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

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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.

Thank you for watching.

[TomTerrific-vmqg]

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.

[michaelkrailo]

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.

[xnjgirl]

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.

[turtlerockfire]

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.

[marcosmercado]

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! 🙂

[smanzoli]

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.

[nats]

In short, the equation must be written in the way the final answer is intended. If the intended answer is really 9, it should be written like this:
(6/2) (1 + 2) = 9 or
(6 ÷ 2) (1 + 2) = 9
And if the intended answer is really 1, it should be written like this:
6 / [2(1 + 2)] = 1
6 / [2×3] = 1
6/6 = 1
Making use of parenthesis and bracket remove the ambiguity?

[ejrupp]

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.

[craigward]

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.

[AmerigoGadsden]

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.

[timsmith]

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.

[jndominica]

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.

[williamjackson]

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

[highlanderthegreat]

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

[MichelSLAGMULDER]

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.

[kychoi]

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) ).

[daviestj]

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.

[samael]

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.

[enomiellanidrac]

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.

[nomis]

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.