48÷2(9+3) = ?

[mechanicx]

Originally Posted By: Volvo_ST1
This thread exemplifies that basic math skills have become a lot more basic over the past 20 years. As I have mentioned in another thread a few weeks ago, 5th grade math is now being taught at uni. I am no longer surprised at that!


No, 5th grade math is taught as remedial courses at mostly community colleges and maybe some universities. College level algebra is much more advanced than normal middle school or even high school algebra. Most universities expect incoming freshman to be at the college algebra or pre-calculus level and so don't even offer remedial math.

Quote:
People seem to not know basic math rules. If they knew the rules, there wouldn't be great confusion and bickering.

48:2(9+3) = ?


This math problem is intentionally written poorly. You would have a point that if the rules were known there would be no confusion, but apparently there is no set in stone rule of order of operation for this problem.

Quote:
There are two groups: 48:2 and (9+3). The 2 does not belong to (9+3), as denoted by the lack of an operator. Therefore we must calculate (48:2):12 = 2.


What rule says to do it this way? I see what you are doing, making 48/2 the numerator and 2(9+3) the denominator which few from either side would agree with. Also the way you rewritten the problem adding parentheses to the beginning and and extra division sign does not seem to follow the rules of order of operation that you claim is generally lacking.

Quote:
If the calculation is written as 48:2*(9+3), we must calculate (48:2)*12 = 288


While I agree with your final answer, your putting parentheses around 48:2 is not neccessary and makes no rhyme or reason with your first solution. Why would * before (9+3) magically not make it the denominator as you claimed before. And what is the really the difference between 2*(9+3) and 2(9+3). You seem to be giving ":" and "*" more precedence that the rules afford.


Quote:
I have an inexpensive Tozai scientific calculator. If I type the calculations as indicated above, I get the respective and proper results, as expected.



That different calculator give different answer depending on their different programming has already been covered ad naseum.

 

[mechanicx]

Originally Posted By: Quattro Pete
Originally Posted By: Reelizmpro
Originally Posted By: hate2work


So, 48/2(9+3) = 48/2(12) = 24(12) = 288.


48/2(12) = 48/24 = 2
LOL...Parentheses first. Ask him to check his work with pen/paper...no calculators.

The rule of parentheses doesn't refer to getting rid of them first. It refers to performing operations in the parenthesis first before proceeding with all other regular business (which is left to right division/multiplication in this case).


This like I said awhile back this is the whole crux of the debate, whether or not the paretheses tie the 2 to the (12) and must be evaulated first. If so, then the 2(12) effectively becomes the numerator as well. I have been saying what you've just said, but a few have posted a link to PurpleMath that states the convention is multiplication by promixity to parentheses is evaluated before other division and multiplication

. You would still solve inside the parentheses first so that's why I've been looking at as 2(12)=2*12, so you would divide 48 by 2 first.

 

[mechanicx]

What does your calculator do if you enter it as the following: 48÷2(12). Would it still get 2 or not?

 

[Quattro Pete]

Originally Posted By: mechanicx

I have been saying what you've just said, but a few have posted a link to PurpleMath that states the convention is multiplication by promixity to parentheses is evaluated before other division and multiplication

.

Yeah, I know. My question is, who is PurpleMath and from where do they draw their math knowledge? Would the experts of the professional math community agree with them? I'm not saying it's wrong. I'm just asking for reputable source of this information, since I've never heard of PurpleMath before. There are many of these math websites out there. Some of them agree with PurpleMath. Others don't (WolframAlpha, Google). How are we to determine who's correct?

 

[Vikas]

I am almost invisible here :-( Change "2" to "1" and tell me your answer.

 

[mechanicx]

Originally Posted By: Quattro Pete
Originally Posted By: mechanicx

I have been saying what you've just said, but a few have posted a link to PurpleMath that states the convention is multiplication by promixity to parentheses is evaluated before other division and multiplication

.

Yeah, I know. My question is, who is PurpleMath and from where do they draw their math knowledge? Would the experts of the professional math community agree with them? I'm not saying it's wrong. I'm just asking for reputable source of this information, since I've never heard of PurpleMath before. There are many of these math websites out there. Some of them agree with PurpleMath. Others don't (WolframAlpha, Google). How are we to determine who's correct?


That's is exactly my sentiments. We have some purportedly knowledgeable math people contradicted what PurpleMath says. What is a person to believe?

 

[mechanicx]

Originally Posted By: Vikas
I am almost invisible here :-( Change "2" to "1" and tell me your answer.


OK then if you factor out the 1 working left to right it's simplified to 48(12)=576. I know, it's compelling to say 1(12)=(12) so it should be simplified to 48÷(12), but I'm not going to contradict myself now lol.

