguity at all.

@MrGreensweightHist 8 ай бұрын

And is also wrong. The answer is 9

@davidbrattain1446 9 ай бұрын

So. Someone needs to tell the elementary and middle school teachers to change the way that they are teaching this. Also, a carpenter using the math that he learned in grade or middle school, is somehow able to build a circular table with six legs, each of equal length. Furthermore, he (or she) is able to determine how much lumber they will need prior to building it. How is that possible without an understanding of the proper use of proper notation and order of operations?

@tomtke7351 8 ай бұрын

when one writes an equation that can only be solved by PMEDASS rather than to employ correct parentheses then I conclude that an unnecessary math element is being relied upon. Restated: the equation was INTENTIONALLY written to be confusing without PMED ASS.

@RichM3000 11 ай бұрын

I'm an engineer. The solution is 1 99% of the time, but the real answer to how to solve the equation is to go back to the underlying formulas to verify what's really going on. I've never seen something so ambiguous in real life but, if someone handed that to me written in that form, I would refuse to sign my name to 1 or 9 without knowing the background. So, I agree that, in the real world, the answer is "undefined", "Insufficient data", etc. Or, if the boss demands an answer: 1 ≤ y ≤ 9 :)

@thierrypauwels 11 ай бұрын

Be careful. Maybe your boss is a dogmatic adherent of one of the conventions...

@timsmith4089 11 ай бұрын

As a retired engineer, I couldn’t agree more!!!

@mikestuart7674 11 ай бұрын

I am also an engineer, and there is nothing ambiguous here at all. The integer leading the parenthesis is a common factor of the parenthesis. 2(1+2) = 2(3) = (2x3) = 6 So 6/2(1+2)=1 See my comment above for more clarification.

@thierrypauwels 11 ай бұрын

@@mikestuart7674 It may not be ambiguous to you, because you have a convention about how to interpret such a thing. But when someone else writes it down, you do not know whether he/she adheres to the same convention as you do. And that is why it is ambiguous

@RichM3000 11 ай бұрын

@@mikestuart7674 It's not ambiguous to me either..not in the slightest. It's 1. But, knowing it's ambiguous to others means it's ambiguous by definition, as there's a lack of clarity. Sad, I know. I share your pain.

@yasdnilknarf1885 11 ай бұрын

Applause. Clear and precise explanation.

@cliffordschaffer5289 7 ай бұрын

Author should be fired for not having parentheses to make it clear to everyone reading it.

@doughendrie5468 7 ай бұрын

@cliffordschaffer5289 The term 6 divided by the term 2(1+2) answer is 1

@cliffordschaffer5289 7 ай бұрын

@@doughendrie5468 Different calculators and computer systems will give different answers. The person who wrote that mess should be sent back to include parentheses so it works the same in any system.

@kripalsinghsaini1821 9 ай бұрын

How can we write the statement : Six is divided by twice the sum of one and two mathematicaly.

@runfayalife 3 ай бұрын

You know that video of the world class violinist playing in a NYC subway and getting zero attention? That's this comment.

@TheMathManProfundities 2 ай бұрын

6/2(1+2) would work fine for established mathematicians and engineers but it we wish to include children and others who still rely on operation order acronyms we would have to use 6/{2×(1+2)}

@buudorobuudronovich1507 8 ай бұрын

why do you put extra brackets on the calculator on the right? shouldn't you be entering them exactly the same to prove your point? don't the added brackets imply a different step order? im sure someone mentioned this before but i don't feel like searching the comments.

@grumpysanta6318 Жыл бұрын

Calculators are more and more using PEJMDAS, where multiplication by juxtaposition takes precedence over other multiplication. That's where the answer of 1 comes in. ... Which is exactly what he covers. Sigh... :)

@plektosgaming 8 ай бұрын

Which is exactly how my father and I were taught it - before pocket calculators were common. The division sign is always shorthand for a horizontal line, or was for hundreds of years. 300 years ago the answer would have been 1. Or 100 year ago. In fact, it's literally a fraction on its side - with the x and y just reduced to dots. As such, the "new" methods are simply wrong. There is no ambiguity except in that people are being taught it wrong.

