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mips
April 8th, 2011, 09:50 PM

Legendary_Bibo
April 8th, 2011, 09:51 PM
2

jerenept
April 8th, 2011, 09:51 PM
https://duckduckgo.com/?q=48%C3%B72%289%2B3%29%3D

cgroza
April 8th, 2011, 09:54 PM
2

sisco311
April 8th, 2011, 09:55 PM
48÷2(9+3)=48/2*(9+3)=48/2*12=48*1/2*12=24*12=288

If you don't believe me:
http://www.wolframalpha.com/input/?i=48%C3%B72%289%2B3%29

:)

dh04000
April 8th, 2011, 09:56 PM
Order of Operations

Parentheses
Multiplication/Division
(Anything special case can mess with this order)

48/2(3+9)=2
48/2(12)=2
48/24=2
2=2

Am I doing your math homework for you for or something?

jerenept
April 8th, 2011, 10:00 PM

48÷2(9+3)=
48÷18+6=
2.6667+6=
8.6667
or
8 2/3

EDIT:wait, i shouldn't have expanded the brackets :redface:

matthewbpt
April 8th, 2011, 10:01 PM
Using the standard order of operations, the answer is EDIT after thinking about it some more and reading some of the responses I am revising my answer to 288.

3Miro
April 8th, 2011, 10:01 PM
Order of Operations

Parentheses
Multiplication/Division
(Anything special case can mess with this order)

48/2(3+9)=2
48/2(12)=2
48/24=2
2=2

Am I doing your math homework for you for or something?

+1.

However, a second set of parenthesis should have been written to avoid any possible ambiguity.

MrNatewood
April 8th, 2011, 10:01 PM
In all practical senses that's just a poorly written calculation. It is not explicit weather the 12 is in the numerator or denominator. No actual mathematical or scientific paper would write the calculation that way.

jerenept
April 8th, 2011, 10:06 PM
in all practical senses that's just a poorly written calculation. It is not explicit weather the 12 is in the numerator or denominator. No actual mathematical or scientific paper would write the calculation that way.

12?

oldfred
April 8th, 2011, 10:10 PM
+1 on MrNatewood

I read it left to right on multiplication and division. So I add the implied * and then they are at same level so you work from lfet to right. But you have to have additional parenthesis to make it correct.

48/2*(12)
24*12

alzie
April 8th, 2011, 10:19 PM
I googled it.. they say 288 :roll:

The way I learned math, 42/2(9+3)= would be read 42/(2(9+3))=2.

But we used slates back then :rolleyes:

MrNatewood
April 8th, 2011, 10:24 PM
12?

Well, all will agree that the (9+3) is the first operation to be made. The only real question is weather the resulting 12 will be in the denominator or numerator, for which there is no clear indication.

kevin11951
April 8th, 2011, 10:29 PM
Parentheses
Exponents
Multiplication/Division

x = 48÷2(9+3)

x = 48/2*(12)

x = 24*(12)

x = 288

I just typed "48÷2(9+3)" verbatim into my sci. calculator and got "288". So I am pretty sure I am right.

edit: Python agrees:

kevin@kevin-desktop:~\$ python
Python 2.6.5 (r265:79063, Apr 16 2010, 13:09:56)
[GCC 4.4.3] on linux2
>>> 48/2*(9+3)
288

thenickrulz
April 8th, 2011, 10:31 PM
288

xc3RnbFO8P
April 8th, 2011, 10:35 PM
288

earthpigg
April 8th, 2011, 10:36 PM
yup, 288.

multiplication and division go left-to-right, not "multiplication first" as the old/broken PEMDAS acronym seems to indicate.

many math books and many math teachers do not force students to realize this, and let them use the imperfect PEMDAS model.

i've observed the following from tutoring my fellow college students in various levels of algebra: introductory algebra generally books don't have problems that break PEMDAS, and college-level algebra teachers will sometimes intentionally exclude a few problems from the book's problem sets that do break PEMDAS.

edit: as kevin stated above, it should be taught as

Parentheses
Exponents
Multiplication/Division

Peter Expertly Made Apricots or something (PEMA), and not Please Excuse My Dear Aunt Sally (PEMDAS).

~Plue
April 8th, 2011, 10:37 PM
PEMDAS going left to right
48/2(9+3)
(48/2)*(9+3)
24*12
288

if the answer is not 288 but 2 (as some has indicated previously), then the extra parentheses should be like 48/(2*(9+3)), but since it's not given as so, the order would be from left to right as (48*2)/(9+3).

rudihawk
April 8th, 2011, 10:41 PM
yup, 288.

multiplication and division go left-to-right, not "multiplication first" as the PEMDAS acronym seems to indicate.

most math books and many math teachers do not force students to realize this, and let them use the imperfect PEMDAS model.

That doesn't resolve the discrepancy as to where the (9+3) belongs.

Is it (48/2)*(9+3) or 48/(2*(9+3)).

The question is ambiguous, and would be much clearer if presented in a proper fashion.

hhh
April 8th, 2011, 10:43 PM
http://img339.imageshack.us/img339/2263/32350721.png =288

AlphaLexman
April 8th, 2011, 10:44 PM
The deceiving part of the original equation is there is no multiplication symbol between the '2' and the '('.

Mathematical rules dictate priority as stated previously, so the answer is unequivocally 288.

wojox
April 8th, 2011, 10:44 PM
48÷2(9+3)=48/2*(9+3)=48/2*12=48*1/2*12=24*12=288

If you don't believe me:
http://www.wolframalpha.com/input/?i=48%C3%B72%289%2B3%29

:)

This is what I got using the FOIL method.

beew
April 8th, 2011, 10:44 PM
the problem is that the way it is written is ambiguous. It can be either (48/2)*(9+3) or 48/(2*(9+3)), which are not the same.

