stupid maths problem

[Captain_Cavman]

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.

I think it's more that people who can't do algebra try and replace what is written by something else which makes arithmetical sense; when what is written makes perfect algebraic sense and no arithmetical sense at all.

As has been said earlier, putting the 2 next to the bracket implies a grouping that takes precedence over the left-to-right order of operations. If there was a 'x' sign, the answer would be 9. There isn't and the answer is 1.

 

[screaming fist]

By addting the star I tried to make it more easy to understand.

For the solution itseld there's no difference if the star is put or not, the rules stay the same.

 

[Captain_Cavman]

5÷2+2= ?
......4

Just wondering what answer ACF or any other 9ers would come up with for the above. 3 maybe?

 

[Magnus]

It's 1.

If it was 9 there'd be no reason not to write it as (1+2)6/2 (or maybe even just write 9).

Writing one in extremely complicated ways seems to be a common mathematician pass time.

Nobody writes 9 in complicated ways...

 

[antoine]

a simplified version of the problem

does 6÷2a = 3a or 3/a?
6 ÷ 2 x a is clearly 3a, but i would bet most people would say 6÷2a = 3/a.
i don't think you can both assume the x is there and deny the assumption that the 2(1+2) is a unit equivalent to (2(1+2)). as written, the problem is ambiguous. there's rules regarding notation to remove as many of the ambiguities as possible. a couple more parentheses would do guarantee that everyone gets the same answer. i blame the problem writer.

 

[Libertine Seguros]

By addting the star I tried to make it more easy to understand.

For the solution itseld there's no difference if the star is put or not, the rules stay the same.

No they don't.

If you put in the asterisk, it makes it clear that 2 and (1+2) are NOT part of the same expression. Therefore it follows a linear form from left to right, where the division takes place before multiplication, and the logical answer is 9. If you include the asterisk, most of us who've said 1 would probably say 9. I would and Hitch would, at least.

If you don't put in the asterisk, it makes it look like 2 and (1+2) are part of the same expression, 2(1+2). Which, as an expression involving brackets, should be worked out first, and then the division follows.

Without the asterisk, you have to make an assumption, otherwise it's impossible to calculate exactly (as both 9 and 1 are valid answers).

An arithmetic approach (taken by yourself, others, and by excel) makes the assumption that the multiplication symbol is there, thus 2(1+2) is comprised of two expressions, (2) and (1+2).

An algebraic approach (taken by myself, Cavman, hitch and others) makes the assumption that the implied brackets are there, thus 2(1+2) is comprised of one expression, (2(1+2)).

Both approaches require an assumption to be made in order to render the other answer incorrect. This is why, if you put =6/2(1+2) into Excel, it gives an error message, and autocorrects.

antoine better explains it above, with the substitute.

6/2*a ≠ 6/2a (a≠1 or -1).

 

[palmerq]

in my opinion when 2 is infront of the brackets like it is here then it means 2 of whatever is in the brackets, like if you had a squared sign there it means the brackets squared, therefore this is all done first, so the answer is obviously 1, but I am not an expert... Of course the question is written to be awkward and it does a great job.

 

[JPM London]

Ok, let's stop this before it gets silly...

Everybody who says one get out of here... Ah, that's better.

This is math - there is no ambiguity. There can be errors, yes, but no ambiguity.

There is no "We're both right" or "You can read it both ways" or "What if I stand on my head".

Math can be confusing, yes, and difficult to understand, yes, which is why some of you think the answer is one.

I'm not even going to argue this one - to do that I would have to repeat what's already written in here and even still have replies like "yes, but what if you turn the six around and add a fish to the oven" - it's not worth it.

Please pick up a basic math book if you're still struggling after having read the correct explanations offered by the niners...

 

[palmerq]

Ok, let's stop this before it gets silly...

Everybody who says one get out of here... Ah, that's better.

This is math - there is no ambiguity. There can be errors, yes, but no ambiguity.

There is no "We're both right" or "You can read it both ways" or "What if I stand on my head".

Math can be confusing, yes, and difficult to understand, yes, which is why some of you think the answer is one.

I'm not even going to argue this one - to do that I would have to repeat what's already written in here and even still have replies like "yes, but what if you turn the six around and add a fish to the oven" - it's not worth it.

Please pick up a basic math book if you're still struggling after having read the correct explanations offered by the niners...

but the niners are wrong


har har har :S

 

[Libertine Seguros]

Ok, let's stop this before it gets silly...

Everybody who says one get out of here... Ah, that's better.