@nfpnone8248 11 ай бұрын

My problem with this viral problem, is why is it viral in the first place, because if you know what constitutes a parenthetical statement, and how to expand parenthetical statements, then the only problem is how to input it into the calculator or spreadsheet of your choice to get the correct answer. The answer is 1 , today, yesterday, and tomorrow! You cannot change an implied operator from multiplication to division, which is what you are doing when you change the problem from 2(2 + 1) to (2 + 1)/2, which violates every mathematical principle there is!

@CEntertainArt 11 ай бұрын

The reason many calculators return 9 is not because they calculate (2 +1)/2. The reason they return 9 is because they evaluate the equation in the following way: 6/2(1 + 2) = 6/2(3) = 6/2*3 = 3*3 = 9 Whether you believe it is truly 9 or if it's 1 is yours. I am simply explaining how they solve it. The only way a calculator would see it as a fraction is if there are two parenthesis calculations with a division symbol in between. Otherwise, it is handled as division. I hope you see I'm not trying to argue and simply explaining the computational aspect.

@DoseofScienceDoS 11 ай бұрын

Uh oh, someone doesn’t know how to do math. Let’s check your answer of one. 6/2(3)=1 6/2=1/3 3=.333334 Clearly one isn’t the answer. Please don’t be the type of person to argue when the proof is right in front of them

@H00H 11 ай бұрын

@@DoseofScienceDoSwtf are you doing ???

@DoseofScienceDoS 11 ай бұрын

@@H00H simple math. What are you doing?

@DoseofScienceDoS 11 ай бұрын

@@H00H I figured out where you are doing your math wrong. The two is a divisor not a multiplier. So it would be (1+2)/2 not 2(1+2) Now you can see 3/2=1.5 6*1.5=9 Sorry you don’t get math good job deleting your non sense comment lol.

@Calmgore 8 ай бұрын

In Germany we say "Bruch klammert" ⇒ Problem solved. This means locking on a fraction numerator and denominator, both are considered to be in brackets. In the initial task no fraction with numerator and denominator is written, so there no brackets would be considered, and the solution would be 9. But I understand that one can get confused when you look at this a bit more philosophical, like in this video.

@vangildermichael1767 10 ай бұрын

I think the way a person looks at the problem, depends entirely on WHAT they do for a living. Back when I was a engineer at university. We all looked at the facts and did the work. No problem. If you are a high school teacher, looking at a (text book). You might "see" a completely different thing. When the numbers are attached to actual, real, measurements. That you just made, your own self. The computation is obvious. It's only when there is a moment a person thinks (even if only for an instant). "What was "the author" going for here. When I write the question. I know EXACTLY what I implied. Else, a lot of brackets are going to be necessary. If you are not in the same room as the project. A lot of mess is going to be necessary to tell EXACTLY what happened. AND that is EXTREMELY important. ELSE, was anything actually done? I watched a airplane thing. Where the plane was lost over the andes mountains. And crashed into em' (killing 150). See there, I implied I was talking about 150 (people). The issue happened all because the pilot could not "communicate" with a South America tower, being from NORTH America. Communication is the principle thing in life. Messy, yea. But, (top shelf), yea.

@oienu 7 ай бұрын

really, when you see that formula is like "what do this?" To make sense you need to know the real original problem where it come.

@1paultv22 Жыл бұрын

Someone pointed out that if a teacher used this problem on a test, they would have to accept both answers because of the different ways math is taught To elementary/primary school children before they get into higher maths like algebra and higher where the ÷ sign is no longer used.

@totoitekelcha7628 Жыл бұрын

Why higher match don't used ÷ sign?

