multiplication by juxtaposition and order of operations

[Ioannes]

I can't believe this thread is dragging for 4 pages lol

P.s. Oh, shiny new post interface!

 

[Meangeneatl]

My knowledge( or lack thereof) has always taught me that there should always be a way to prove any math operation. As of right now, all you PEMDAS'ers are only standing on a understanding of the basic order of operations. It seems to all work fine if everthing is all multiplication, but throw in a divisor into the mix and it doesn't change anything in your mind. Can any of you create a secondary equation from the original to prove your answer of "9"? Can you substitue "X" for a part of the original equation to verify it? My teachers told me you could always verify your work that way.

6÷2(1+2)=?
X÷2(1+2)=9
You would have to simplify the sides.
X÷2(1+2)=9
X÷2(3)=9
X÷6=9
X÷6 * 6=9 * 6
X=54

This X=54 disproves the PEMDAS because X should have finished out to an answer of "6" to prove your answer. Having a final answer of "1" does satisfy this type of verification. Please talk me out of my way of thinking.

upon seeing this question, my first reaction was that there couldnt possibly be that many dumb people... i took a moment to calculate it in my head and found that i had a distinct urge to group the 2 with the parentheses (which would yield an answer of 1) but after some consideration i felt that my urge went against order of operations. i tried to verify my answer...



i am not asking whether you think the answer is 1 or 9. i am not asking for your math professor's expert opinion. i am asking for a set of rules for which such an equation would have only one valid interpretation.

 

[camelCase]

2011 ;D

X÷2(1+2)=9
(X÷2)(1+2)=9
(X)(1+2)=18
(X+2X)=18
3X=18
X=6

I don't see anything wrong here.
You're forgetting that division and multiplication have the same level of precedence.
1) Bracket
2) Division/Multiplication
3) Addition/Subtraction

In the event that you have something like this:
2/3*4

You execute them from left to right.

 

[Meangeneatl]

2011 ;D

Camel Case .... didn't ask for a remark just because you feel like its an old topic. I learned one way of working this problem, now there seems to be a new way and I want to learn the correct ( best) way to work them. Don't need your crap.

 

[camelCase]

Yes, and you need to learn your crap. Your math is weak.

X÷2(1+2)=9
is more accurately re-written as:
X/2*(1+2)=9

If you wish for it to be so explicit:
X/2*(1+2)=9
(X/2)*(1+2)=9
2*[(X/2)*(1+2)]=2*9
2*[(X/2)*(1) + (X/2)*(2)]=2*9
2*[(X/2) + (X)]=2*9
2*[(X/2) + (2X/2)]=2*9
2*[3X/2]=2*9
6X/2=18
3X=18
X=6

 

[Accname]

Wait, is math told differently over there in the US?
I would say the result is 1 because multiplication comes before division.

It would be 6 / (2 * (2 + 1)) == 6 / (2 * 3) == 6 / 6 == 1
Thats how we got it in school.

But to be honest, i hate this priority bs. If i had to define math, i would just say go from left to right and put parenthesis.

 

[camelCase]

Multiplication does not come before division. That was never a rule. PEMDAS (or w/e it is) doesn't say that multiplication comes before division.

Quick google search: http://www.mathsisfun.com/operation-order-pemdas.html

How Do I Remember It All ... ? PEMDAS !



P Parentheses first

E Exponents (ie Powers and Square Roots, etc.)

MD Multiplication and Division (left-to-right)

AS Addition and Subtraction (left-to-right)

Divide and Multiply rank equally (and go left to right).
Add and Subtract rank equally (and go left to right)

PEMDAS says that multiplication and division rank equally. left to right.

[EDIT]
Yes, this priority thing is bullshit. Any person decent at math would never dream of writing their equations in a manner that would ever leave doubt for misinterpretation. These kinds of questions are worse than OS wars because it's a play on notation.

 

[Accname]

Multiplication comes first here. This is odd, really seems like a different system.
I really dont understand the reasoning behind the priorities. What do you gain with it?
It seems to me like a waste of time to fiddle around with that.

 

[Meangeneatl]

Yes, and you need to learn your crap. Your math is weak.