(48/2)*(9+3) = 288 whereas 48/(2*(9+3)) = 2.

hhh
April 8th, 2011, 10:45 PM
That doesn't resolve the discrepancy as to where the (9+3) belongs.
Of course it does, the parenthesis is a set, everything outside the parenthesis is a set.

the problem is that the way it is written is ambiguous.
No, it's not.

ilovelinux33467
April 8th, 2011, 10:45 PM
2

LemursDontExist
April 8th, 2011, 10:46 PM
yup, 288.

multiplication and division go left-to-right, not "multiplication first" as the PEMDAS acronym seems to indicate.

most math books and many math teachers do not force students to realize this, and let them use the imperfect PEMDAS model.

Exactly right. You can check the wiki page (http://en.wikipedia.org/wiki/Order_of_operations) - multiplication and division are done together from left to right (division can be thought of as multiplication by the inverse). Juxtaposition is unequivocally implied multiplication.

earthpigg
April 8th, 2011, 10:46 PM
That doesn't resolve the discrepancy as to where the (9+3) belongs.

Is it (48/2)*(9+3) or 48/(2*(9+3)).

The question is ambiguous, and would be much clearer if presented in a proper fashion.

sure it does. zero ambiguity.

Parenthesis
48÷2(9+3) = 48÷2(12)

Exponents
(N/A)

Multiplication/Division left to right
48/2 is leftmost, in this case. 48÷2(12) = 24(12)

Multiplication comes next, in this case.
24(12) = 288.

Done.

edit: person above me has a very smexy understanding.

(division can be thought of as multiplication by the inverse)

examples:

5/2 = 5 * (1/2)

5 * 3 = 5 / (1/3)

equal is to be taken absolutely literally. whatever is on the left of that equal sign is exactly 100% completely identical to whatever is on the right. it may look different, but that is because our writing system for math is imperfect. in my opinion.

that is part of why multiplication and division go left to right, not with one being prioritized over the other. any (yes, any) multiplication expression can be expressed as division, and vice versa. the other part of that 'why' is the arbitrary European language convention of reading left-to-right.

I have no idea how this works for native Arabic speakers (and others), but I do believe that in the case of Arabic - numbers are still written in such a way that an English speaker could read them left-to-right and still correctly read the number after transliterating the symbols to the European number system character-for-character. It might get a bit ugly for non-Arabic speakers once mathematical operators are thrown in there - again, I have no idea.

kevin11951
April 8th, 2011, 10:49 PM
sure it does. zero ambiguity.

Parenthesis
48÷2(9+3) = 48÷2(12)

Exponents
(N/A)

Multiplication/Division left to right
48/2 is leftmost, in this case. 48÷2(12) = 24(12)

Multiplication comes next, in this case.
24(12) = 288.

Done.

+1 exactly...

hhh
April 8th, 2011, 10:49 PM
For those who insist it's ambiguous, and thus maybe 2, it's not...
http://en.wikipedia.org/wiki/Set_%28mathematics%29
http://en.wikipedia.org/wiki/Bracket_%28mathematics%29

beew
April 8th, 2011, 10:50 PM
Of course it does, the parenthesis is a set, everything outside the parenthesis is a set.

No, it's not.

Yes it is. It uses the division sign but without the multiplication so it would be natural to think that 2(9+3) should be performed first (i.e a parenthesis is being suppressed) No one would get confused if it is written as (48/2)(9+3) or (48/2)*(9+3). If a math teacher asks a question like that either answer should be marked as correct. it has nothing to do with conceptual understanding, just ****** notations.

tastygrue
April 8th, 2011, 10:51 PM
42

beew
April 8th, 2011, 10:56 PM
For those who insist it's ambiguous, and thus maybe 2, it's not...
http://en.wikipedia.org/wiki/Set_%28mathematics%29
http://en.wikipedia.org/wiki/Bracket_%28mathematics%29

Look those links have nothing to do with it. I teach University level math, ok? It is a poor way to write it like that. If you cannot communication your question clearly then it is not the fault that others give you confusing answers. The bottom line is none would be confused if the proper parentheses are inserted so the way the question is stated is problematic.

hhh
April 8th, 2011, 10:57 PM
Yes it is. It uses the division sign but without the multiplication so it would be natural to think that 2(9+3) should be performed first (i.e a parenthesis is being suppressed) No one would get confused if it is written as (48/2)(9+3) or (48/2)*(9+3). If a math teacher asks a question like that either answer should be marked as correct. it has nothing to do with conceptual understanding, just ****** notations.
Oy. There is no way to interpret it so that you perform the multiplication first. You would have to specify 48/{2(9+3)}, to create a set and a subset. Crap, unless math has changed in the 30 years since I took Algebra 1.

hhh
April 8th, 2011, 10:59 PM
I teach University level math, ok?
I'd like another professional mathematicians opinion, please.

BTW, this is not a personal attack on you, I just can't believe that math is ambiguous in this case.

earthpigg
April 8th, 2011, 11:00 PM
If a math teacher asks a question like that either answer should be marked as correct. it has nothing to do with conceptual understanding, just ****** notations.

Nonetheless, they don't mark either as correct.

They generally mark "my" way as correct, and any/all other ways as wrong.

and they are the ones with advanced degrees in mathematics. as a humble tutor with no degree, i would be doing my clients a disservice by doing anything other than trusting that the math professors understand math - even when they are in direct conflict with each-other. (crazy, i know.)

edit: ok, you teach university level math. you are kind enough to make things easy on your students. not all of your peers are so kind, i assure you. i've un-taught and/or modified the understanding of PEMDAS many times, but don't always seem to need to for clients to be successful on tests and assigned homework. Your students, i suppose, would be examples of ones that would be OK using the basic model of PEMDAS. So be it - you are the professor, and that is your prerogative. Tutoring your students would be a tad easier on me, and I am ok with that...

beew
April 8th, 2011, 11:02 PM
Oy. There is no way to interpret it so that you perform the multiplication first. You would have to specify 48/{2(9+3)}, to create a set and a subset. Crap, unless math has changed in the 30 years since I took Algebra 1.