@quantumtacos Жыл бұрын

@@totoitekelcha7628 On youtube there's a video by Syed Institute that explains why that symbol is avoided. TLDW: because it requires more brackets to achieve the requisite precision and it doesn't read as well anyway.

@Lord_Volkner Жыл бұрын

@@totoitekelcha7628 I minored in math in college and never once saw that symbol throughout all four years. I never thought about it at the time, but I think the OP is correct.

@drziggyabdelmalak1439 Жыл бұрын

Not in the UK's GCSE level papers. They'd expect '9' as the answer. Anything else and they'd give you zero marks.

@juliavixen176 Жыл бұрын

@@totoitekelcha7628 In Germany ÷ is used for subtraction.

@dookoonu2741 Жыл бұрын

I'm no Math genius but I disagree ...My understanding was that the parenthesis should be cleared first. well it seems mathematics is not an exact science

@fabmystery6433 7 ай бұрын

Yea man I do agree as math is a variable which is utilised to find out the laws and behaviour of the universe.. actually we have created maths, it does not exist, just as we use variable to find out unknown value..and yea math is inaccurate 😊

@enomiellanidrac9137 8 ай бұрын

If it's written manually: learn how to write unambiguous formula is the answer. If it's an input into a calculator or math program: RTFM is the answer.

@jignessmishra3941 2 күн бұрын

Guys,guys,guys 6/2(1+2) =6/(2+4) = 6/6 =1 OR According To BODMAS(ik it’s basic stuff) =6/2*3 =3*3 =1

@smanzoli 9 ай бұрын

There IS an occult multiplication operator before "(". It could be a dot, an X or an * but it IS there by common used mathematical notation, when it's hidden, the 2 parts ate ONE single part... 2(3) is one thing... a hidden parentheses is there 2(3) = (2*3) That's how mathematicians, physicists and engineers use it in books and papers. According to professionals, PEMDAS is just a simplification, for kids. So: 6/2(3) = 1 {a/b=1} 6/2*3 = 9 {a/b*c=9} It's NOT ambiguous for scholars, mathematicians, physicists, engineers. That's exactly how it's used by 100% of them myself included), 100% of time. Use say an HP10s to calculate this, and get what any mathematician would answer: 1 ANOTHER thing is the notation a calculator or excel demands... and it's simply because some were not programmed to assume that. It must be user friendly for everyone, including kids, so professional/book notation is not allowed. Texas do use PEMDAS. But HP, justaposition multiplication comes first than division.

@MrGreensweightHist 8 ай бұрын

"a hidden parentheses is there" No such thing as a hidden () You are adding () where there are none The correct answer is 9 and only 9 "justaposition multiplication comes first than division." There is no juxtaposition multiplication in this problem

@smanzoli 8 ай бұрын

⁠⁠@@MrGreensweightHistyou are free to be as wrong as you want. Have just tried that in my HP10S and the answer is 1, as ANY mathematician would say, as ANY book related to math, physics or engineering uses all the time. Check how ALL formulas and expressions ate written in books and papers.

@smanzoli 8 ай бұрын

@MrGreensweightHist 8 ай бұрын

@@smanzoli Except I am not wrong and your HP10S is. Or to be more precise, GIGO, Garbage In Garbage Out. "ANY mathematician would say," I taught math. Mathematicians do not agree with you.

@dbtest117 8 ай бұрын

Great we need more of these accurate videos on this issue. Thanks!

@MrGreensweightHist 8 ай бұрын

Except this video is inaccurate

@dbtest117 8 ай бұрын

@@MrGreensweightHist Nope it's accurate. The only other acceptable answer would be that it's ambiguous. And that is only because people have been taught PEDMAS and similar stupid conventions that goes against previous conventions that made sense.