You're a PEMDAS'er and I have an old link to implicit multiplication in my mind. Just because I posted to a 2011;D forum doesn't mean I needed your little quick post before you edited it. After I posted my orig, I saw the way you worked it. I agree that your way works against the PEMDAS rules. I say there is an old rule that PEMDAS has tried to forget or push to the side.

 

[camelCase]

Multiplication comes first here. This is odd, really seems like a different system.
I really dont understand the reasoning behind the priorities. What do you gain with it?
It seems to me like a waste of time to fiddle around with that.

I cannot comment on this multiplication difference as I have never experienced anyone else using a different system. I doubt mathematicians with an Erdos number have this problem, though. They probably have a well-defined system and stick to it. I would look for it if I was really so interested (but I'm not). PEMDAS is a well-defined rule-set for basic arithmetic and I have no reason to go against it.

And, yes, I do find it a waste of time, too. As said, anyone with decent math would try to not write ugly stuff like the one in this thread. These things are usually written to bring about flame wars.

You're a PEMDAS'er and I have an old link to implicit multiplication in my mind. Just because I posted to a 2011;D forum doesn't mean I needed your little quick post before you edited it. After I posted my orig, I saw the way you worked it. I agree that your way works against the PEMDAS rules. I say there is an old rule that PEMDAS has tried to forget or push to the side.

C uses PEMDAS, too, and it's a language far older than my puny lifespan of 19 years. I have no idea what you are talking about.

No, I really have no idea what you are talking about. Try to gather your thoughts into coherent English if you want a discussion.

[EDIT]
People usually hate when Wikipedia is used as a citation. I generally like it.

Mnemonics are often used to help students remember the rules, but the rules taught by the use of acronyms can be misleading. In the United States the acronym PEMDAS is common. It stands for Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. ... Canada and Australia use BEDMAS. ...

These mnemonics may be misleading when written this way, especially if the user is not aware that multiplication and division are of equal precedence, as are addition and subtraction. Using any of the above rules in the order "addition first, subtraction afterward" would also give the wrong answer to the problem

 

[Meangeneatl]

Look at the very first post back from 2011;D... there are 1.5 million people that see this math problem the same way I do. Yes, there are 2.5 million that see it your way.

 

[camelCase]

You're forgetting that there are billions of people in the world. There are also billions that use the internet. There are millions that answered the question.

You are forgetting that many people do not like math. You are forgetting that many people were taught math wrong.

The order of operations used throughout mathematics, science, technology and many computer programming languages is expressed here

Coding is my bread and butter. PEMDAS is used in programming languages. Any coder that tries to fight this convention usually gets hung from a rope off a 100-storey building.

Conventions are there for a reason. They exist so people may communicate with the same frame of reference. The 1.5 million aren't going to ever do more than basic math and it's okay. Where they come from, the order of multiplication and division doesn't matter because they're just going to use it for taxes.

But for people who need to use math alongside other people, it helps a whole lot if a standard is followed. Standards can be evil but they are always necessary. They are created implicitly over time or explicitly.

[EDIT]
Better yet, don't take it from me. Take it from this: http://planetmath.org/orderofoperations
Written by a guy called Aaron Krowne. Let's look at his resume here: http://implode-explode.com/akrowne/br/akrowne_resume.html

Degrees:MS Computer Science (2003)
BS Computer Science (2001)
BS Applied Discrete Mathematics (2001)
Theses/dissertations:

• Krowne, A. An Architecture for Collaborative Math and Science Digital Libraries. 2003. (Master's thesis) online access.

Book chapters:

• Edward A. Fox, Marcos Andr� Gon�alves, Ming Luo, Yuxin Chen, Aaron Krowne, Baoping Zhang, Kate McDevitt, Manuel A. P�rez-Qui�ones, Ryan Richardson, Lillian N. Cassel: Harvesting: Broadening the Field of Distributed Information Retrieval. In Distributed Multimedia Information Retrieval, Springer-Verlag, SIGIR 2003 Workshop on Distributed Information Retrieval, Toronto, Canada, August 1, 2003, Revised Selected and Invited Papers; Lecture Notes in Computer Science, Vol. 2924; Callan, Jamie; Crestani, Fabio; Sanderson, Mark (Eds.), 2004, ISBN: 3-540-20875-5, pages 1-20

Papers/articles (published and peer-reviewed):