Since division is the reciprocal of multiplication, working left to right 48*1/1(12)=48(12)=576

.

 

[OVERKILL]

Originally Posted By: Quattro Pete
My question is, who is PurpleMath and from where do they draw their math knowledge?


http://www.purplemath.com/resume.htm

Quote:
Educational History

Mesa Community College, Mesa, Arizona
Fall 1996 semester: a course for teachers in community colleges

Washington University, Saint Louis, Missouri
August 1994 to December 1994: courses geared toward a teaching degree; GPA: 3.92/4.00

Meramec Community College, Saint Louis, Missouri
Interim and Summer, 1994: courses for Missouri teacher certification; GPA: 4.00/4.00

Washington University, Saint Louis, Missouri
August 1992 to May 1994: M.A., Mathematics; GPA: 3.36/4.00

Wright State University, Dayton, Ohio
August 1991 to June 1992: B.S., Mathematics, summa cum laude; GPA: 3.922/4.000
January 1988 to June 1991: graduate study, teaching experience; GPA: 4.000/4.000


My sister is more qualified. By far.

 

[onion]

23 pages of this nonsense?

Good gawd... and I thought I was anal.

The problem is poorly written. It's ambiguous. To get an answer everybody can agree upon, there needs to be some clarification.

I guess some folks just have a driving need to be 'right' no matter what the question. In this case there really is no 'right' answer.

 

[Volvo_ST1]

Originally Posted By: mechanicx
Originally Posted By: Volvo_ST1

People seem to not know basic math rules. If they knew the rules, there wouldn't be great confusion and bickering.

48:2(9+3) = ?


This math problem is intentionally written poorly. You would have a point that if the rules were known there would be no confusion, but apparently there is no set in stone rule of order of operation for this problem.


It is not poorly written. It is written in a manner that requires knowing a particular rule, one which apparently is not taught in high school.

Originally Posted By: mechanicx
Originally Posted By: Volvo_ST1

There are two groups: 48:2 and (9+3). The 2 does not belong to (9+3), as denoted by the lack of an operator. Therefore we must calculate (48:2):12 = 2.


What rule says to do it this way? I see what you are doing, making 48/2 the numerator and 2(9+3) the denominator which few from either side would agree with. Also the way you rewritten the problem adding parentheses to the beginning and and extra division sign does not seem to follow the rules of order of operation that you claim is generally lacking.


The rule you don't know says so! Without knowing this rule you can't know, of course! I added the parenthesis as an alternative and clearer way of presenting the problem.

Originally Posted By: mechanicx
Originally Posted By: Volvo_ST1

If the calculation is written as 48:2*(9+3), we must calculate (48:2)*12 = 288


While I agree with your final answer, your putting parentheses around 48:2 is not neccessary and makes no rhyme or reason with your first solution. Why would * before (9+3) magically not make it the denominator as you claimed before. And what is the really the difference between 2*(9+3) and 2(9+3). You seem to be giving ":" and "*" more precedence that the rules afford.


How can I expect you this to make sense, if you don't know the rule? Consider that the lack of an operator between 2 and the opening parenthesis makes the division symbol between 48 and 2 the de facto operator. At first glance, due to how the problem is written, 48 divided by two is the numerator, 2(9+3) is the denominator.

Originally Posted By: mechanicx
Originally Posted By: Volvo_ST1

I have an inexpensive Tozai scientific calculator. If I type the calculations as indicated above, I get the respective and proper results, as expected.



That different calculator give different answer depending on their different programming has already been covered ad naseum.


ad nauseam

Comprehension is not being taught in high school any longer either, I gather. It's the same calculator that gives the two proper and expected results if the problem is typed in with or without operator between the 2 and the opening parenthesis. The calculator follows the rule, which you don't know and which you insist to not exist.

 

[MNgopher]

Onion, you just summed up this engineers feelings on this whole thread perfectly.

 

[Al]

Originally Posted By: MNgopher
Onion, you just summed up this engineers feelings on this whole thread perfectly.

Another engineer (me) agrees with you.

Originally Posted By: onion

I guess some folks just have a driving need to be 'right' no matter what the question. In this case there really is no 'right' answer.

I think that's where we are.

 

[mechanicx]

But it is a real simple question that most of us agree, except Volvo_STI who has his own rules, simplifies to whether or not "a(b)" takes precedence over normal multiplication and division from left to right because the paratheses tie "a" and "b" together. That a seemingly simple order of operation has no consensus is amusing to some

.