@degrass5408 8 ай бұрын

@@dbtest117nope it's not accurate because he wrote in the calculator 6÷2(1+2) vs 6÷(2(1+2)) which is not equal to each other because the second one has (2(1+2)). This is done first because it's in parentheses. Thus, according to PEMDAS, we get 6÷2(3)=6÷2×3=9 vs 6÷(2(3))=6÷6=1. PEMDAS may be an arbitrary convention that is accepted but his example doesn't demonstrate the ambiguity of PEMDAS

@dbtest117 8 ай бұрын

@@degrass5408 Did you watch the video even? You are making a fool out of yourself.

@jonnvessel Жыл бұрын

Again at 9:21. It appears the calculator does it though. Adding brackets it assumes should be there?

@GanonTEK Жыл бұрын

Yes, the calculator added those after equals is pressed, which is very good practice to show you exactly how it is interpreting it.

@Dethneko 11 ай бұрын

I consider the distribution property of multiplication, which states: 2(1 + 3) = ((2*1) + (2*2)) = ((2(1)) + (2(2))) = (2(1) + 2(2)) Therefore 6 / 2(1 + 3) = 6 / (2(1) + 2(2)) and the operations should be clear from there: = 6 / (2 + 4) = 6 / 6 = 1 If you argue that the distribution should be (6/2(1) + 6/2(2)) then there's already a clear problem, because to distribute the entirety of "6/2" then the problem should be written as: (6 / 2)(1 + 3) = ((6 / 2)(1) + (6 / 2)(2)) = 3(1) + 3(2) = 3 + 6 = 9 My 8th grade math teacher taught me the cumulative property of addition. A college professor taught me that subtraction is adding the opposite. Therefore: 2 - 1 = 2 + (-1) = (-1) + 2

@DoseofScienceDoS 11 ай бұрын

Well you forgot that your seventh grade teacher taught you to check your work because you got a big fat F.

@Neptunianist Жыл бұрын

It’s a great video and absolutely understands the ambiguity in the cases where a mathematical question is written in this way. However I think there is an approach, an extension of the one taken in the video (which inspired this idea, actually). The approach will lead to only one answer: 1. My thinking on the solution to this is that we need more information about the question. What do the values represent? What real-world problem or situation is the question trying to portray? Are we, say, dividing six pieces between 2 teams where each team originally had 2 people and then one more joined each team? Are we saying that we have six pieces, or six of anything actually, which are divided equally between 2. But then multiplied by the sum of the numbers in the brackets; 3. For this we have to see that the things can be scaled up, increased, and therefore they can’t be physical things unless we’re talking in abstraction. This could be units of heat or force, instead. It could be physical but abstracted, yes, like eggs. We could say we need so many for a recipe so start with 6, divide by 2 and then multiply by the number in the brackets, which might be people, to give the number of eggs required. We cannot multiply something that we have already broken and divided into pieces. Where is the extra material, the extra pieces, coming from to allow this multiplication, this expansion? So the last one has to be abstract. If we had not divided the six first, it would be fine because we would not be combining two different types; the pieces and the people in the team. The same applies to any object, where division is used. It’s always one type of thing being divided into quantities, a different paradigm, quality and thing entirely.

@bepohal 8 ай бұрын

in the real world, outside the US, the answer is always 9. always...

@Neptunianist 8 ай бұрын

@@bepohal Yes, because we use BODMAS. I get that rule, completely. But I do think that it’s a rule which shouldn’t be blindly followed. In my view we should try and understand what the values in any equation are and what the equation is trying to represent.

@bepohal 8 ай бұрын

@@Neptunianist generally spoken this equation will only lead to 9. pemdas is what the whole world uses. especially the stem field

@MrGreensweightHist 7 ай бұрын

@@bepohal This isn't a U.S. thing. The answer is 9 everywhere. And there are people getting it wrong, everywhere as well.

@KathrynLiz1 Жыл бұрын

I was taught (back in the 1950s) to resolve what is in the brackets first then using the usual priorities go left to right.. which yields 9. Nested bracket can remove all ambiguities... having been a programmer, nested brackets pose no issues for me, so when writing such expressions I use them to remove all possibility of misunderstandings.

