48÷2(9+3) = ? --> How smart are you?

[spude]

288

[jwb]

Holy shit 98 pages!

http://www.teamliquid.net/forum/viewmessage.php?topic_id=210235

and it is still 2.

a÷bc isn't the same as a÷b*c

this is an interesting paper on how math is taught poorly today.

http://math.berkeley.edu/~wu/order5.pdf

[Parker]

How the fuck do you get four?

At the time he was practicing on breaking a German Shepard spine...

[sync pulse]

[FREAKgeek]

Do we believe wiki or the American Maths Society?

The convention used by the Mathematical Reviews of the American Mathematical Society (AMS), Mathematical Reviews Database - Guide for Reviewers states that "multiplication indicated by juxtaposition is carried out before
division." Thus, in general, for any variables a, b and c, we would
have a/bc = a/(bc) (assuming, of course, that b and c are nonzero).

Only this notation is correct:

_a_  =   _a_
bc         (bc)



However,

a/(bc) =   _a_
               bc

a/bc   =  a(c)
             b

yeilds two different quantities.



If you want to divide a series of terms, ex. ab, cd, ef :

it's written (ab) / (cd) / (ef)

or (ab) ÷ (cd) ÷ (ef)

or    ab
     _cd_
       ef


If you don't use parentheses, you violate left to right associativity, and will get an incorrect answer. It's that simple.

you would then get:

 ab / cd / ef   =     ((((a* b) /c) * d ) / e) * f


or  ab  ÷ cd ÷ ef  =  (((a *b) ÷ c) * d) ÷ e) * f

It yields a different quantity.




That's why, to get the answer of 2, you need parentheses :

 48÷(2(9+3))

[Ron]

(48 ÷ 2) * (9 + 3) = 288

But if you apply this to someone in the workplace, you gotta make it so that it is easy to understand, or you will have a ton of mistakes on it.  Hence, the problem with everyone having a calculator and computer.  Soon, they won't be able to even do basic division or multiplication at all.

[spude]

Only this notation is correct:

_a_  =   _a_
bc         (bc)



However,

a/(bc) =   _a_
               bc

a/bc   =  a(c)
             b

yeilds two different quantities.



If you want to divide a series of terms, ex. ab, cd, ef :

it's written (ab) / (cd) / (ef)

or (ab) ÷ (cd) ÷ (ef)

or    ab
     _cd_
       ef


If you don't use parentheses, you violate left to right associativity, and will get an incorrect answer. It's that simple.

you would then get:

 ab / cd / ef   =     ((((a* b) /c) * d ) / e) * f


or  ab  ÷ cd ÷ ef  =  (((a *b) ÷ c) * d) ÷ e) * f

It yields a different quantity.




That's why, to get the answer of 2, you need parentheses :

 48÷(2(9+3))

congratulations! your cognitive abilities certainly aren't any lesser than the promises and expectations aroused by your screen name...you sir are 100% correct!

[Dr Dutch]

Answer is 2
Haven't read the whole thread though.
By now it'll concern hoe's and gays and your mom I guess.

[jwb]

Only this notation is correct:

_a_  =   _a_
bc         (bc)



However,

a/(bc) =   _a_
               bc

a/bc   =  a(c)
             b

yeilds two different quantities.



If you want to divide a series of terms, ex. ab, cd, ef :

it's written (ab) / (cd) / (ef)

or (ab) ÷ (cd) ÷ (ef)

or    ab
     _cd_
       ef


If you don't use parentheses, you violate left to right associativity, and will get an incorrect answer. It's that simple.

you would then get:

 ab / cd / ef   =     ((((a* b) /c) * d ) / e) * f


or  ab  ÷ cd ÷ ef  =  (((a *b) ÷ c) * d) ÷ e) * f

It yields a different quantity.




That's why, to get the answer of 2, you need parentheses :

 48÷(2(9+3))

As stated numerous times the answer is indeed 2.

48/2(9+3)

The 2 above is a factor of (9+3). The (9+3) are the terms of 2. This statement written in English is:

Forty eight divided by twice the sum of nine plus three.