This is math - there is no ambiguity. There can be errors, yes, but no ambiguity.

wrong.

http://www.xamuel.com/ambiguous-math/

Please pick up a basic math book if you're still struggling after having read the correct explanations offered by the niners...

Please pick up a basic math book if you're still struggling to see why this equation is unclear, and why it would be better expressed with additional parentheses or as a fraction.

It may be a schooling thing.

http://www.purplemath.com/modules/mathtext.htm

Please pay attention to the following parts:

(1/2)x + 5



Without the parentheses around the "one-half", it will be unclear whether or not the variable is meant to be included in the denominator.

1/(2x + 5)



The parentheses make it clear that the "five" is included in the denominator.

 

[palmerq]

http://www.purplemath.com/modules/mathtext.htm

if this purple math site is to be believed then the answer is one.

http://www.purplemath.com/modules/orderops2.htm

down at the bottom of the page

 

[Libertine Seguros]

using a graphical calculator (from that link):

but even there, it is pointed out that different graphical calculators give different responses and different teachers may teach different things.

 

[Elagabalus]

...I think it's more that people who can't do algebra try and replace what is written by something else which makes arithmetical sense; when what is written makes perfect algebraic sense and no arithmetical sense at all....

I tend to agree. Perhaps due to monetary constraints in the schools they are no longer teaching "new math" and have reverted to "old math"?

ACF, I hate to break this to you but 6-2(3) IS zero*.

Once again the use of parenthesis denotes the use of algebraic notation.

6-2 in algebraic notation is actually shorthand for 6+ -2 (there's, once again, implied brackets around the -2 but for the sake of clarity I used a different color)

therefore, we have,

6+-2(3)

The expressions with the brackets are worked out first, then we have:

6+-6 or 6-6 and

6-6=0

And now for my own amusement, I will now type in the original problem as written 6-2(3) into my aforementioned SHARP™ EL-5150 "Scientific Calculator"

waiting...

waiting...

0, But I knew that already...


There you have it, Ladies and Gentlemen!!

QED

Mods, please close this thread lest I be forced to suffer the grinding, gnashing and ankle-biting of the flat-earthers!

 

[Alpe d'Huez]

I would have never thought such a topic could get so much traction.

I went to the same school as Cobblestones. To us the answer is 9.

 

[Magnus]

Ok, let's stop this before it gets silly...

Everybody who says one get out of here... Ah, that's better.

This is math - there is no ambiguity. There can be errors, yes, but no ambiguity.

There is no "We're both right" or "You can read it both ways" or "What if I stand on my head".

There's plenty of ambiguity. Take for instance, convexity. A function can be convex and a set can be convex. But a function, as defined by Carol Schumacher in Chapter Zero, is a set. And a function that is convex in the function sense is only convex in the set sense if it is also concave in the function sense.

 

[icefire]

Can't believe this is taking such a long argument. The standard order of operations, or precedence, is expressed here:

terms inside brackets
exponents and roots
division and multiplication
addition and subtraction

http://en.wikipedia.org/wiki/Operator_precedence

It is helpful to treat division as multiplication by the reciprocal (multiplicative inverse) and subtraction as addition of the opposite (additive inverse).

6÷2(1+2) = 6 * 0.5 * (1+2) = ?

What's the next poll? Does the Earth turn around the Sun or is it the opposite?

 

[Libertine Seguros]

Algebraically, multiplication or division involving brackets (items placed directly next to brackets) supercedes multiplication or division not involving brackets, as they are part of the same expression as the brackets.

The argument is whether the 2 being placed next to (1+2) makes it part of the same expression as the brackets. The 1ers say yes, and have algebraic notation on their side. The 9ers say no, and have arithmetic notation on their side.

From the wiki link you gave:
"In any case where there is a possibility that the notation might be misinterpreted, it is advisable to use brackets to clarify which interpretation is intended.

Similarly, care must be exercised when using the slash ('/') symbol. The string of characters "1/2x" is interpreted by the above conventions as (1/2)x. The contrary interpretation should be written explicitly as 1/(2x). Again, the use of brackets will clarify the meaning and should be used if there is any chance of misinterpretation."

There IS a chance of misinterpretation, and different teachers and schooling systems vary with this notation on whether "1/2x" should be interpreted as "(1/2)x" or "1/(2x)". The division symbol or slash is necessary in computing, but as noting division in a linear form isn't as clear as expressing it as fractions (which would be preferable and much simpler), it is unclear, and thereby extra brackets should be included in order to clarify.