@werffjvander Жыл бұрын

@arnoldca8377 Жыл бұрын

resolve what is in the brackets first. -- Yes you keep working until the brackets are out of the equation, at 2(3) the brackets still exists therefore must go first....which yields 1

@plektosgaming 8 ай бұрын

The singular thing that people who teach this forget is that the sign is literal shorthand (as per the creator's intentions in 1659) for a horizontal division line. Which was created due to how typesetting worked at the time. This saved several lines on each page and being two dots and a horizontal line, caught on quickly as it was very clear what it meant. All they need to do is remember this fact and it is clear - none of the idiocy above. 6 ----- 2(3) Which there is only one answer to no matter how you try to solve it. But computers and lazy teachers...

@babakbahrami3384 8 ай бұрын

In your specified calculator example, you're getting different results because you have extra parenthesis on right calculator around 2(1+2) and 6 / (2(1+2)) is indeed 1 but the left calculator has not extra parenthesis thus its 9

@GanonTEK 8 ай бұрын

No, the same expression was typed on both. Some calculators after you press = put brackets in to clarify how it interprets implicit multiplication. It's a great feature. Depends on the scientific calculator but here are some that give one or the other if you type exactly 6÷2(1+2) into all of them: These give 1: Casio FX 83GTX, Casio FX 85GT Plus, Casio 991ES Plus, Casio 991MS, Casio FX 570MS, Casio 9860GII, Sharp EL-546X, Sharp EL-520X, TI 82, TI 85 These give 9: Casio FX 50FH, Casio FX 82ES, Casio FX 83ES, Casio 991ES, Casio 570ES, TI 86, TI 83 Plus, TI 84 Plus, TI 30X, TI 89.

@MrGreensweightHist 8 ай бұрын

@@GanonTEK But the right calculator CHANGED the problem from what was written. Therefore the right calculator was not solving the same problem and was wrong.

@GanonTEK 8 ай бұрын

@@MrGreensweightHist No, it is written ambiguously. That's the issue. Academically, multiplication by juxtaposition implies grouping so 1 is correct answer in that context. Literally/programming-wise, multiplication by juxtaposition implies only multiplication so 9 is correct in that context. Both calculators are correct, it depends on context. Scientific calculators that give 9 are more common in the US and scientific calculators that give 1 are more common in Europe. It's the question itself that's wrong. It's badly written. Like, "I saw the man with a stick" is fine, the man has the stick, but "I hit the man with a stick". So, does the man still have the stick, like the 1st sentence, and I hit him, or do I have the stick and am using it to hit him? Following modern international standards like ISO-80000-1 and ISO-80000-2 the correct way to write the expression is (6/2)(1+2) to always be 9 6/(2(1+2)) to always be 1. 6÷2(1+2) is just poor notation.

@marksolum1794 9 ай бұрын

Use enough parenthesis (grouping) to remove all ambiguity (like the way this equation was written). (6/2)*(2+1)=9 or 6/(2*(2+1))=1. Work your way from the inside out no need to work from left to right. The obelus, ÷, because it is ambiguous is not used anymore. If working on paper then use a horizontal line, vinculum, for division and things correctly fall into place. For inline equations the vinculum is replaced by the solidus, /, and proper parenthesis. If one has the ideal gas law PV=nRT and wants to solve for T by dividing both sides by nR one has T=(PV)/(nR). adding an explicit multiplication sign T=(P*V)/(n*R)and everything is fine. If one writes using an obelus and uses PEDMAS and left to right convention one has T=P*V÷n*R that will give an incorrect result.

@MrGreensweightHist 7 ай бұрын

There is no ambiguity People getting 1 are just wrong

@marksolum1794 7 ай бұрын

@@MrGreensweightHist There is the real world (ISO 80000-1,2 and scientific journal notation standards) and this jr. high math that is teaching bad habits.