What do sets have to do with it??? The brackets here just indicate the ordering of operations. Sets have NOTHING whatsoever to do with it.

Things haven't changed in the last 30 years but your memory certain has. :)

jerenept
April 8th, 2011, 11:02 PM
DuckDuckGo (WolframAlpha) says 288 (https://duckduckgo.com/?q=48%C3%B72%289%2B3%29%3D). Google says 288 (http://www.google.com/search?ie=UTF-8&oe=UTF-8&sourceid=navclient&gfns=1&q=48%C3%B72%289%2B3%29%3D). Python says 288. (http://ubuntuforums.org/showpost.php?p=10654212&postcount=15) My calculator (http://edu.casio.com/products/ntd/fx85es/) says 288.

Case closed. It's 288.

undecim
April 8th, 2011, 11:03 PM
I can never tell in these threads from the incorrect answers who is truly incorrect and who is just trying to start an argument.

hhh
April 8th, 2011, 11:05 PM
What do sets have to do with it??? The brackets here just indicate the ordering of operations. Sets have NOTHING whatsoever to do with it.

Things haven't changed in the last 30 years but your memory certain has. :)
How is (9+12) not defined as a set??? And therefore, isn't the set (42/2) also implied?

-edit- OK, this was flat on wrong on my part, set is not the term I'm looking for, I think it's operation.

lisati
April 8th, 2011, 11:05 PM
(The following has been edited somewhat after reading other contributions.)

As someone else has pointed out, the question looks a bit like a trick question intended to encourage people to recall the proper priorities.

I was taught BOMDAS:

Brackets
Of
Multiplication
Division
Subtraction

If I recall correctly, the teacher made a comment about going left to right for multiplication and division, putting division first if it appears first, similarly with addition and subtraction.

One thing I recall meeting briefly is the use of a full-stop/period/decimal point to represent multiplication.

Beyond these hazy recollections of school days that were a long time ago........ sigh.

42

AlphaLexman
April 8th, 2011, 11:05 PM
Nonetheless, they don't mark either as correct.
I see this as a simple high school level trick question. The ambiguity is inserted on purpose, and the student is forced to recall the order of priority in mathematics.

beew
April 8th, 2011, 11:07 PM
edit: ok, you teach university level math. you are kind enough to make things easy on your students. not all of your peers are so kind, i assure you. i've un-taught PEMDAS many times.

Well I don't think I am unusual in that regard. But I have seen teachers in high schools making students very harshly just because they have little understanding themselves and think that math is about blindly following rules, so if students do things different than they are taught (even just formally) they got marks taken off. I have no time to waste with these people.

beew
April 8th, 2011, 11:08 PM
I see this as a simple high school level trick question. The ambiguity is inserted on purpose, and the student is forced to recall the order of priority in mathematics.

I can see that too. If a teacher has to trap students like that he/she shouldn't be teaching math.

earthpigg
April 8th, 2011, 11:09 PM
I edited my post above this one. Bad habit of mine to do that in rapidly progressing discussions. Please re-read. :)

edit: clearly, i do not tutor spelling.

jerenept
April 8th, 2011, 11:11 PM
The ability of UF-ers to argue over irrelevancies never ceases to amaze me.

earthpigg
April 8th, 2011, 11:13 PM
The ability of UF-ers to argue over irrelevancies never ceases to amaze me.

not at all irrelevant when one derives income from the subject of the discussion at hand. :)

best case result would be for our fellow UF-er that is a math professor to have a chat with his fellow professors at the next big gigantic math professor symposium and achieve consensus that currently does not exist.

hhh
April 8th, 2011, 11:13 PM
So, we're at least all in agreement that the equation should either be written (48/2)(9+12) or 48{2(9+12)}, and whoever gave posed this question in this format is a jerk?

hhh
April 8th, 2011, 11:16 PM
BTW, just in case my edit was missed, I'm not sure if set is the term I'm looking for, as I understand a set is usually something like "the set of even numbers". But I meant as the set of the operation (9+12), which I thought implied that 42/2 was it's own non-ambiguous operation.

-edit- I still don't see how you can come up with 2. 9+3 has to equal 12, that is clear. So the equation become 42 divided by 2 times 12, and I just don't see how you can justify doing 2 times 12 first and then dividing 48 by that result.

earthpigg
April 8th, 2011, 11:17 PM
So, we're at least all in agreement that the equation should either be written (48/2)(9+12) or 48{2(9+12)}, and whoever gave posed this question in this format is a jerk?

nope.

that would be calling the authors of many math books and many professors of mathematics jerks. i see no reason at all to offer such name calling, because i am not qualified to question their expertise.

The only thing I am qualified to do is help some specific students of a specific set of professors succeed on tests written by that specific professor - with no guarantee that the identical strategy will be useful with any future professor or in any real life scenario.

All I can conclude is that over the last several thousand years, no academic consensus has been achieved on the matter. Failure to achieve consensus does not make any person or group of people jerks.

hhh
April 8th, 2011, 11:23 PM
Fine, I withdraw jerk. Sheesh.

-edit- BTW, I didn't mean that mips was a jerk for posting this question.

earthpigg
April 8th, 2011, 11:28 PM
Fine, I withdraw jerk. Sheesh.

I was being a bit obnoxious, I concede. Stemming from my own frustration with the matter. :)

I have seen math books and many college math tests, mid-terms, etc, pose questions nearly identical to the one in the OP.

I have never seen the methodology resulting in an answer of "2" (in this example) be applied in such a way that it is marked as a correct answer.

Either the professor would simply not ask such a question, or s/he would ask such a question and accept 288 as the only correct answer.

