6?2(1+2)= ?

[Vlad-Stupid]

Found this answer online: (appreciate it's not gospel!)

 

I am your college professor that you requested, with a doctorate in Mathematics. I will break this down as simply as possible and end this debate as approx. 10 students have already asked me this today.

The problem as it is written is 6?2(1+2) , the ? cannot be substituted with a fraction bar because they have different ranks on the order of operations. It is an illegal math move to do this. The bar ranks with parentheses, ? is interchangeable with *. therefore the problem must be solved as 6?2(1+2) NOT 6 (over) 2(1+2) we do the parentheses first, so 6?2(3), the parentheses are now no longer relevant, because the number inside is in it's simplest form. Every single number has implied parentheses around it.

6?2(3)

(6) ?(2)(3)

6?2*3,

or even converting the division to multiplication by a reciprocal (a legal math move)

(6)(1 (over) 2)(3)

are all correct ways to write this problem and mean exactly the same thing. Using pemdas, where md and as are interchangeable, we work from left to right, so (3)(3) or

3*3= 9

 

Just because something is implied rather than written does not give it any special rank in the order of operations.

 

The problem in it's simplest form, with nothing implied would look like this:

(1+1+1+1+1+1 (over) 1) ? (1+1 (over) 1) * ((1(over) 1) + (1+1 (over) 1))

From here, nothing is implied, This again, works out to 9.

 

If the symbol '/' was used this whole debate would be ambiguous since that symbol can mean "to divide by" or it could mean a fraction bar.

 

HOWEVER, because the ? symbol is used, it can not be changed to mean a fraction bar because that would change the order of operations and thus the whole problem, you can't change a symbol to mean something because you want to, in doing so you are changing the problem.

 

Once and for all, the answer is 9.

 

Hopefully some of my students see this so I can stop answering this question.

 

End of debate... hopefully.

 

Source(s):

 

Doctorate, 9 years teaching experience.

 

Answer by Steven 21 hours ago Report Abuse

[Victorian]

Jim, shut up.

 

It's 1. If you don't believe me, put in a = 6, b = 2, c = 1 and evaluate the expression using basic algebra. The resulting expression forces you to resolve the denominator first, as if there was any ambiguity in the first place.

 

i follow your thinking, i'm not a hobo. the trouble is that the belief that it's worked that way is a matter of opinion and hasn't been demonstrably proven, even with the whole internet at everyone's fingertips.

 

there is no ambiguity. the simple and correct way to work it is to resolve the bracket and then calculate it from left to right.

 

numerator... denominator...

 

MEH

BAAH

PFFT

[I P Knightley]

Not seen much "evidence" from the 9-sayers apart from a bunch of desperate ignoramuses agreeing with each other.

 

That would be like heading West and concluding that Buckfast is a fine drink.

 

Mathematics says it's 1. That's good enough for me.

[craigie jambo]

Found this answer online: (appreciate it's not gospel!)

 

I am your college professor that you requested, with a doctorate in Mathematics. I will break this down as simply as possible and end this debate as approx. 10 students have already asked me this today.

The problem as it is written is 6?2(1+2) , the ? cannot be substituted with a fraction bar because they have different ranks on the order of operations. It is an illegal math move to do this. The bar ranks with parentheses, ? is interchangeable with *. therefore the problem must be solved as 6?2(1+2) NOT 6 (over) 2(1+2) we do the parentheses first, so 6?2(3), the parentheses are now no longer relevant, because the number inside is in it's simplest form. Every single number has implied parentheses around it.

6?2(3)

(6) ?(2)(3)

6?2*3,

or even converting the division to multiplication by a reciprocal (a legal math move)

(6)(1 (over) 2)(3)

are all correct ways to write this problem and mean exactly the same thing. Using pemdas, where md and as are interchangeable, we work from left to right, so (3)(3) or

3*3= 9

 

Just because something is implied rather than written does not give it any special rank in the order of operations.