@KyleTremblayTitularKtrey 4 ай бұрын

@@MrGreensweightHist1 is correct. If you attempted to follow your same logic through other standard equations they break as the OP already showed you. Whether you see it or not you do actually swap between bedmas and juxtaposition having priority.

@powdercowboy90 3 жыл бұрын

So this is the way I see it....wouldn't you see the problem like this.....the 6 is bieng divided by the 2(1+2). So 2(1+2) is its own separate expression that must be simplified first? Am i Incorrect? To simplify you use the distributive property to get 6.

@joncrichton7670 3 жыл бұрын

my 9 year old thought this same thing but I guess not at higher level math

@srikrishna2561 2 жыл бұрын

Yes. That's the correct one indeed.

@eonshade6297 2 жыл бұрын

Multiplication and division have the same priority, so you go left to right. 6÷2(1+2) 6*(1/2)*(1+2) (6*(1+2))/2 (6*(3))/2 18/2 9 You cannot go wrong by using lots of brackets (where they can be used). 6÷(2(1+2)) 6÷(2(3)) 6÷(6) 1 If the problem were written like 6÷(2(1+2)) Then the result would have been 1, but it isn't. Brackets really tell everything. Or even like this with distribution 6÷(2(1+2)) 6÷(2*1+2*2) 6÷(2+4) 6÷(6) 1

@muffaloaf Жыл бұрын

@@eonshade6297 the problem doesn’t have to be written like that to equal 1. Until the 2 is multiplied with what’s inside the parentheses , then the parentheses remains. And getting rid of the parentheses is the 1st step

@natenatenate10 Жыл бұрын

@@muffaloaf Once an expression inside of a set of parenthesis has been resolved, the parenthesis are removed. Afterwards, the expression is solved from left to right. Parenthesis don't remain and emit residual effects on the order of operations.

@LOCKSHADES Жыл бұрын

I’ve never even heard of PEDMAS or whatever that is😂.

@Mesa_Mike Жыл бұрын

It's the American version of BIDMAS, BODMAS, BOMDAS, or whatever you learned where you grew up.

@the_god_killah 8 ай бұрын

Well I went to a French school so that’s how we called it

@typicalhguy9290 8 ай бұрын

But when you did it on your own two calculators (at 0:40), you didn't enter it the same way. You entered 6/2(1+2) in one case, and 6/(2(1+2)) in the other case. Since multiplication/division associates left to right, in the first case the 6/2 is executed first, giving 6/2 = 3, 3(1+3) = 9. In the second case, with the extra layer of parentheses, the (2(1+2)) is executed first, giving 2(3) = 6, 6/6 = 1. What do you get when you actually enter it the same in both, without forcing the precedence with the extra parentheses? Since both calculators are the same brand, I would expect they're both implementing the same rules and will give the same result.

@GanonTEK 7 ай бұрын

@janvenken4719 8 ай бұрын

Don't leave out the multiplication sign and use brackets when needed and even when not. And, write it as a division with nominator and denominator. I'm an engineer and I would never write it like that.

@cakepigs Жыл бұрын

I never knew about implied multiplication, I always treated implied multiplication as bracket multiplication making it B in BIDMAS therefore making it higher priority.

@alext8828 Жыл бұрын

Yes, exactly. I see the number just outside the parenthesis as part of the parenthesis. You have to be a maniac to disregard that number. Or just a robot.

@joenarbaiz1640 Жыл бұрын

@@alext8828 The only process in the brackets step is evaluation of the contents WITHIN those brackets. The remainder of that bracketed expression is evaluated in the multiplication step. If you want to interpret 2(1+2) as a bracketed expression, include another set of brackets.

@alext8828 Жыл бұрын

@@joenarbaiz1640 No, that's not true. Real math is not done that way. Complicated equations are not processed that way. Casio calculators were all changed to reflect that error. That was silly math to teach 3rd graders.