Including in this thread, I have never encountered a math professor or a student of a professor that both 1) would ask such a question and 2) would accept 2 as a valid answer.

cheapie
April 8th, 2011, 11:30 PM
I got this for the original question:
` __
2.18

(Yes, the awful font IS required for proper spacing, and ignore the funky apostrophe thingy (I think it's called an accent grave or something), it's also for spacing.)

hhh
April 8th, 2011, 11:35 PM
I was being a bit obnoxious, I concede. Stemming from my own frustration with the matter. :)
I appreciate that, earth! It's a fun debate for me, since I think I'm right. You think the answer is 288 too, so yay! :D

red_Marvin
April 8th, 2011, 11:49 PM
The answer is 288 as division and multiplication has the same precedence.
a*b*c/d/e will be evaluated as ((((a*b)*c)/d)/e)

Hyporeal
April 8th, 2011, 11:50 PM
There is an uncommon practice of regarding juxtaposition as having greater precedence than the symbolic division operator. (Supposedly some calculators use this convention, but I can't verify that.) However, unless told otherwise you should generally assume that juxtaposition is a shorthand for *, and use the usual precedence and ordering rules. When you write a formula, it is a good idea to avoid this issue altogether with judicious use of parentheses and fraction bars.

NightwishFan
April 9th, 2011, 12:19 AM
I saw the thread title and did the math real quick and I found the answer to be 288. At least I got a similar answer to other folks. (I am terrible at math) :D

48/2(9+3)=?
48/2*12=?
24*12=288

? = 288

earthpigg
April 9th, 2011, 12:21 AM
There is an uncommon practice of regarding juxtaposition as having greater precedence than the symbolic division operator. (Supposedly some calculators use this convention, but I can't verify that.)

Lord Almighty.

Such calculators, if they actually exist, should be burned without mercy for their Heresy.

Only the Math Gods are fit to judge such vile creations, and we must send them for judgment immediately.

Who is with me!?

NightwishFan
April 9th, 2011, 12:28 AM
Who is with me!?

_
http://ubuntuforums.org/attachment.php?attachmentid=188514&stc=1&d=1302305304

earthpigg
April 9th, 2011, 12:30 AM
Exactly.

We can call our movement the 288 Crusade.

LowSky
April 9th, 2011, 12:40 AM

Source: 15 years studying MATH & a calculator.

NightwishFan
April 9th, 2011, 12:43 AM

Source: 15 years studying MATH & a calculator.

Well I'll be. :) Good to know.

sprocket10
April 9th, 2011, 12:50 AM
Strictly based on operators:
48÷2(9+3)=
48÷2(12)=
48÷2*12=
24*12=
288

Order of operations:
Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction

Kind of confusing. I hardly ever see the ÷ symbol. I see / much more often.

hhh
April 9th, 2011, 01:00 AM

Oh yeah? Pffffthhthhth ;) (click for full size)

http://img833.imageshack.us/img833/5620/screenshot0408201107544.png (http://img849.imageshack.us/img849/5620/screenshot0408201107544.png)

gcalctool gives the answer 2 as well though.

But these two say 288...
http://www.picalc.com/
http://www.ecalc.com/

-edit- beautiful, this one says "Illegal entry" at the first bracket...
http://www.onlinescientificcalculator.org/

...and the answer here is "Error"...
http://www.mathopenref.com/calculator.html

LowSky
April 9th, 2011, 01:08 AM
Strictly based on operators:
48÷2(9+3)=
48÷2(12)=
48÷2*12=
24*12=
288

Order of operations:
Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction

Kind of confusing. I hardly ever see the ÷ symbol. I see / much more often.

The multiplication of 2(12) is handled first before the division as you must resolve the parenthesis. Yes it is a multiplication in the basic sense but the rule states parenthesis are dealt with before multiplication and division so the answer is 2.
48÷2(9+3)=
48÷2(12)=
48÷24=
=2

hhh
April 9th, 2011, 01:10 AM
Extcalc says 288.

sprocket10
April 9th, 2011, 01:10 AM
I thought that you only perform the operations within the parenthesis. When they are all performed, the parenthesis can be dropped.

pi3.1415926535...
April 9th, 2011, 01:10 AM
If one follows PEMDAS, first;
48÷2(9+3)

48÷2x12

24x12

288

I cannot believe that it is actually quite funny that this has turned into an at least 7 page discussion.

pi3.1415926535...
April 9th, 2011, 01:12 AM
The multiplication of 2(12) is handled first before the division as you must resolve the parenthesis. Yes it is a multiplication in the basic sense but the rule states parenthesis are dealt with before multiplication and division so the answer is 2.
48÷2(9+3)=
48÷2(12)=
48÷24=
=2

As I learnt it, a(b) is exactly the same as a x b or a · b

jerenept
April 9th, 2011, 01:12 AM
If one follows PEMDAS, first;
48÷2(9+3)

48÷2x12

24x12

288

I cannot believe that it is actually quite funny that this has turned into an at least 7 page discussion.

2 pages...

NightwishFan
April 9th, 2011, 01:13 AM
I thought that you only perform the operations within the parenthesis. When they are all performed, the parenthesis can be dropped.

This was my reasoning as well.

hhh
April 9th, 2011, 01:15 AM
I thought that you only perform the operations within the parenthesis. When they are all performed, the parenthesis can be dropped.
Correct. 9+3=12, parenthesis resolved.

-edit- crap...
"Distributive property of multiplication over addition. Early Algebra problem.

The distributive property of multiplication CLEARLY states that the 2(9+3) is an entire statement and CANNOT be broken up. 2(9+3) follows the distributive property which can be rewritten as (2*9+2*3). Let me repeat the 2 outside of the parenthesis follows the distributive property of multiplication and must be factored and simplified before performing any other operations on it. You do NOT compute this expression from left to right until you use Algebra to simplify the statement 2(9+3)."

