A Simple Math Problem? - Page 35

On April 08 2011 09:24 -{Cake}- wrote:
Mathematical/linguistic rules are not a good way to justify correctness. (meaning pedmas or w/e is not an acceptable defense)

Notation is subjective, there is no such thing as correct or incorrect notation. You can redefine any convention, notation, language, etc in any way you want because they are all arbitrary constructs to begin with

If you're personally solving the problem, you can use 48&2@9#3 or w\jx(ptE) or even weiogheroighjtoh940tiuojeithdiohj5hj if you like

If you do not know your target audience, using massive amounts of parenthesis ((48)/(2))*(9+3) is more likely to result in your idea being communicated successfully, but that doesn't make it more correct

Either answer can be correct depending on how individuals interpret the expression, because under different conventions, the expression means different things

On April 08 2011 09:30 Grumbels wrote:
I had a math teacher for high school who sometimes wrote cos x^2 without brackets, and I just couldn't tell what he meant: (cos x)^2 or cos(x^2).

On April 08 2011 09:30 Grumbels wrote:
I had a math teacher for high school who sometimes wrote cos x^2 without brackets, and I just couldn't tell what he meant: (cos x)^2 or cos(x^2).

I think a problem is that you want your equations to be presentable and the order of operations is just a trick we use to prevent cluttering them with brackets. Another way to make clear what happens is to use special symbols to let the reader get a good impression which 'components' are interacting with eachother, or what abstract concept is expressed by this equation.
If you want to have x/2, generally you'll use a special 1/2 symbol just to make this clear, then. And 1 / (2x) will have the horizontal line dividing it, making it even more unambiguous.

I have honestly never seen a slash used in any textbook, as far as math goes it's just used for informal writings since it's the ascii representation for the horizontal line. I know it has a different meaning for a calculator, since there it does mean x/2, but if you read 1/2x as an informal representation it's easy to imagine it does mean 1/(2x).

I would never use 1/2x in any homework assignment though, since it's just so ambiguous.

On April 08 2011 09:32 kevconsim wrote:
I learned PEMDAS
Please Excuse My Dear Aunt Sally
Parentheses
Exponents
Multiplication
Division
Addition
Subtraction

I was taught that M and D are interchangeable
and A and D are interchangeable
You do whatever is on the left first

So:
48÷2(9+3)=48/2*12
48/2*12= 24*12
24*12= 288

On April 08 2011 09:34 mahnini wrote:

that is poppycock

if the equation was 4 + 5 * 3 no one would answer 27 and argue it was the correct answer because people would follow the order of operations. i don't get why people are getting so defensive about it, it's a tricky question which tests your understanding of the order of operations, there's no need to bring relativism into this.

On April 08 2011 09:36 Aruno wrote:


Ah I think in my schooling I missed that M and D were interchangeable

On April 08 2011 09:38 iNSiPiD1 wrote:
The issue with this thread is that mathematics should never be written in the form described by the OP. I just wrote a 23 page math paper for my B.S. in math, and it's just misleading to assume that because people cannot interpret the form given by the OP that they suck at math.

I argue only those who know very little about math would be concerned over something as trivial as someone getting the answer to this wrong. For those who appreciate math would know to add an extra set of parenthesis, in order to make our meaning as unambiguous as possible. It's all about elegance of presentation.

On April 08 2011 09:39 DTK-m2 wrote:


Yes, but the order of operations is only absolute in doing parentheses first, then exponents, then multiplication and division, then addition and subtraction.

For addition and subtraction, the order does not matter, as it can't possibly have an effect on the answer. Therefore, PEMDAS is the same as PEMDSA.

For multiplication and division, this is where you get ambiguity, and while a lot of people in this thread are saying PEDMAS, I learned it as PEMDAS in elementary school, as did basically everyone else I know. I have never heard it as PEDMAS until this thread.

On April 08 2011 09:23 space_yes wrote:


You get the result you do b/c machine parsing puts each element into a stack and using reverse polish notation creates a syntax tree. Wolfram Alpha is a special case b/c it's designed for...newbies (see poll results) . If you put in "1/2 x":



Note the space in the above. Now before everyone who got the second question wrong jumps in and argues Wolfram Alpha's parsing of the expression with a space validates their interpretation understand that machine parsing isn't evidence for anything. If you use Mathematica with spaces you get:



With no spaces:



Generally most machines will interpret the expression as above. I don't have the symbolic computing package for Matlab on the computer I'm currently using but I believe it interprets 1/2x the same way Mathematica does.

There is no ambiguity; the question tests whether you understand order of operations. If you got the first question correct you should get the second one right also if you apply the same rules

+ Show Spoiler +

On April 08 2011 09:41 mahnini wrote:

there is no ambiguity. order of operations dictates that operations of the same priority (multiplication and division and addition and subtraction) follow a left to right convention where left is of higher priority.

On April 08 2011 09:38 iNSiPiD1 wrote:
The issue with this thread is that mathematics should never be written in the form described by the OP. I just wrote a 23 page math paper for my B.S. in math, and it's just misleading to assume that because people cannot interpret the form given by the OP that they suck at math.

I argue only those who know very little about math would be concerned over something as trivial as someone getting the answer to this wrong. For those who appreciate math would know to add an extra set of parenthesis, in order to make our meaning as unambiguous as possible. It's all about elegance of presentation.

On April 08 2011 09:44 shabinka wrote:


http://www.wolframalpha.com/input/?i=1/2x
I'm sorry.

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 or "Please Excuse My Dear Aunt Sally" is common. It stands for Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. In other English speaking countries, Parentheses may be called Brackets, or symbols of inclusion and Exponentiation may be called either Indices, Powers or Orders, and since multiplication and division are of equal precedence, M and D are often interchanged, leading to such acronyms as BEDMAS, BIDMAS, BIMDAS, BODMAS, BOMDAS, BERDMAS, PERDMAS, and BPODMAS.

In college mathematics, the rules of priority are (usually) taught correctly, and students are taught the commutative law, associative law, and distributive law, which replace the grade school "rules". The "left to right" rule is not a law of mathematics.

On April 08 2011 09:34 mahnini wrote:

that is poppycock

if the equation was 4 + 5 * 3 no one would answer 27 and argue it was the correct answer because people would follow the order of operations. i don't get why people are getting so defensive about it, it's a tricky question which tests your understanding of the order of operations, there's no need to bring relativism into this.