Poll: 6÷2(1+2)

[wannabedamned]

So we've established that BODMAS and it's associated "left to right" rules are a cut down version of mathematics that are only used to teach kids very basic functions and therefore should not be taken as gospel?

If the OP had stated "please approach this problem with the mindset of an 8 year old" then I will agree that the answer is 9.

The question asked is basic, what's the problem with using a basic principal to solve it exactly?? Integrals need a complete different formula, that's obvious, as do loads of parts of mathematics. BUT the question asked here, is solved with BODMAS, nothing else. If you approach it with a rule that isnt supposed to be used, ofcourse you'll get a different answer. Regardless of your age, Which to be quite frank I dont see what a 9 year olds mind set has to do with anything. Maths is maths, Its a solid foundation regardless of age

 

[FoxEye]

gabmitt: is the meaning of this equation ambiguous or not?

(4x-1)y
_______
2xy+5

Will there ever be two (or more) valid answers when you solve this equation? If not, what principles ensure only one answer?

 

[bloodiedathame]

Anything to do with brackets is done first, as stated in BIMDAS.

Therefore multiply out the brackets: 2x1 = 2, 2x2 = 4, 2+4 = 6

6/6 = 1

 

[gambitt]

gabmitt: is the meaning of this equation ambiguous or not?

(4x-1)y
_______
2xy+5

Will there ever be two (or more) valid answers when you solve this equation? If not, what principles ensure only one answer?

No, that expression is quite clear. This is what grown up maths looks like, the ÷ is for kids who would find big fractions intimidating. As I've said, if you want people to regress to thinking like children then of course the answer is 9.

At degree level you don't even use the 'x' sign for multiplication, often a . is used instead.

 

[dowie]

The conventions I follow were established by solving thousands of equations over my academic career. Not once in any of these equations did I have to resort to using the so called "left to right" rule.

Well yes - if your maths course contained a problem such as 4*5÷2

I'd be a bit worried.

Still just because you've not had to consider a very simple problem for a while doesn't negate convention and you were taught these conventions before you started solving equations otherwise you'd have ended up with multiple different answers.

Perhpas because you're such a genius you've forgotten that you're even following conventions and everything is second nature to you.

Still you're surely aware that 2x^2 isn't ambiguous or open to interpretation you know that we actually mean 2(x^2) and not (2x)^2
and why do you know we mean that - well we've got conventions that remove the need for extra parenthesis. Just because you've not seen something as simple as the problem posed in the OP for a while doesn't mean there are two possible answers - that is quite frankly ridicules.

Now how about you tell me how you would go about solving the expression I posted above.

Its a silly question and rather sidetracking the thread.

 

[dowie]

As I've said, if you want people to regress to thinking like children then of course the answer is 9.

Ok so conversely under what convention could it be 1?

 

[gambitt]

Well yes - if your maths course contained a problem such as 4*5÷2

I'd be a bit worried.

Why is that? Simple expressions like this present themselves all the time inside the working of bigger equations, but they would be clearly presented as 4*5 all over 2 or similar, not as 4*5÷2 where I would have to apply the left to right "rule".

Its a silly question and rather sidetracking the thread.

I'll take that as an "I can't do it because my 'conventions' for 8 year olds don't extend past silly ambiguous questions"

 

[dowie]

Just to summarise - for people who have forgotten how to divide.

wikipedia:

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

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.

http://mathforum.org/library/drmath/view/57222.html

What's going on here, I suspect, is that when you look at

105 / ab

what you _see_ is

105 / (ab)

but that's not what it _says_. What it says is

(105 / a)b

Wolfram Alpha

http://www.wolframalpha.com/input/?i=6/2(1+2)

http://www.wolframalpha.com/input/?i=6/(2(1+2))

kids:

http://www.youtube.com/watch?v=pDQkU1mk3Jw

 

[gambitt]

http://mathforum.org/library/drmath/view/57222.html

But my son has a sixth-grade math teacher...

 

[Strife212]

I guess you ignore the part where the Dr says afterwards that it was right though

 

[dowie]

I'll take that as an "I can't do it because my 'conventions' for 8 year olds don't extend past silly ambiguous questions"

Nah just you're sidetracking the thread tbh... and the last time I was drawn into answering one of your sidetracking questions you decided to call me arrogant - so essentially its a bit pointelss

The question in the OP IS a question an 8 year old could answer.