 

The problem in it's simplest form, with nothing implied would look like this:

(1+1+1+1+1+1 (over) 1) ? (1+1 (over) 1) * ((1(over) 1) + (1+1 (over) 1))

From here, nothing is implied, This again, works out to 9.

 

If the symbol '/' was used this whole debate would be ambiguous since that symbol can mean "to divide by" or it could mean a fraction bar.

 

HOWEVER, because the ? symbol is used, it can not be changed to mean a fraction bar because that would change the order of operations and thus the whole problem, you can't change a symbol to mean something because you want to, in doing so you are changing the problem.

 

Once and for all, the answer is 9.

 

Hopefully some of my students see this so I can stop answering this question.

 

End of debate... hopefully.

 

Source(s):

 

Doctorate, 9 years teaching experience.

 

Answer by Steven 21 hours ago Report Abuse

 

[Das Root]

Jim, shut up.

 

It's 1. If you don't believe me, put in a = 6, b = 2, c = 1 and evaluate the expression using basic algebra. The resulting expression forces you to resolve the denominator first, as if there was any ambiguity in the first place.

 

 

That's wrong, there is no denominator. That's a fraction, this is a division as denoted by the division symbol. There is no fraction symbol like you would find for 1/2 (half).

[craigie jambo]

That's wrong, there is no denominator. That's a fraction, this is a division as denoted by the division symbol. There is no fraction symbol like you would find for 1/2 (half).

 

'?' is same as using '/'

[Guest Ultraviolet Catastrophe]

That's wrong, there is no denominator. That's a fraction, this is a division as denoted by the division symbol. There is no fraction symbol like you would find for 1/2 (half).

 

Every expression/real number (up to a limit) can be expressed as a fraction if you fancy it.

[RobboM]

Maybe it's easier if you replace the numbers with something like apples?

[turnkey1874]

The answer is 9!

[craigie jambo]

Maybe it's easier if you replace the numbers with something like apples?

 

OK

 

An apple to the power of zero = same answer as this problem

 

1

 

[Commander Harris]

some say 9, some say 1; I'm opting for a quantum superposition.

[Guest Ultraviolet Catastrophe]

some say 9, some say 1; I'm opting for a quantum superposition.

 

This. As soon as the calculation is performed the wave function collapses.

[Vlad-Stupid]

Wtf does the giraffe mean btw?!

[Ivan Drago]

Wtf does the giraffe mean btw?!

 

1

[craigie jambo]

Wtf does the giraffe mean btw?!

 

He's having one

[P-Dizzle]

some say 9, some say 1; I'm opting for a quantum superposition.

 

[Sten Guns]

Who's gonna argue now, eh!

 

[Hansel]

Wtf does the giraffe mean btw?!

I'd like to know as well.

 

Hate Giraffes

[craigie jambo]

Who's gonna argue now, eh!

 

 

[Victorian]

i'm going out soon, safe in the knowledge of 9. i will probably have 9 jack daniels single barrells to celebrate life.

 

i'll see yous all on sunday.

 

[Vlad-Stupid]

I found my old casio fx-83ms calculator from school (could probably be classed a relic these days) and it says 1

 

I'm sad that all the buttons confuse me now simple quadratics is about my limit. Thanks drink and drugs

[P-Dizzle]

i'm going out soon, safe in the knowledge of 9. i will probably have 9 jack daniels single barrells to celebrate life.

 

i'll see yous all on sunday.

 

 

Have a good 1

[craigie jambo]

I'd like to know as well.

 

Hate Giraffes

 

See #265

[Victorian]

Have a good 1

 

[Vlad-Stupid]

Who's gonna argue now, eh!

 

Is that Jim at the bar ordering his JD's?

[Das Root]

'?' is same as using '/'

 

 

 

Not in mathematical equations. Different ranks, therefore not interchangeable on this occasion. If the equation had been written with / then the answer would be 1. It was written with the division sign (obelus) and therefore the answer is 9.

[Bigsmak]

poor retort once more it must be said.

 

one glance at the beginnings of the thread will alert one to the fact that i arrived at the correct answer from the outset. it is only when people started questioning google, excel, calculators and what-not that i decided to see what happened when one was used.