That is from one of the links in post 2 of this thread.

sprocket10
April 9th, 2011, 01:26 AM
Correct. 9+3=12, parenthesis resolved.

-edit- crap...
"Distributive property of multiplication over addition. Early Algebra problem.

The distributive property of multiplication CLEARLY states that the 2(9+3) is an entire statement and CANNOT be broken up. 2(9+3) follows the distributive property which can be rewritten as (2*9+2*3). Let me repeat the 2 outside of the parenthesis follows the distributive property of multiplication and must be factored and simplified before performing any other operations on it. You do NOT compute this expression from left to right until you use Algebra to simplify the statement 2(9+3)."

That is from one of the links in post 2 of this thread.

I would say that would apply if it was (2(9+3)). In this case I'm not very confident in that....I gotta keep thinking about it :popcorn:

Here's my thinking:
48÷2(9+3)
48÷2*(9+3)
Order of operations:
Parenthesis first
48÷2*(12)
No more operations to perform within parenthesis, so:
48÷2*12
then, multiplication/division (left to right):
24*12
288

Perhaps doing the distributive property mentioned above is done looking specifically at that shortened expression. Order of operations is not being applied to the whole expression: 48÷2(9+3), just the 2(9+3) part. My rule is: if in doubt, throw in more parenthesis or brackets :P

hhh
April 9th, 2011, 01:32 AM
^I think I'm changing my answer to 2 as this statement makes sense...

"Some of you are treating the parenthetical as an actual multiplication symbol. It's not. It serves as a multiplier, but to the number it is attached to. The 2 is attached to the parenthetical, which means you must solve it as part of the first step in the order of operations. This isn't rocket science."

So 2(9+3) can be rewritten as 2*12.
Again from another forum. Apparently this one is making the rounds today.

doorknob60
April 9th, 2011, 01:33 AM
Did it in my head, got 288. The way that's written (order of operations), that should be right.

EDIT: Actually, maybe not. Maybe when there's no symbol between the 2 and the ( then you have to multiply that first maybe unless there was also () around the 48/2. That's why I never use a ÷ sign, always put one thing over the other like a fraction, then it's never an issue :P However, I'll stick with 288, because to me 2(12) is exactly the same as 2*12, so it's 288.

beew
April 9th, 2011, 01:39 AM
^I think I'm changing my answer to 2 as this statement makes sense...

"Some of you are treating the parenthetical as an actual multiplication symbol. It's not. It serves as a multiplier, but to the number it is attached to. The 2 is attached to the parenthetical, which means you must solve it as part of the first step in the order of operations. This isn't rocket science."

So 2(9+3) can be rewritten as 2*12.
Again from another forum. Apparently this one is making the rounds today.

Now you are changing your answer would you agree that the question is ambiguous and a student who answers either 288 or 2 should get full mark?

red_Marvin
April 9th, 2011, 01:51 AM
48/2(9+3)
48/2*(9+3)
48/2*(12)
48/2*12

The multiplication and division are on the same level and has the same precedence, it is then standard to begin from the left.

24*12
288

There is no ambiguity.

Does anybody think that 4-2+(1+1) = 0? That equation is not structurally different from the one above, apart from different operations (but same relative level of precedence) they are the same. The not explicitly written multiplication in the original equation is there since if you have the variables A,B then AB is the same as A*B. Not explicitly writing it out does not change the precedence of it.

undecim
April 9th, 2011, 01:51 AM

Source: 15 years studying MATH & a calculator.

hmm... bug in gcalctool.

Replace the implied multiplication with an explicit * and it works right though.

hhh
April 9th, 2011, 01:52 AM
Now you are changing your answer would you agree that the question is ambiguous and a student who answers either 288 or 2 should get full mark?

beew, I have just finished a little refresher on elementary algebra. 2(9+3) is one term containing 2 factors, 2 and 12. We resolve that term as 24. The equation is what is forty eight divided by twenty four, or 48/24=?

I humbly and unequivocally answer 2. :o

I explained it better than you! :D

I haven't done math in years, that was fun.

-edit- Source and relative passage...
http://www.themathpage.com/alg/algebraic-expressions.htm#parentheses

Problem 2. In the following expression, how many terms are there? And each term has how many factors?

2a + 4ab + 5a(b + c)

There are three terms. 2a is the first term. It has two factors:
2 and a.
4ab is the second term. It has three factors: 4, a, and b.
And 5a(b + c) is all one term. It also has three factors: 5, a, and
(b + c). The parentheses mean that we should treat whatever is enclosed as one number.

If anyone wants to argue 288 any more, give me a source link as I have joined the Dark Side!

3Miro
April 9th, 2011, 01:57 AM
OK, time to pull rank, Ph.D. in Math here.

The expression is an example of bad Math. In USA, the answer can be 2 and 2 only. In USA, any other answer should be marked as wrong.

If you live in another country, then your high-school teacher may be using different scheme. In USA and usually in Bulgaria, multiplication is done before division. Bulgarian math schemes are mostly derived from East European/Russian, and USA methods should be similar to other West-European countries, so I think we can generalize here to Vancouver-Vladivostok scheme, the should would be 2.

However, if you were to write this in some international journal of Math, then the editor/reviewers would have yelled at you for using ambiguous notation. If a person means something other than 2, then they should have specified it in another way. (also, even if they mean 2, they should specify)

In C/C++, the expression evaluates to 288. You should never use ambiguous expressions in C/C++.

"Some computer languages make it hard for you to shoot yourself in the foot, C/C++ makes it easy to shoot yourself in the head!", My Undergraduate Adviser.