 

[Quattro Pete]

Originally Posted By: Volvo_ST1
There are two groups: 48:2 and (9+3). The 2 does not belong to (9+3), as denoted by the lack of an operator. Therefore we must calculate (48:2):12 = 2.

So "the lack of an operator" is in fact a division sign (":")? Can you direct me to some scientific literature supporting this?

I'm not trying to be difficult. I'm just trying to learn at this point. Having not taken basic algebra in this country, I may have missed something.

 

[Volvo_ST1]

The lack or presence of the operator indicates proper distribution.

48:2(9+3)=?

48
-------- = 2
2(9+3)

 

[UncleS2]

"The 2 does not belong to (9+3), as denoted by the lack of an operator. Therefore we must calculate (48:2):12 = 2."

???

Just plain Wrong! 2(12) = 2*12 = 2*(12). Period.

Mechanicx, the only answer I gave was 288. I thought that stating that an outside multiplier does NOT nullify the order of operations made it clear. That's the problem most people get hung up on

As to the continued arguing by others, it will go on forever. Note that some were talking about a consensus, as if that made anything right or wrong. If 4 out of 5 people say that 1+2=5, that doesn't make it right. It's not a matter of opinion, it's a matter of following the rules. (BTW- It's easy to tell those who have grown up with the idea that "all opinions are equal". What nonsense! Only *Informed* opinions have any value.)

You are completely right about 5th-6th grade math havimg to be taught at most junior colleges. One of the courses I used to teach was "Intermediate Algebra", at a 4 yr university. This was a rehash of high school Alg II, taught as a remedial, not for credit course. Skills & scores of most of the "traditional" students were apalling, to put it mildly.

I'm now through with this, on to Door Number 3.

 

[onion]

Quote:
As to the continued arguing by others, it will go on forever. Note that some were talking about a consensus, as if that made anything right or wrong. If 4 out of 5 people say that 1+2=5, that doesn't make it right. It's not a matter of opinion, it's a matter of following the rules. (BTW- It's easy to tell those who have grown up with the idea that "all opinions are equal". What nonsense! Only *Informed* opinions have any value.)



Actually consensus does matter. If a rule is so obscure and unclear that nobody can come to a consensus as to what it means... then that ain't a very effective means of communication, now is it?

How about we say what we mean and mean what we say?

If you mean (48/2)*(9+3), then say so.

Or if you mean 48/(2*(9+12)), then say so.

But if you insist on saying 48÷2(9+3)... then you won't accomplish a whole [censored] of a lot except a pointless argument.

I mean [censored], you could write the same math problem as a word problem in Portuguese and be technically correct. You could chide everybody else all day long for not understanding it. But that would be a pretty ineffective method of communicating a math problem among English speakers.

 

[Astro14]

Originally Posted By: onion
Quote:
As to the continued arguing by others, it will go on forever. Note that some were talking about a consensus, as if that made anything right or wrong. If 4 out of 5 people say that 1+2=5, that doesn't make it right. It's not a matter of opinion, it's a matter of following the rules. (BTW- It's easy to tell those who have grown up with the idea that "all opinions are equal". What nonsense! Only *Informed* opinions have any value.)



Actually consensus does matter. If a rule is so obscure and unclear that nobody can come to a consensus as to what it means... then that ain't a very effective means of communication, now is it?

How about we say what we mean and mean what we say?

If you mean (48/2)*(9+3), then say so.

Or if you mean 48/(2*(9+12)), then say so.

But if you insist on saying 48÷2(9+3)... then you won't accomplish a whole [censored] of a lot except a pointless argument.

I mean [censored], you could write the same math problem as a word problem in Portuguese and be technically correct. You could chide everybody else all day long for not understanding it. But that would be a pretty ineffective method of communicating a math problem among English speakers.


The whole point of the OP was to stir up controversy.

The problem was carefully chosen to be ambiguous unless you rigorously applied the rules of order of operations...

And from all these posts - Vikas was incredibly successful in his intent...you guys seem to have lost sight of that intent...

 

[onion]

We're an easily manipulated bunch.

 

[Volvo_ST1]

Originally Posted By: Astro14

The whole point of the OP was to stir up controversy.


Kudos for that realization, and kudos for NickR.

http://www.wallstreetoasis.com/forums/48÷293
http://www.physicsforums.com/showthread.php?t=488334
http://forum.bodybuilding.com/showthread.php?t=133389973
http://forum.grasscity.com/general/787504-48%F72-9-3-%3D.html
etc, etc

http://www.google.com/search?client=safari&rls=en&q=48:2(9%2B3)&ie=UTF-8&oe=UTF-8

This board can't display all links as links. Copy and paste.