 

it's as clear as day that once the brackets have been resolved that you work the sum from left to right, multiplication and division not over-riding each other, and that the simplified sum becomes 6 / 2 x 3.

 

you either know it and accept it or you don't.

 

 

You haven't resolved the brackets in your answer, you simplified them but did not resolve.

[Hansel]

See #265

 

Got it.

[craigie jambo]

Not in mathematical equations. Different ranks, therefore not interchangeable on this occasion. If the equation had been written with / then the answer would be 1. It was written with the division sign (obelus) and therefore the answer is 9.

 

WRONG

[I P Knightley]

This is a BODMAS calculation, BODMAS means Brackets, Other, Division, Multiplication, Addition, Subtraction. This tells you that in simple calculations to do Brackets first then Division then Multiplication then Addition then Subtraction. Other means things like Squaring, Cubing or Square-Rooting. Sometime BIDMAS is used instead of BODMAS where the I stands for Index. Index means powers like square and cube.

 

So...

 

1 + 2 = 3

6 / 2 = 3

3 x 3 = 9

 

1 is wrong, 9 is right. You can close the thread now

 

Having "other" kind of undermines any subsequent points you make.

 

 

 

Source(s):

 

Doctorate, 9 years teaching experience.

 

9 years of teaching shite.

[Victorian]

Pint of red stripe.

 

 

Not having 9 of those though.

 

No.

[Commander Harris]

craigie jambo 42

davemclaren 20

LPjambo91 18

Jim Panzee 16

el profesor 13

HMFC_Riley 12

 

 

 

just saying...

 

 

[Das Root]

Having "other" kind of undermines any subsequent points you make.

 

 

Do feel free to explain further.

[Bigsmak]

Do feel free to explain further.

 

Brackets and other things associated with the brackets.. the 2(1+2) for example.. the 2 is associated with the bracket!

[P-Dizzle]

aka implied multiplication

[Das Root]

Brackets and other things associated with the brackets.. the 2(1+2) for example.. the 2 is associated with the bracket!

 

 

Wrong. Null point for you.

[Boomstick]

Craigiejambo's use of unfunny pictures is killing his argument because I no longer take him serious.

[I P Knightley]

Do feel free to explain further.

 

 

Oh dear. A Niner admitting he hasn't a clue what he's talking about. It's all crumbling down.

 

"O" in BODMAS (which is sometimes, giving more clarity, called BEDMAS) does not stand for "Other".

 

What "Other" would it be?

[I P Knightley]

craigie jambo 42

davemclaren 20

LPjambo91 18

Jim Panzee 16

el profesor 13

HMFC_Riley 12

 

 

 

just saying...

 

 

 

Cripes. 54% of Craigie's total posts are on this one thread.

[Das Root]

Oh dear. A Niner admitting he hasn't a clue what he's talking about. It's all crumbling down.

 

"O" in BODMAS (which is sometimes, giving more clarity, called BEDMAS) does not stand for "Other".

 

What "Other" would it be?

 

 

Oh dear, I do believe if someone had bothered to read the full post it would have meant them not making a fool of themselves

 

Other means things like Squaring, Cubing or Square-Rooting.

 

I do not see any exponents in the equation...did you? The "O" or indeed the "E" depending on how you wish to phrase it has no relevance here.

[southside1874]

Can the 1 sayers come up with any actual evidence rather than just opinion?

 

Why have the 1+2 in brackets in the first place?

 

If you wanted the answer to be 9 then (6/2)x(1+2) would be how I would set it out

[Das Root]

Why have the 1+2 in brackets in the first place?

 

If you wanted the answer to be 9 then (6/2)x(1+2) would be how I would set it out

 

 

The brackets are necessary so that you calculate 1+2 first. If not, you would calculate the addition aspect of the equation last and the answer would be 5 (as long as the multiplication sign was in place). With two sets of brackets, the answer would indeed be 9.

[southside1874]

The brackets are necessary so that you calculate 1+2 first. If not, you would calculate the addition aspect of the equation last and the answer would be 5 (as long as the multiplication sign was in place). With two sets of brackets, the answer would indeed be 9.

