stupid maths problem

[Captain_Cavman]

One thing I never lose is deabtes about mathematics. I can also do high level mathematics quite well. and my degree also involves that...

I bet all the 9s are thrilled you're on their side then.

theswordsman, you can't use an algerbraic proof to show how order of operations works as there aren't variables involved in it as you are solve the equation not solving for x or y, etc...

Oh. Maybe not.

 

[Elagabalus]

...Oddly enough, I used two different calculators and one said 9 was the answer and the other said one...

Congratulations!

You just proved that Krebs is correct and you are...ah...not completely right...

 

[ergmonkey]

ACF is right about mathematics and wrong about Cadel Evans.

Which is kind of ironic, since you would expect Cadel's obvious limitations to be provable with mathematical certainty.

 

[Libertine Seguros]

Are we still at it?

As Hitch says, google autocorrects it to 6/2*(1+2). This is also what excel does.

If I saw 6/2x(1+2) I would answer 9, because the (1+2) and the 2 are clearly not part of the same expression.

However, I read 2(1+2) as an expression.

Expressions involving brackets should be dealt with first. Therefore, you expand the brackets, 2(1+2) = 2x1 + 2x2 = 2+4 = 6.

n/n(n+n) will ALWAYS be ambiguous regardless of which numbers you plug in.

If 2(1+2) is not meant to be read as an expression it should be written differently to avoid confusion.

The problem is badly written. ACF's degree may involve a level of mathematics and he answers 9; but my mother is a maths teacher and she answers 1.

The reason is, as pointed out, no proper maths expression would be as ambiguous as this.

This is the reason why google and excel both autocorrect it - because =6/2(1+2) doesn't clarify whether we have an algebraic operator (as read by those answering 1) or an arithmetic operator (as read by those answering 9).

The ambiguity of this equation can only be solved by adding further clarification, such as expressing it as a fraction (clearing up whether 6/2 is a modifier or 2(1+2) is a denominator) or adding the extra set of brackets (or the multiplier symbol that clearly makes it linear, as chosen by excel).

 

[Elagabalus]

... However, I read 2(1+2) as an expression.

...Expressions involving brackets should be dealt with first. Therefore, you expand the brackets, 2(1+2) = 2x1 + 2x2 = 2+4 = 6....


...but my mother is a maths teacher and she answers 1....


...This is the reason why google and excel both autocorrect it - because =6/2(1+2) doesn't clarify whether we have an algebraic operator (as read by those answering 1) or an arithmetic operator (as read by those answering 9)....

....The ambiguity of this equation can only be solved by adding further clarification, such as expressing it as a fraction (clearing up whether 6/2 is a modifier or 2(1+2) is a denominator) or adding the extra set of brackets (or the multiplier symbol that clearly makes it linear, as chosen by excel)....

Thank you! I think the third quote is key. It's clearly an algebraic operator as you have pointed out. And thank you for enlisting the help of your mother. It saved me from doing the same with my brother who is also a maths teacher! (And I'm sure he would also say the answer is 1).Which brings me to another pertinent point-perhaps the other posters high maths lernin' ain't "high" enough!(JK!)

Also, here in the Northern Hemisphere we are usually taught that the ÷ symbol is another way of expressing a fraction so everything below the line would be done first.

Folks, this ain't rocket surgery! The answer is 1. I knew it all along ...

Anybody who says 9 is just a jealous hater ...

 

[Rip:30]

but my mother is a maths teacher

My dad is a professor of mathematics. I'm a molecular biologist. In north america the answer is 9. Anybody citing PEDMAS or BODMAS as support for 1 is making my head hurt.

 

[Elagabalus]

My dad is a professor of mathematics. I'm a molecular biologist. In north america the answer is 9. Anybody citing PEDMAS or BODMAS as support for 1 is making my head hurt.

So... you didn't actually ask your father did you?


jealous...jealous haterz

 

[Libertine Seguros]

My dad is a professor of mathematics. I'm a molecular biologist. In north america the answer is 9. Anybody citing PEDMAS or BODMAS as support for 1 is making my head hurt.

But that was my point - ACF is somebody who uses maths as part of their degree - so clearly isn't an idiot - and answers 9. My mother is somebody who teaches maths - so clearly isn't an idiot - and answers 1.

To me, and the way I've been taught, P/B in the acronyms applies to bracketed expressions, not just the contents of the brackets. 2(1+2) is one entity to me.