Our notation with parenthesis is flawed (regardless of the country), there is the reversed Polish notation and pre-fix notaton that do not require parenthesis. Unfortunately, nobody is using those ... this is another topic.

beew
April 9th, 2011, 01:59 AM
, i assure you. i've un-taught and/or modified the understanding of PEMDAS many times, but don't always seem to need to for clients to be successful on tests and assigned homework. Your students, i suppose, would be examples of ones that would be OK using the basic model of PEMDAS. So be it - you are the professor, and that is your prerogative. Tutoring your students would be a tad easier on me, and I am ok with that...

I don't know what PEMDAS is. all my students are at a level ready to learn calculus at the minimum, or they have no business in my class. For the most part we do proofs. I am not familiar with the schemes they use in elementary school or remedial math(?). in any case, my point is simply that if you have a way to communicate with minimal confusion, use that. There is no point in sticking to an ambiguous way to communicate and citing some obscure rules to justify it while you can easily fix the problem by inserting a pair of brackets.

These rules are just conventions and they can be pretty loose when you get to the higher level because they have nothing to do with the conceptual substance of mathematics. I remember in high school our physics teacher took marks off for people who wrote degree Kelvin with a little circle followed by a K, there shouldn't be the little circle he said. Well he could be correct but what do I care when I read Nobel Laureates in physics writing it with the little circle?

I think these rules are just learning aids and conventions, most of the time we don't adhere to them strictly because we understand the meaning from context (just as no one would present a mathematical proof in first order logic except in logic classes)If in doubt just clarify the question with a pair of brackets and problem solved. The elementary school teachers don't know math and think that it is about reciting rules, that unfortunately turns a lot of people off math for the wrong reasons.

So going back to my original point, all research mathematicians I know would not hesitate to add a pair of brackets if students are confused by a question like this in an exam, or failing to do so, they won't hesitate to give full marks to anyone who answers 2 or 288.

Dennis N
April 9th, 2011, 02:04 AM
288 is correct

written showing all operators clearly:

48/2*(9+3)

= 48/2*12 as grouping symbols have #1 priority

from this point we next evaluate multiplication and division in the order they appear from left to right:

= 24*12
= 288

note:

48/2*(9+3) is not equal to 48/[2*(9+3)] since division is not associative with multiplication. (48/2)*x is not equal to 48/(2*x) where x = 9+3.

LemursDontExist
April 9th, 2011, 02:05 AM
Ok, I did some research - and apparently there isn't yet consensus on the issue. A good examination of the history can be found here (http://jeff560.tripod.com/operation.html), and an interesting discussion here (http://mathforum.org/library/drmath/view/57021.html).

Basically, juxtaposition is sometimes evaluated before division instead of at the same time, though I think the evaluation of juxtaposition at the same time is more standard.

I think that most mathematicians would get an answer of 288 (I have a math degree and have taught math, and that's certainly the answer I came to first), but not *all* mathematicians. In any case, most mathematicians avoid this division operator entirely, so it's sort of a moot point.

hhh
April 9th, 2011, 02:11 AM
Reposting as I heavily edited the original to provide a source...

Now you are changing your answer would you agree that the question is ambiguous and a student who answers either 288 or 2 should get full mark?

beew, I have just finished a little refresher on elementary algebra. 2(9+3) is one term containing 2 factors, 2 and 12. We resolve that term as 24. The equation is what is forty eight divided by twenty four, or 48/24=?

I humbly and unequivocally answer 2. :o

I explained it better than you! :D

I haven't done math in years, that was fun.

-edit- Source and relative passage...
http://www.themathpage.com/alg/algebraic-expressions.htm#parentheses

Problem 2. In the following expression, how many terms are there? And each term has how many factors?

2a + 4ab + 5a(b + c)

There are three terms. 2a is the first term. It has two factors:
2 and a.
4ab is the second term. It has three factors: 4, a, and b.
And 5a(b + c) is all one term. It also has three factors: 5, a, and
(b + c). The parentheses mean that we should treat whatever is enclosed as one number.

It's 2, and that's coming from the guy who insisted it was 288!

Roasted
April 9th, 2011, 02:13 AM
288

pi3.1415926535...
April 9th, 2011, 02:17 AM
This ambiguity is relatively dangerous. Considering that a group of people who have studied math at high levels are disagreeing, would, to me, make the problem at least ambiguous. Imagine if one actually needed to evaluate an expression like this, then it could cause confusion and incorrect answers.

hhh
April 9th, 2011, 02:19 AM
288

This is an algebra equation. 2(9+3) is one term in algebra. Using the distributive property a(b+c)=ab+ac, (2*9)+(2*3)=18+6=24 so

48/24=

2.

http://www.helpalgebra.com/articles/gettingridofparentheses.htm

sprocket10
April 9th, 2011, 02:20 AM
In this case, the whole problem: 48÷2(9+3) is a single term. And each term must follow order of operations.

Pulling out random sources from websites talking about order of operations is causing confusion in this thread

sisco311
April 9th, 2011, 02:23 AM
This is an algebra equation.

Are you sure?

I only see some Hindu-Arabic numerals and some strange symbols... ;)

hhh
April 9th, 2011, 02:24 AM
In this case, the whole problem: 48÷2(9+3) is a single term. Each term must follow order of operations.
No, it's an equation...
48÷2(9+3)=

containing two terms...
48 and 2(9+3)

http://en.wikipedia.org/wiki/Term_%28mathematics%29
http://en.wikipedia.org/wiki/Distributivity

Pretty sure, sisco, but I'm a violinist.

There shouldn't be any ambiguity in an algebraic equation using whole numbers.

I know I'm on solid footing now, I just had to relearn the language.

sprocket10
April 9th, 2011, 02:31 AM
No, it's an equation...
48÷2(9+3)=

containing two terms...
48 and 2(9+3)

http://en.wikipedia.org/wiki/Term_%28mathematics%29
http://en.wikipedia.org/wiki/Distributivity

Pretty sure, sisco, but I'm a violinist.

There shouldn't be any ambiguity in an algebraic equation using whole numbers.

I know I'm on solid footing now, I just had to relearn the language.