 

So if you wanted the answer to be 9 without doubt you would write the task down with both brackets. If you wanted the 2 to belong to the brackets then you would write it with one set of brackets. If it was an arithmetical question then you would not have brackets at all.

[P-Dizzle]

The entire point is the ambiguity, southside.

[Das Root]

So if you wanted the answer to be 9 without doubt you would write the task down with both brackets. If you wanted the 2 to belong to the brackets then you would write it with one set of brackets. If it was an arithmetical question then you would not have brackets at all.

 

 

Why? Maths is not here to waste time. The rules are in place that the second set of brackets are not required given the division symbol is in place so that it is the second part of the full equation worked out. Maybe if you are a 1st year school student you would require both sets of brackets, so it's easy enough for you to understand what to calculate first to come to the correct answer. If you want the answer to be 5 you would have no brackets. In this case whoever wanted the answer to be 9 had the single set of brackets so the calculation would work out so, and as this is not a problem set for a 12yr old the second set of brackets was not included.

 

Ambiguity? Only for beginners. Or for those who need calculators to work out simple sums.

[Budgie.]

Found this answer online: (appreciate it's not gospel!)

 

I am your college professor that you requested, with a doctorate in Mathematics. I will break this down as simply as possible and end this debate as approx. 10 students have already asked me this today.

The problem as it is written is 6?2(1+2) , the ? cannot be substituted with a fraction bar because they have different ranks on the order of operations. It is an illegal math move to do this. The bar ranks with parentheses, ? is interchangeable with *. therefore the problem must be solved as 6?2(1+2) NOT 6 (over) 2(1+2) we do the parentheses first, so 6?2(3), the parentheses are now no longer relevant, because the number inside is in it's simplest form. Every single number has implied parentheses around it.

6?2(3)

(6) ?(2)(3)

6?2*3,

or even converting the division to multiplication by a reciprocal (a legal math move)

(6)(1 (over) 2)(3)

are all correct ways to write this problem and mean exactly the same thing. Using pemdas, where md and as are interchangeable, we work from left to right, so (3)(3) or

3*3= 9

 

Just because something is implied rather than written does not give it any special rank in the order of operations.

 

The problem in it's simplest form, with nothing implied would look like this:

(1+1+1+1+1+1 (over) 1) ? (1+1 (over) 1) * ((1(over) 1) + (1+1 (over) 1))

From here, nothing is implied, This again, works out to 9.

 

If the symbol '/' was used this whole debate would be ambiguous since that symbol can mean "to divide by" or it could mean a fraction bar.

 

HOWEVER, because the ? symbol is used, it can not be changed to mean a fraction bar because that would change the order of operations and thus the whole problem, you can't change a symbol to mean something because you want to, in doing so you are changing the problem.

 

Once and for all, the answer is 9.

 

Hopefully some of my students see this so I can stop answering this question.

 

End of debate... hopefully.

 

Source(s):

 

Doctorate, 9 years teaching experience.

 

Answer by Steven 21 hours ago Report Abuse

 

As stated above, you can't just decide to change it to a fraction as this breaks the rules of maths and changes the sum entirely.

 

Maths textbooks say 9.

 

The scientific calculator says 9.

 

Excel says 9.

 

Maths websites say 9.

 

A professor of mathematics says 9.

 

Some folk on a football forum say 1.

 

Conclusion...

 

You do the math!

[southside1874]

Why? Maths is not here to waste time. The rules are in place that the second set of brackets are not required given the division symbol is in place so that it is the second part of the full equation worked out. Maybe if you are a 1st year school student you would require both sets of brackets, so it's easy enough for you to understand what to calculate first to come to the correct answer. If you want the answer to be 5 you would have no brackets. In this case whoever wanted the answer to be 9 had the single set of brackets so the calculation would work out so, and as this is not a problem set for a 12yr old the second set of brackets was not included.

 

Ambiguity? Only for beginners. Or for those who need calculators to work out simple sums.