As pointed out before, it depends on whether you see an algebraic operation (n=1), where the fraction is 6 over 2(1+2), or you see a linear arithmetic operation (n=9) where the fraction is 6 over 2, and this result then modifies (1+2).

If somebody says 6/2a to me, I see (6)/(2a) with assumptive brackets, not (6/2)(a), because if they wanted to express to me that they wanted a to be modified by both the 6 and the 2, there are less misleading ways to report it even without brackets, such as 6a/2.

 

[Mambo95]

But that was my point - ACF is somebody who uses maths as part of their degree - so clearly isn't an idiot - and answers 9. My mother is somebody who teaches maths - so clearly isn't an idiot - and answers 1.

Qualifications aren't really all that relevant here. No 'mathematician' should have seen the division sign after the age of about 10. You certainly wouldn't see it in algebra.

As you said, it's deliberately ambiguous - something 'proper' maths certainly isn't.

 

[Garry Allen]

Look at the language, how it is written. Whoever composed the question used algebraic notation with the 2(1+2) and intended this precedence to dominate the divisor sign. Yes its confusing but I would be willing to bet that is what the composer of the question intended. there is no multiplication sign there. It is implied and because the 2(1+2) is grouped together, there is an implied set of brackets around both of them
Put a multiplication sign between the 2 and the (1+2), the answer is 9. But as it is written, the answer is 1 because of the implied set of brackets around them.

 

[Elagabalus]

...No 'mathematician' should have seen the division sign after the age of about 10. ...

That's what I was alluding to with my "perhaps the other posters high maths lernin' ain't "high" enough" quip but you managed to put it more succinctly than I ever could. And for that...I thank you.

 

[online-rider]

answer is 9

 

[auscyclefan94]

Just to let you know gary, just because they have put the 2 right next to the brackets does not mean they are inside them. I still think it is 9 but I think I will check with some other people who I know who are better than me.

2x(1+2) = 2(1+2)

Is 1x the same as 'x'?

 

[Mambo95]

That's what I was alluding to with my "perhaps the other posters high maths lernin' ain't "high" enough" quip but you managed to put it more succinctly than I ever could. And for that...I thank you.

But I'm a niner. A jealous 'hater'. Nine is the one true faith. The oner heathens will be put to death. It is written in the Bodmas* scriptures.

*The true Bodmas scripture, not the Bodmas scripture corrupted by decedance and brackets.

 

[Rip:30]

 

[krebs303]

It's the mixing of algebraic and arithmetic notation. All arithmetic signs the answer is 9. All algebraic the answer is 1. It's like a bad Google translation.
It may be some sort of left brain/right brain type of thing on how you perceive the information.
very clever.

 

[Cobblestoned]

The answer is 42, people....the answer is 42.
Trust me.

 

[Libertine Seguros]

Just to let you know gary, just because they have put the 2 right next to the brackets does not mean they are inside them. I still think it is 9 but I think I will check with some other people who I know who are better than me.

2x(1+2) = 2(1+2)

Is 1x the same as 'x'?

The point is, if you express 2 x (1+2) instead of 2(1+2) then there is no difference.

But once you start adding further functions, then it does make a difference, because if you say 6/2 X (1+2) then it is clear that 2 and (1+2) are two separate expressions (therefore 6/2x3=9), but if you don't use the multiplier then it is unclear whether 2 and (1+2) are meant to be one or two expressions. 2(1+2) reads as one expression, and as an expression with brackets, should be worked out before anything else. Which then gives 2(3)=6, then 6/6 = 1.

As krebs points out - the mixing of algebraic and arithmetic notation is what creates this problem, as if you read it algebraically your answer will be 1, and if you read it arithmetically your answer will be 9. Both answers are wholly valid unless the expression is clarified - and this is why both google and excel have to autocorrect in order to provide an answer to the ambiguous statement. Both correct it arithmetically, which would be in line with the majority on this poll.

As Mambo says, a true mathematician wouldn't use the division sign here, especially not in algebra. If they DID, they would use additional brackets to clear up the ambiguity, because if there's one thing mathematics is not supposed to be, it's ambiguous.

If the answer were to be 9 I would write it as:

6
_ (1+2)

2

If the answer were to be 1 (as is my first instinct) I would write it as:

6
_____

2(1+2)

 

[Moondance]

As many people have said the answer is 9.
For the first time on the forum ACF is completely 100% right

 

[Garry Allen]

Just to let you know gary, just because they have put the 2 right next to the brackets does not mean they are inside them. I still think it is 9 but I think I will check with some other people who I know who are better than me.