Also as mentioned before with the shorthand notation of 2(9+3) this can be in fact written many different ways, such as:

2(9+3) = 3(3+1) = (2*9+2*3) = (3*3+3*1) = (2*12) etc etc. The 2 is exclusive to whatever is inside the parenthesis. It is outside only to denote factored form. If I had an expression as:

(5+6+4)(8+9+7) this would imply:

(5*8+5*9+5*7+6*8+6*9+6*7+4*8+4*9+4*7)


With 48 / (5+6+4)(8+9+7) you wouldn't divide out the (5+6+4) by 48 THEN multiply the answer to the second set of parenthesis. The two together denote a single statement. They are 'factored' need to be simplified THEN can be calculated.

So with 48 / 2(9+3) we clearly see this:

Operand = 48
Operator = / <--- which is also a fraction bar
Operand 2(9+3) = (2*9+2*3)=(2*12) = etc etc

2(9+3) simplified using the Distributive property of multiplication over addition shows that 2(9+3) = (2*9+2*3). The two is inside the parenthesis the entire time. Only reason it's outside is for factored form purposes.
Yes that's correct, just because you see the number '2' outside does not mean it's an operand by itself. It's notation for being directly next to the parenthesis means it was factored 'out' and is in fact part of the statement inside the parenthesis which we just saw.

So following algebra rules of simplifying, distributive property, factored form and then FINALLY your order of operation you end up with:

48 / 2(9+3) <---- remember this is one statement. 2 factored out and belongs inside according to Dist. property.

48 / (2*12) or (2*9+2*3) or 24
48 / 24 = 2.

Lastly calculators are meant to work from left to right NO MATTER WHAT. Whatever you put inside it's intention is to work left to right. No corollaries, theorems, principles, properties etc. etc. After a certain level of math you are free to use calculators in tests simply because they have limits. Be very careful when relying on internet calculators.

OR,

This question has certainly created some controversy as to whether or not this is either 2 or 288. There seems to be confusion between the order of operation, distributive property, precedence of multiplication over division etc etc.

Some have cited online calculators, their home calculators or recited the mnemonic PEMDAS.
I'll show you here how you can indeed use those to check your answer.

The main question is does the 48 get divided by 2 and then multiply (9+3) or is the 2(9+3) a single statement and uses a property of distribution?

I provided several variations with proofs but many insisted that Google and other online calculators can never fail us so yes we will use our trusty online calculators to finally close the book on this expression.

We'll do a simple way to check our work using variables.

Set the 2 in the equation to the variable x and rewrite the expression as an equation now:
48 / x(9+3) = 2

Rewriting the equation this way will help us check the answer of 2 in the original problem.

Now let's go ahead and continue to simplify this.
48 / (x*9+x*3) = 2

Which leaves us with 48 / 12x = 2

Now that we made it this far there should be NO QUESTION as to what is going on here. We have now:

48 / 12x = 2

Let's continue to simplify and make things easier for everyone shall we? 48 / 12x, well 48 divides amongst 12 a total of 4 times so we can reduce this fraction to 4 / x. Did we all see how this was done?

So now we are left with 4 / x = 2

With me so far?

Now that you've gotten this far we have a reduced, easy, clean, neat and straightforward equation. Go ahead and type:

4 / x = 2

in any online calculator or solve this with good ole fashioned pencil and paper.

What does everyone end up with?

Does x = 2?

AND IF YOU BELIEVE I WROTE THE ABOVE OR MOST OF WHAT I HAVE POSTED I HAVE SWAMP LAND TO SELL YOU

IT IS INTERESTING HOW IF YOU INPUT 48÷2(9+3) INTO THIS CALCULATOR IT SAYS 2 BUT IF YOU INPUT 48/2(9+3) IT SAYS 288.

http://www.mathway.com/problem.aspx?p=basicmath

GOOGLE FOR PAGES CONTAINING 48÷2(9+3) AND YOU CAN SEE WHY WWIII WILL PROBABLY EVENTUALLY OCCUR FOR A HALF ASSED REASON.

[The_Leafy_Bug]

(48 ÷ 2) * (9 + 3) = 288

But if you apply this to someone in the workplace, you gotta make it so that it is easy to understand, or you will have a ton of mistakes on it.  Hence, the problem with everyone having a calculator and computer.  Soon, they won't be able to even do basic division or multiplication at all.