 

I wouldn't look at it as beginners and first year thing at all. I would look at it in a simple manner. In my previous post I showed you how I would set out the workings to show 9 so that there would be no ambiguity. If you use mathematics to work out resolutions to problems and the outcome of the answer means the difference between something failing or working, you don't use ambiguity. Mathematics came about for reasons to explain what was previously unexplainable. Mathematics is not an art so its not really open to interpretation. If you have to prove something through first principles and the answer is wrong, then you check back through your calculations. If you set out your calculations so someone can interpret them differently then your obviously asking for trouble. As I said, for me to reach 9 I would set the problem down with two sets of brackets and take away any doubt. If I was wanting it to be 1 then by what other means should I set out the figures

[Das Root]

I wouldn't look at it as beginners and first year thing at all. I would look at it in a simple manner. In my previous post I showed you how I would set out the workings to show 9 so that there would be no ambiguity. If you use mathematics to work out resolutions to problems and the outcome of the answer means the difference between something failing or working, you don't use ambiguity. Mathematics came about for reasons to explain what was previously unexplainable. Mathematics is not an art so its not really open to interpretation. If you have to prove something through first principles and the answer is wrong, then you check back through your calculations. If you set out your calculations so someone can interpret them differently then your obviously asking for trouble. As I said, for me to reach 9 I would set the problem down with two sets of brackets and take away any doubt. If I was wanting it to be 1 then by what other means should I set out the figures

 

 

 

You may do that, us real mathematicians would do it the proper way Read back to my earlier posts, it fully explains the rules in working out these simple equations. If you read it you will quickly understand why the 2nd set of brackets is unnecessary and therefore has little bearing on the final result. With little bearing, there is no need to include, and therefore it is not included.

[P-Dizzle]

As stated above, you can't just decide to change it to a fraction as this breaks the rules of maths and changes the sum entirely.

 

Maths textbooks say 9.

 

The scientific calculator says 9.

 

Excel says 9.

 

Maths websites say 9.

 

A professor of mathematics says 9.

 

Some folk on a football forum say 1.

 

Conclusion...

 

You do the math!

 

The calculators, websites and spreadsheets say nine because you've put the data in incorrectly. How do you not understand this? A piece of software cannot account for the ambiguity of the sum, therefore parentheses around 2(1+2) are required to avoid to getting a math error. 2(3) is implied multiplication, therefore it takes precedence over division leaving you with 6/6. Whether you use an obelus or a forward slash is irrelevant as they both indicate division and assert no supremacy over implied multiplication which is taken as given before you would divide anything.

 

I'd question the authenticity of that coming from a professor, but even if it is, it proves nothing and he is still wrong. This really doesn't require that level of understanding when it comes to mathematics.

 

I cannot pass comment on textbooks supporting your argument, but given your history of citing sources I'd seriously doubt your interpretation.

 

 

Oh, and it's maths. You do the mathematic? Don't think so, where does that fit into your textbook analysis?

[Das Root]

The calculators, websites and spreadsheets say nine because you've put the data in incorrectly. How do you not understand this? A piece of software cannot account for the ambiguity of the sum, therefore parentheses around 2(1+2) are required to avoid to getting a math error. 2(3) is implied multiplication, therefore it takes precedence over division leaving you with 6/6. Whether you use an obelus or a forward slash is irrelevant as they both indicate division and assert no supremacy over implied multiplication which is taken as given before you would divide anything.

 

I'd question the authenticity of that coming from a professor, but even if it is, it proves nothing and he is still wrong. This really don't require that level of understanding when it comes to mathematics.

 

I cannot pass comment on textbooks supporting your argument, but given your history of citing sources I'd seriously doubt your interpretation.

 

 

There is no ambiguity, it's very straightforward. I have provided you with a full explanation as to why. If you can provide a counter argument that refutes my position and confirms your own let us read it. Just typing stuff out, and saying "it's 1 cos it is" has little relevance given the actual cold hard facts supporting the correct answer of 9. I think you are beaten. I think you are hurting now. Accept it, you'll feel better