@joenarbaiz1640 Жыл бұрын

@@alext8828 You do know that CASIO calculators can give either answer dependent on the model, right? 😆🤣😂😹

@mikestuart7674 11 ай бұрын

@@joenarbaiz1640 As 2(1+2) = ( 2+4) = (6) = 6 Solve parenthesis first.

@DustinSilva Жыл бұрын

Maybe I need to watch it again, I dont quite understand why implied multiplication by juxtaposition isnt a thing, ie, if its used, the answer is one...Isnt it supposed to be used? Is the reason its ambiguous is because calculators differ on the answer? Seems like poorly coded calculators are the issue then. When I attended college, there were a list of acceptable calculators for my Algebra/2, Trig, Pre-Calc/Calculus classes. I HAD to have a calculator that was on the list, and the one I still have 17 years later still says this is 1.

@juliavixen176 Жыл бұрын

Computers are dumb, and to use as little memory and cpu time as possible, they only look at the two tokens immediately to the left and right of any operator symbol that they find. Ultimately, what's going on is that the composition of multiple binary operators forms a binary tree, and the algebraic infix notation that we're using because of historical accident is really bad at representing a tree structure as a linear sequence of discrete symbols read from left to right. Basically a/bc means something to a human depending on which context it appears, but machines don't know the context. It could mean (a/b)*c if they evaluate in the most lazy way possible, or it could mean a/(b*c) which is usually what the human meant. Math notation was created by humans for humans to read, not electronic devices with only two general purpose registers.

@plektosgaming 8 ай бұрын

Your response explains it, actually. :) [ Algebra/2 ]. This is a convention used by early typesetters and typewriters to use this [ / ] symbol for multiple things to save space. The proper division sign is with a horizontal line, and the meaning is crystal clear when looked as what it is, which is shorthand for a fraction. Fractions written properly are more complex to write but absolutely clear on the order of operations. Shorthand for the same thing changes nothing. It's what it was originally used for as well, over 350 years ago. There is no "debate" - just students who were unfortunately taught incorrectly.

@SaintStryfeArgentEngraving 8 ай бұрын

Can I be angry over the Serif font on the right calculator?

@occamraiser 8 ай бұрын

The only problem with ab / cd being perceived as (ab)/(cd) is that people don't visualise the implicit 'x' between the a and b and between the c and d. It is not a problem of notation or nomenclature it is a manifestation of the invisible X being ignored by people who are being casual with their reading of the notation.

@edvsilas8281 Жыл бұрын

Finally ,somone recognizes that there is ambiguity in the answer . Finally ,someone recognizes that conventions change but the mathematical answer can not change simply because a particular convention ( or fashion) says so. Finally,common sense has won the argument .

@drziggyabdelmalak1439 Жыл бұрын

It hasn't though, really, has it? Look at my comment above.

@mikestuart7674 11 ай бұрын

Mathematics describe the real world. If we used this formula in 1916 6/2(1+2)= #gunpowder and we needed 1 lb of powder in the cannon. Now you say we changed convention so it says we need 9lbs now. Will you touch off the cannon with 9lbs now? After all we changed math. NOT Some professor wrote a book. But nobody noticed.

@edvsilas8281 11 ай бұрын

@@mikestuart7674 The quantity of powder charge to a cannon being changed is simply a recipe change that will change the magnitude of the blast ;however, changing the order of mathematical operation is akin to not only changing the quantity of powder but changing the powder composition itself .

@xenuno 8 ай бұрын

No ambiguity at all. The fact there is no sign between the 2 and the parenthesis indicates a special case where it is multiplied immediately on the value calculated within the parenthesis. It's that simple ..

@edvsilas8281 8 ай бұрын

@@xenunoAmbiguity if you use pemdas or bidmas convention since juxtaposition prioritizing does not apply but in algebraic math it does . I would completely ignore any series of operations having an obelis and parentheses in same series .