1. James Gardner, Aaron Krowne and Li Xiong. NNexus: An Automatic Linker for Collaborative Web-Based Corpora (demo track). 12th International Conference on Extending Database Technology (EDBT), March, 2009.
2. James Gardner, Aaron Krowne, Li Xiong. NNexus: An Automatic Linker for Collaborative Web-Based Corpora. IEEE Transactions on Knowledge and Data Engineering, vol. 21, no. 6, pp. 829-839, June 2009, doi:10.1109/TKDE.2008.136 (online access)
3. Gardner, J., Krowne, A., Xiong, L. NNexus: Towards an Automatic Linker for a Massively-Distributed Collaborative Corpus. CollaborateCom 2006, Mobility, Collaborative Working, and Emerging Applications workship. November, 2006. (online access)
4. Chopra, R., Krowne, A. Disciplining Search/Searching Disciplines: Perspectives from Academic Communities on Metasearch Quality Indicators. First Monday: WebWise 2006 Issue, August 2006 (online access)
5. Krowne, A., Puzio, R. The Fog of Copyleft. First Monday, July 2006 (May 10th Anniversary Conference Issue) (online access)
6. Krowne, A., Gadi, U. QMSearch: A Quality Metrics-Aware Search Framework. ARIADNE, May 2006. (online access.)
7. Krowne, A., How Free Culture Will Save Digital Libraries. In: Proceedings of the Symposium on Free Culture and the Digital Library, Emory University, Atlanta, GA. October 2005. (online access)
8. Corneli, J., Krowne, A., A Scholia-based Document Model for Commons-based Peer Production. In: Proceedings of the Symposium on Free Culture and the Digital Library, Emory University, Atlanta, GA. October 2005. (online access)
9. Milson, R., Krowne, A., Adapting CBPP Platforms for Instructional Use. In: Proceedings of the Symposium on Free Culture and the Digital Library, Emory University, Atlanta, GA. October 2005. (online access)
10. Krowne, A., Halbert, M. An Initial Evaluation of Automated Organization for Digital Library Browsing. In: JCDL 2005 proceedings, June 2005. (Nominated for the Vannevar Bush award).
11. Krowne, A. The FUD-Based Encyclopedia, Free Software Magazine, issue 2, April 2005. http://www.freesoftwaremagazine.com/free_issues/issue_02/fud_based_encyclopedia/
12. Goncalves, M., Krowne, A., Calado, P. The Effectiveness of Automatically Structured Queries in Digital Libraries., In proceedings of JCDL, June 2004. (Won "best student paper")
13. Krowne, A., Halbert, M. Combined Searching of Web and OAI Digital Library Resources. In proceedings of JCDL, June 2004.
14. Krowne, A., Bazaz, Anil., Authority Models for Collaborative Authoring. In proceedings of HICSS, January 2004.
15. Krowne, A., Fox, E. A., An Architecture for Multischeming in Digital Libraries. In proceedings of ICADL, December 2003.
16. Krowne, A. Building a Digital Library the Commons-Based Peer Production Way. D-Lib Magazine, Oct. 2003. http://www.dlib.org/dlib/october03/krowne/10krowne.html.
17. Suleman, H. Fox, E. A., Kelapure, R., Krowne, A., Luo, M.. Building Digital Libraries from Simple Building Blocks. Online Information Review. 2003-5, October.
18. Goncalves, M. A., Panchanathan, G., Ravindranathan, U., Krowne, A., Fox, E. A., Jagodzinski, F., Boots-Cassel, L. The XML Log Standard for Digital Libraries: Analysis, Evolution, and Deployment. JCDL 2003.

Technical Reports and Pending Papers:

1. Krowne, A., Hickcox, A., Ingram, S. Semantic Clustering in the Wild (submitted, Digital Humanities '07)
2. Gardner, J., Krowne, A., Xiong, L. Nnexus: An Automatic Linker for Collaborative and Distributed Corpora (submitted, WWW07) online access.
3. Ingram, S., Krowne, A. Towards Automatic Facetization: Hierarchical Document Clustering Using Multiplicative Up-Propagation (technical report; 2005) online access.

I don't know about you, but I'm not willing to doubt a dude with that much experience in math and code.

 

[The Helper]

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