How about you explain why you believe it could correctly be '1'. It is apparent that some people have mistakenly assumed that '2(2+1)' is the divisor and have arrived at 1 incorrectly but where have you ever learned that that is a valid use of '÷' thus leaving the question actually ambiguous.

Again 2x^2 is 2(x^2) and not (2x)^2
1/2x is (1/2)x and not 1/(2x)

Unless you normally deal with equations that are a mess of parenthesis then you know full well that conventions exist and choosing to ignore them and declare a very simple problem 'ambiguous' simply because you've forgotten very basic maths is a bit silly.

 

[wannabedamned]

But my son has a sixth-grade math teacher...

You have a proper attitude here, Why? Just explain to us why its 1 then? Talk us through it, Why is BODMAS wrong?

 

[guyfawkes5]

You have a proper attitude here, Why? Just explain to us why its 1 then? Talk us through it, Why is BODMAS wrong?

Just read even the last ten pages of this thread. All of this has been covered before, explanations for boths side given, and then the topic 'resets' itself as new posters, ignorant of the previous argument, give their opinions ad infinitum.

If you want the best explanation of the issue at the heart of the thread, look for Beta's rather long post(s) a few pages or so back.

And just to clarify, no-one is saying that the answer is definitively '1'; the entire disagreement revolves around the answer being 'definitive' at all. In fact this is one of the major problems that've made the thread have such a long (after)life - some people can't mentally process competing arguments without some sort of simplistic binary being applied.

This isn't a dig at you and I'm not saying you think this way, but an awful lot of this 'debate' has been coloured (not that it's been a healthy pink anyway) by 'rebuttals' of "go on tell us why it's 1 then" after explainations of why it could be either.

 

[dowie]

This isn't a dig at you and I'm not saying you think this way, but an awful lot of this 'debate' has been coloured (not that it's been a healthy pink anyway) by 'rebuttals' of "go on tell us why it's 1 then" after explainations of why it could be either.

Go on - tell us why it could be either

 

[gambitt]

Nah just you're sidetracking the thread tbh... and the last time I was drawn into answering one of your sidetracking questions you decided to call me arrogant - so essentially its a bit pointelss

Nah you've had an answer for everything until this point so I believe you are stumped because your BODMAS rules can't be applied.

Basic operations in maths including addition, subtraction, multiplication and division (when presented correctly as a fraction) ALL hold true even for the most complex of equations INCLUDING integration, differentiation etc. Maths is built from the ground up by proving something from first principals.

The ÷ symbol clearly does NOT hold true in all instances and is therefore not used in higher level maths because is presents these ambiguous scenarios where one assumes the "left to right rule" is invoked.

 

[guyfawkes5]

Cheeky comment fail

I've already said in the same post you've quoted:

Just read even the last ten pages of this thread. All of this has been covered before, explanations for boths side given, [...].

If you want the best explanation of the issue at the heart of the thread, look for Beta's rather long post(s) a few pages or so back.

The biggest problem here is once it's been explained posters ignore it and continue on their same unaltered line on the next page. Such is the interwebs.

 

[wmb]

1/(2+3)
1/(5)
1/5

Where did those brackets come from, there are none in what I posted?

 

[FoxEye]

Where did those brackets come from, there are none in what I posted?

Do you know what the word implied means?

The dividing line of a fraction implies brackets around both the numerator part and the denominator part.

http://www.onemathematicalcat.org/algebra_book/online_problems/basic_zero_one.htm

is the very first google result for "numerator denominator implied parenthesis"

http://lmgtfy.com/?q=numerator+denominator+implied-parenthesis

 

[silversurfer]

This is just a question of knowing the rules for which operation is performed first. I forget exactly if divide or multiply has priority but brackets is first

6/2(1+2)

1 plus 2 is 3

then its 6 divided by two then times 3 which is 9
or its two times 3 then 6 divided by six which is 1

Just look up which has priority multiply or divide


what Foxeye wrote is probably correct, I did A level maths and I forgotten the right order lol

 

[dowie]

Nah you've had an answer for everything until this point so I believe you are stumped because your BODMAS rules can't be applied.

I've not mentioned BODMAS specifically tbh.. But you're being incredibly naive if you don't believe you follow conventions when solving equations.