The wiki link suggests that 9 should be the answer. The purplemath link suggests 1 should be the answer. The purplemath site even includes graphical calculator outputs showing the answer to be 1 - but also adds that other graphical calculators programmed differently may not concur.

It requires a long argument, because no mathematician would express this problem in this way. Excel treats "=6/2(1+2)" as an error, and autocorrects it. It autocorrects it to =6/2*(1+2), but as the 1ers pointed out, this makes an assumption that (1+2) is not intended to be part of the denominator. The 1ers make the assumption that because 2 is placed immediately next to the brackets, it is part of the same expression. Not an unreasonable assumption to make, in fact thoroughly logical if you follow algebraic notation. This then places assumptive brackets around the expressions, (6)/(2(1+2)) which gives the answer 1.

 

[thrawn]

I'm with Libertine on this one.

 

[icefire]

Misinterpretation of the expression 1/2x is just a problem for humans. Computers use a formal grammar to evaluate expressions that does not leave margin for alternative interpretations and programmers cannot skip the multiplication sign the way it's done in handwriting.

1/2x = 1 / 2 * x

Division and multiplication have the same precedence. In that case, operations are evaluated taking the operands in pairs as read from left to right. This is equivalent to the "It is helpful to treat division as multiplication by the reciprocal (multiplicative inverse)" in my previous post.

As previously said, if you mean the multiplication 2x be evaluated before the division, the correct expression is 1/(2*x)

 

[User Guide]

civil war

In 30 yrs the we will be engulfed in global civil war the "1ers" vrs the "9ers"(like a bad star trek script)


I also did a smidge of maths at Uni(masters in astrophysics) default answer would be 1 (algerbraic solution ie 6 divide by 2a) however as has been pointed out the original terms are written without precsion so 9 is also not wrong(but not right lol)

 

[Libertine Seguros]

Misinterpretation of the expression 1/2x is just a problem for humans. Computers use a formal grammar to evaluate expressions that does not leave margin for alternative interpretations and programmers cannot skip the multiplication sign the way it's done in handwriting.

1/2x = 1 / 2 * x

Division and multiplication have the same precedence. In that case, operations are evaluated taking the operands in pairs as read from left to right. This is equivalent to the "It is helpful to treat division as multiplication by the reciprocal (multiplicative inverse)" in my previous post.

As previously said, if you mean the multiplication 2x be evaluated before the division, the correct expression is 1/(2*x)

The problem with this is that the way algebraic notation works, there is an implied precedence of terms without symbols, because they are perceived as being locked to the same expression.

Thereby 2*x holds less prominence than 2x.

But this is implicit, not explicit. Hence in this equation, by not clearly marking that 2 and (1+2) are to be seen as separate expressions, it makes it appear that they are part of the same expression, and thus implied brackets are placed around the separate expressions (6)/(2(1+2)).

When people who study or studied mathematics, teach mathematics and use mathematics in their daily job all disagree, it is clear that there is not enough clarity to say who is right and who is wrong. Different teaching systems teach us different ways of dealing with this ambiguity. Clearly the arithmetic method is more common (9 is ahead of 1 in the poll), but the algebraic method cannot be considered incorrect, because with the question posed in this form, both answers require an assumption to be made (the implied multiplication symbol removing (1+2) from the denominator in the case of the 9ers, the implied brackets retaining (1+2) in the denominator in the case of the 1ers) in order to make the other answer demonstrably false.

 

[Anonymous]

Google doesnt say 9. It changes the equation and then says 9.

If you type it into google it gives the following answer

(6 ÷ 2) * (1 + 2) = 9

That is a different equation.

No, it isn't, because the multiplication is implicit. Just because you don't see it does not negate its presence. The answer is clearly 9. The reason Google changes it is because it is doing the correct calculation. You are not.

 

[Anonymous]

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).

It auto corrects because that is correct.

 

[Anonymous]

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.

Check out the big brain on Brad!

 

[The Hitch]

Glad to see the 9 ers are so open minded

Weve already had "Im tired of seeing this" from Parrulo and " I never lose maths debates" from ACF. Another example of respect to other peoples opinions right here.

Why does it annoy some of you guys so much that other people were taught differently.

Ive been taught from a very young age that unless specified otherwise numbers in brackets are ONLY multiplied by the number next to it. From the looks of it, im not the only one.

Youll have to do a lot better than "we are cleverer than you" to convince us we are wrong.

That aside, still glad to see TFF back

Though looking at the "moderators" thread, one wonders how long.