Place foot in mouth 

[spude]

(48 ÷ 2) * (9 + 3) = 288

But if you apply this to someone in the workplace, you gotta make it so that it is easy to understand, or you will have a ton of mistakes on it.  Hence, the problem with everyone having a calculator and computer.  Soon, they won't be able to even do basic division or multiplication at all.

HELL YEAH! The Boss agrees with me...you sir are smarter than you look!

[sync pulse]

Everyone is confusing programming languages with algebraic notation...

[suckmymuscle]

  Idiots, terms in a mathematical expression that are between paranthesis are resolved before they are included in the rest of the expression. This is Algebra I, which you take in sixth grade. Wtf?!

SUCKMYMUSCLE

[tbombz]

 Idiots, terms in a mathematical expression that are between paranthesis are resolved before they are included in the rest of the expression. This is Algebra I, which you take in sixth grade. Wtf?!

SUCKMYMUSCLE

              

the confusion stems from whether or not you divide 48 by 2 and then mulitply or whethe you divide 48 by the product of 2 and 9+3 genius.

there are two right answers depending on which method you are following. algrebra or computer programming.

[suckmymuscle]

the confusion stems from whether or not you divide 48 by 2 and then mulitply or whethe you divide 48 by the product of 2 and 9+3 genius.

there are two right answers depending on which method you are following. algrebra or computer programming.

  Wow, you are so dumb that you awe me. So now a mathematical expression is interchangeable with computer language? Nice. Let's have the Clay Institute notified and throw away all middle school math books because "tbombz" at Getbig.com message boards thinks that computer programming language has replaced traditonal mathematical notation as the way mathematical expressions are conveyed.

SUCKMYMUSCLE

[The_Leafy_Bug]

 Wow, you are so dumb that you awe me. So now a mathematical expression is interchangeable with computer language? Nice. Let's have the Clay Institute notified and throw away all middle school math books because "tbombz" at Getbig.com message boards thinks that computer programming language has replaced traditonal mathematical notation as the way mathematical expressions are conveyed.

SUCKMYMUSCLE

[NordicNerd]

always parenthesis first

its a divisor of 12 or quotient of

im a calculus PHD

Indeed, so it's 48 divided by 24 ;-).

NN

[HTexan]

What happened to the first 5 math teachers?  I've yet to see their conclusions.

"1"

6th grade

[tbombz]

 Wow, you are so dumb that you awe me. So now a mathematical expression is interchangeable with computer language? Nice. Let's have the Clay Institute notified and throw away all middle school math books because "tbombz" at Getbig.com message boards thinks that computer programming language has replaced traditonal mathematical notation as the way mathematical expressions are conveyed.

SUCKMYMUSCLE

         

your reading comprehensions is severely lacking.

you called everyone idiots because you think they dont know that parenthesis need to be solved first. almost every single person in the thread knows that.

the confusion lies in whether or not you multiply first. or divide first.  

the problem equals 2 if you follow the rules of algebra precisely, pemdas left to right.  

but if you just follow pemdas, then you get two answers. either 2 or 288.

[Primemuscle]

shouldn't be that difficult... however, 65% of stupid meatheads on another board had it wrong... i have high hopes for you fella getbiggers

to make the situation similar than on that another board i'll give you two options...is the right answer 2 or 288?

Not a mathematician here. Solved it on my own; answer 288. Set out to prove my answer. While there are many who maintain the answer is 2 the general consensus is that 288 is the correct answer.

[jwb]

Type the exact question into mathway and see what happens.... 48÷2(9+3)

[Primemuscle]

always parenthesis first

its a divisor of 12 or quotient of

im a calculus PHD

Really? A calculus PHD? I wouldn't have guessed this about you. Where did you get your PHD? To which definition of PHD do you refer? ....pick from the list below.

[Primemuscle]

Falcon,

Is this what you went through for your PhD in calculus?

Prerequisites
 
The Department of Mathematics offers 2 PhD degrees, one in Mathematics and one in Applied Mathematics. Applicants for admission to either PhD program are expected to have preparation comparable to the undergraduate major at Berkeley in Mathematics or in Applied Mathematics. These majors consist of 2 full years of lower-division work (covering calculus, linear algebra, differential equations, and multivariable calculus), followed by 8 one-semester courses including real analysis, complex analysis, abstract algebra, and linear algebra. These eight courses may include some mathematically based courses in other departments, e.g., physics, engineering, computer science, or economics.
 