It's still one term

You're assuming that the 2(9+3) go together. Why not separate:
48/2*(9+3)

?

Chronon
April 9th, 2011, 02:33 AM
Reposting as I heavily edited the original to provide a source...

beew, I have just finished a little refresher on elementary algebra. 2(9+3) is one term containing 2 factors, 2 and 12. We resolve that term as 24. The equation is what is forty eight divided by twenty four, or 48/24=?

The entire expression is one term. It has factors 48, 1/2, and either 12 or 1/12, depending on how you view this. This strikes me as a trick question intended to either enforce a particular convention or to emphasize the need for unambiguous notation.

48/2*(9+3)=288 while 48/2/(9+3)=2
I consider 48/2(9+3) to be the same as the first expression rather than the second.

kevin11951
April 9th, 2011, 02:33 AM

What is the difference between (4+1x) and (4+1*x)?

hhh
April 9th, 2011, 02:35 AM
Lol, good job Legendary_Bibo!

visitron
April 9th, 2011, 02:37 AM
My first answer was 2 and then after reading posts I wasn't so sure.

Now I'm sticking with 2.

hhh
April 9th, 2011, 02:40 AM
@sprocket and Chronon. Again...
http://en.wikipedia.org/wiki/Term_%28mathematics%29

In elementary mathematics, a term is either a single number or variable, or the product of several numbers or variables separated from another term by a + or - sign in an overall expression. For example, in

3 + 4x + 5yzw

3, 4x, and 5yzw are all terms.

48 ÷ 2x=

where x = (9+12)

-edit- Crap, ÷ isn't a + or - sign, is it? Hmmm...

Telengard C64
April 9th, 2011, 02:43 AM
Me:
48÷2(9+3) =
(48÷2)(9+3) =
(24)(9+3) =
(24)(12) =
24 * 12 =
288

TI-84 Plus:
48÷2(9+3)[ENTER]
288

bc:
48/2*(9+3)
288

SpeedCrunch:
48/2*(9+3)
288

Before we can come to agreement, I think each of us needs to decide on the meaning of the division symbol. When you see 48÷2(9+3), which of these do you think is intended?

48
-- * (9+3)
2

or

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

Consider a somewhat simpler hypothetical problem.

I think most reasonable people would agree with:
6÷3*4 = (6÷3)*4 = (2)*4 = 2*4 = 8

It seems some folks in this thread would prefer:
6÷3*4 = 6÷(3*4) = 6÷(12) = 6÷12 = 1/2 = .5

sprocket10
April 9th, 2011, 02:44 AM
@sprocket and Chronon. Again...
http://en.wikipedia.org/wiki/Term_%28mathematics%29

48 ÷ 2x=

where x = (9+12)

-edit- Crap, ÷ isn't a + or - sign, is it? Hmmm...

Because the (9+3) is multiplied by something, the whole expression is one term. You would simply evaluate the expression in the () first, then continue on calculating the value of the whole term

hhh
April 9th, 2011, 02:47 AM
The entire expression is one term. It has factors 48, 1/2, and either 12 or 1/12, depending on how you view this. This strikes me as a trick question intended to either enforce a particular convention or to emphasize the need for unambiguous notation.

48/2*(9+3)=288 while 48/2/(9+3)=2
I consider 48/2(9+3) to be the same as the first expression rather than the second.
I see what you mean now, which is why I argued so strongly for 288 in the first place. But doesn't writing the division symbol as an obelus make you want to lean towards seperating 48 and 2(9+3) as individual terms?

sprocket10
April 9th, 2011, 02:51 AM
I see what you mean now, which is why I argued so strongly for 288 in the first place. But doesn't writing the division symbol as an obelus make you want to lean towards seperating 48 and 2(9+3) as individual terms?

I think that's what's confusing alot of people. I hardly ever see the ÷ symbol. I use / pretty much exclusively

Tibuda
April 9th, 2011, 02:51 AM
2 or 288, "every number is infinite; there is no difference" said a wise man.

Dennis N
April 9th, 2011, 02:55 AM
Essentially, the original expression becomes 48/2*12 after performing the operation inside the grouping symbols.

Now, what do you do next? Does it matter?

Is (48/2)*12 = 48/(2*12)? NO. The reason is the associative property (changing the grouping) does not apply with different operations (mult and div). And, without grouping symbols, the rule is you must do all multiplications and divisions from left to right in the order that they appear. (And, if there were any, you would then do any additions and subtractions in order from left to right).

So you get 288. The division MUST be done first in this case, and then multiply the result by 12. There is really no ambiguity here.

hhh
April 9th, 2011, 02:58 AM
So I was right!

lulz

Always go with your instincts. Except when you don't.

hhh
April 9th, 2011, 03:04 AM

For example, in mathematics and most computer languages multiplication is done first; in the expression 2 + 3 × 4, the algebraic answer is 14.

How many people who don't refresh their math studies would come up with 14? 20 for the average Joe, left to right, right?

Math. Imprecise. Who'd a thunk it.

3Miro
April 9th, 2011, 03:06 AM
Essentially, the original expression becomes 48/2*12 after performing the operation inside the grouping symbols.

Now, what do you do next? Does it matter?

Is (48/2)*12 = 48/(2*12)? NO. The reason is the associative property (changing the grouping) does not apply with different operations (mult and div). And, without grouping symbols, the rule is you must do all multiplications and divisions from left to right in the order that they appear. (And, if there were any, you would then do any additions and subtractions in order from left to right).

So you get 288. The division MUST be done first in this case, and then multiply the result by 12. There is really no ambiguity here.

No! The rule is PEMDAS Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction. Thus the result should be 2. See earlier post for more details.

GWBouge
April 9th, 2011, 03:11 AM
My first thought was 2, then I read some posts and doubted myself, but I'm back to 2. My calculator says 288, but to quote my first algebra teacher: "A calculator is only as smart as the operator."