2x(1+2) = 2(1+2)

Is 1x the same as 'x'?

When you write 2(1+2) it is shorthand for (2(1+2)) or (2*(1+2)). Then you do the simplification. As everybody else has said, the confusion arises from the use of algebraic notation. And constructing an equation with a divide sign in the middle, the stuff in brackets to the left of the divide sign will be evaluated together and the stuff to the right of the divide sign will be evaluated together
e.g
we have a function F(z) = (z+2)/(2z^2-7z+3) (courtesy of Signal Analysis by A Papoulis)
If we factorise this, we would write
F(z) = (z+2)/(2z-1)(z-3)
Using arithmetic notation we would have to bracket this to apply BODMAS
F(z) = (z+2)/((2z-1)(z-3))
But thats a PITA. Instead we infer the brackets and evaluate the stuff to the left of the divisor separately to the stuff of the right of the divisor. Otherwise magic happens and suddenly the (z-3) is being multiplied together with (z+2) and we're getting really strange results out of our digital filters

 

[Timmy-loves-Rabo]

i straight away said 9.

 

[auscyclefan94]

When you write 2(1+2) it is shorthand for (2(1+2)) or (2*(1+2)). Then you do the simplification. As everybody else has said, the confusion arises from the use of algebraic notation. And constructing an equation with a divide sign in the middle, the stuff in brackets to the left of the divide sign will be evaluated together and the stuff to the right of the divide sign will be evaluated together
e.g
we have a function F(z) = (z+2)/(2z^2-7z+3) (courtesy of Signal Analysis by A Papoulis)
If we factorise this, we would write
F(z) = (z+2)/(2z-1)(z-3)
Using arithmetic notation we would have to bracket this to apply BODMAS
F(z) = (z+2)/((2z-1)(z-3))
But thats a PITA. Instead we infer the brackets and evaluate the stuff to the left of the divisor separately to the stuff of the right of the divisor. Otherwise magic happens and suddenly the (z-3) is being multiplied together with (z+2) and we're getting really strange results out of our digital filters

The divide sign is not confusing. If it was to equal one then it would have to be a bracket outside the 2. There is not. Again, you can't necessarily apply algebra to this.

Saying it equals 1 means you ar breaking the bond between the 2 and the division sign. This is arithmetic not algerbra ergo the answer is 9 no matter where you come from.

If think that you multiply the 2 first then you are wrong because it is like saying 6-2(3) = 0. That is incorrect as you can't split the negative symbol away from the number. Same principle. You can't split the diviosn awa from the 2. Th2 is out side the brackets and the connection with a number and a bracket is multiplication. When you have a multiplication and a division in anequation left you always go from left to right. Thererfore you divde 6 by 2 then you mul;tiply what is inside what is in the brackets.

Mathmatics is universal so you can't say that it is a 'cultural thing'. Gary's equation above infers there is a bracket around the 2 which there is not.

Therefore the equation can be read (without the division sign as)

6.............. x (1+2)
2

then multiply what is inside the brackets. Because there is no algebra invoved you just add the numbers up, multiply and there you go.

 

[Garry Allen]

2(1+2) implies that there is a multiplication sign between the 2 and the (1+2). BUT and it is a huge but, it also implies that there are brackets around them as well. They must be evaluated together before you evaluate the rest of the calculation, applying BODMAS..

The answer would be 9 if the algorithm had been written as
6/2*(1+2). But it wasn't, the brackets are inferred and the answer is 1

 

[screaming fist]

My english is not really that good that I may use the right words for math, but here's the solution

6 ÷ 2 * (1+2) = x


we have three terms that I mark in different colors:

6 ÷ 2 * (1+2) = x

So, the 2nd term is not "2" but "÷ 2". It's not the order in which you solve but that you always use the complete term. The part "÷ 2" may also be written "1/2" or 0.5 The division belongs to that term and to that term only.

So it is

6 * 0.5 * 3 = 9

in algebra:
a ÷ b * c = x
a * 1/b * c = x
6 * 0,5 * 3 = 9

or


a ÷ b * c = x | *b
a * c = b * x
6 * 3 = 2 * x
18 = 2 * x
x = 9

As posted above, the way to get to one was to put brackets after the division sign, in that case the whole part after "÷" would be one term.

 

[The Hitch]

My english is not really that good that I may use the right words for math, but here's the solution

6 ÷ 2 * (1+2) = x

You added the star here. WIth the star I think most people that say 1 would agree the answer is 9. Its without the star that we say the answer is 1.