Applicants for admission are considered by the Department's Graduate Admissions and Appointments Committees. The number of students that can be admitted each year is determined by the Graduate Division and by departmental resources. In making admissions decisions, the Committee considers, among other things, grades in mathematics courses, level of mathematical preparation, letters of recommendation, and GRE scores.
 
Experience has shown that the score on the Mathematics Subject GRE is a partial indicator of preparation for Berkeley's PhD program. A score below the 80th percentile suggests inadequate preparation and must be balanced by other evidence if a favorable admission decision is to be reached.
 
Degree Requirements
 
In outline, to qualify for the PhD in either Mathematics or Applied Mathematics, the candidate must meet the following requirements.
 
1.During the first year in the PhD program:
 
a.take at least 4 courses, 2 or more of which are graduate courses in mathematics;
 

b.and pass the six-hour written Preliminary Examination covering primarily undergraduate material. (The exam is given just before the beginning of each semester, and the student must pass it within their first 3 semesters.)
 


2.Pass a three-hour, oral Qualifying Examination emphasizing, but not exclusively restricted to, the area of specialization. The Qualifying Examination must be attempted within two years of entering the program.
 

3.Complete a seminar, giving a talk of at least one hour duration.
 

4.Pass one language examination in French, German, or Russian.
 

5.Write a dissertation embodying the results of original research and acceptable to a properly constituted dissertation committee.
 

6.Meet the University residence requirement of two years or four semesters.
 

The detailed regulations of the PhD program are as follows:
 
Course Requirements

During the first year in the PhD. program, the student must enroll in at least 4 courses. At least 2 of these must be graduate courses in mathematics. Exceptions can be granted by the student's Graduate Advisor.

Preliminary Examination
 
The Preliminary Examination consists of 6 hours of written work given over a two-day period. Most of the examination covers material, mainly in analysis and algebra, that should be part of a well-prepared student's undergraduate training. The Preliminary Examination is offered twice a year---during the week before classes start in both the Fall and Spring Semesters. A student may repeat the examination twice. A student who does not pass the Preliminary Examination within 13 months of the date of entry into the PhD program will not be permitted to remain in the program past the third semester. In exceptional cases, a fourth try may be granted upon appeal to Committee Omega.
 
Qualifying Examination
 
To arrange for the Qualifying Examination, a student must first settle on an area of concentration, and a prospective Dissertation Supervisor, someone who agrees to supervise the dissertation if the examination is passed. With the aid of the prospective supervisor, the student forms an examination committee of 4 members, at least 2 of which must be members of the Department. The Graduate Division requires that at least one committee member be from outside the Department and that the committee chair be someone other than the Dissertation Supervisor. The syllabus of the examination is to be worked out jointly by the committee and the student, but before final approval it is to be circulated to all faculty members of the appropriate Sections. The Qualifying Examination must cover material falling in at least 3 subject areas and these must be listed on the application to take the examination. Moreover, the material covered must fall within more than one Section of the Department. Sample syllabi can be seen in 910 Evans Hall.
 
Before attempting the Qualifying Examination, the student must pass one language examination. The student must attempt the Qualifying Examination within twenty-five months of entering the PhD program. If a student does not pass on the first attempt, then, on the recommendation of the student's examining committee, and subject to the approval of the Graduate Division, the student may repeat the examination once. The examining committee must be the same, and the re-examination must be held within thirty months of the student's entrance into the PhD program.
 
For a student to pass the Qualifying Examination, at least one identified member of the subject area group must be willing to accept the candidate as a dissertation student, if asked. The student must obtain an official Dissertation Supervisor within one semester after passing the Qualifying Examination or leave the PhD program. For more detailed rules and advice concerning the Qualifying Examination, consult the Graduate Assistant in Room 910 Evans Hall.
 

[jwb]

I think he was quoting somebody else dude.... maybe a higher power

[The_Leafy_Bug]

Not a mathematician here. Solved it on my own; answer 288. Set out to prove my answer. While there are many who maintain the answer is 2 the general consensus is that 288 is the correct answer.

You do realize that by the way you typed it in there it is going to multiply the parenthesis by 1 right? I am horrible at math and always made average grades in math and still know this.