Depends on where you're from and who taught you. Strictly following order of operations: 288

BUT ... I consider operators to be separators of terms/items/elements/whatever ... so:

48÷2(9+3) = 2
48÷2*(9+3) = 288

Change 2 to a variable, I'd solve something like this:

48÷x(9+3) = 48/(9x+3x)

Dennis N
April 9th, 2011, 03:21 AM
No! The rule is PEMDAS Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction. Thus the result should be 2. See earlier post for more details.

Check this by using Gnumeric (or any other) spreadsheet:

Enter =48/2*(9+3) into a cell, press enter, and you get 288.

Try it with Qalculate (available in the repos) which also allows use of grouping symbols.

You get 288.

With ONLY Mult. and Div. in your expression and NO grouping, multiplication has no operational priority over division.

Dennis N
April 9th, 2011, 03:34 AM
Googling P.E.D.M.A.S., it says:

P.E.M.D.A.S.
Parenthesis | Exponents | Multiplication | Division | Addition | Subtraction

Perform the operations inside a parenthesis first
Then exponents
Then multiplication and division, from left to right
Then addition and subtraction, from left to right

Notice it says LEFT to RIGHT. The division in this case is done first, since it is on the left.

Using this as stated, the result is 288. No ambiguity.

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

sisco311
April 9th, 2011, 03:41 AM
No! The rule is PEMDAS Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction. Thus the result should be 2. See earlier post for more details.

gsmanners
April 9th, 2011, 03:46 AM
288

If this isn't your answer, you seriously need to go back to middle school and relearn basic arithmetic.

3Miro
April 9th, 2011, 03:52 AM
Check this by using Gnumeric (or any other) spreadsheet:

Enter =48/2*(9+3) into a cell, press enter, and you get 288.

Try it with Qalculate (available in the repos) which also allows use of grouping symbols.

You get 288.

With ONLY Mult. and Div. in your expression and NO grouping, multiplication has no operational priority over division.

SATI test teaches PEMDAS, they wouldn't even let me in this country (USA) if I didn't know this rule. I gave a verbose explanation in an earlier post.

Notation is ambiguous, most places would say 2, but not necessarily all. We need all to switch to prefix or postfix.

wewantutopia
April 9th, 2011, 04:08 AM
So why is it not 2 terms?

48 and 2(9+3) with the 2 being distributed to both the 9 and 3 prior to the addition?

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

48
---------- =
(18+6)

48
-------- = 2 ?
24

hhh
April 9th, 2011, 04:23 AM
So why is it not 2 terms?

In elementary mathematics, a term is either a single number or variable, or the product of several numbers or variables separated from another term by a + or - sign in an overall expression.

-edit- Crap, ÷ isn't a + or - sign, is it? Hmmm...
Without a plus or minus it's still all one term.

hhh
April 9th, 2011, 04:35 AM

Agreed. Several have said it before, when people with advanced math degrees are arguing, and knowing that a simple extra set of brackets would clarify everything, I'm going back to my "it's a jerk question" statement.

The English equivalent might be "He gave her cat food." Needs some clarifying (more than 2 possible meanings, though).

He gave her food to eat that was meant for cats?
He gave a woman food to give to her cat?
He gave a woman's cat some food?

Hyporeal
April 9th, 2011, 04:52 AM
In USA and usually in Bulgaria, multiplication is done before division.

This has not been so in my education. In fact, I do not know of a single calculating tool that uses this rule. PEMDAS is itself ambiguous, as it does not specify where the order is strict. My instruction has taken it as P>E>M=D>A=S. Are you saying that you believe it is P>E>M>D>A>S? Would you say that 10-5+1 is equal to 4? I regard this as a highly unusual convention.

Most of the debate here is about juxtaposition. To remove the question of multiplication before division, consider this expression:

2(1+1)^2

Is this 8 or 16? gcalctool and Wolfram|Alpha disagree.

hhh
April 9th, 2011, 04:56 AM
SATI test teaches PEMDAS, they wouldn't even let me in this country (USA) if I didn't know this rule. I gave a verbose explanation in an earlier post.
Everything I'm reading, University sites, etc... are saying that multiply and divide are interchangeable and when in doubt work left to right...
http://www.studygs.net/pemdas/

...or that there is no consensus...
http://www.math.vanderbilt.edu/~schectex/commerrs/#Operations

Ambiguously written fractions. In certain common situations with fractions, there is a lack of consensus about what order to perform operations in. For instance, does "3/5x" mean "(3/5)x" or "3/(5x)" ?

For this confusion, teachers must share the blame. They certainly mean well -- most math teachers believe that they are following the conventional order of operations. They are not aware that several conventions are widely used, and no one of them is universally accepted. Students may learn one method from one teacher and then go on to another teacher who expects students to follow a different method. Both teacher and student may be unaware of the source of the problem.
Nicely said.

Notation is ambiguous, most places would say 2, but not necessarily all. We need all to switch to prefix or postfix.
Ding ding ding, winner.

sprocket10
April 9th, 2011, 05:03 AM
Concerning:
Please Excuse My Dear Aunt Sally (PEMDAS)

Most people remember this mnemonic, but the disadvantage of the acronym is it cannot convey the fact that M & D carry the SAME priority (along with A & S), carried out in order from left to right.

Gotta remember that caveat, not just look up PEMDAS and apply it :popcorn:

rJ~
April 9th, 2011, 05:10 AM
TL;DR: Use more parentheses to clarify your intention!

Obnoxious internet plague. Apparently it was from some parent disagreeing with the teacher about his child's homework.

1) Stuff inside parentheses first, multiplication second, addition third (Division and subtraction can be rewritten as multiplication and addition respectively). Division can be rewritten as multiplication by the inverse:

48÷2(9+3) =
48/2*(12) =
48*(1/2)*(12) =
48*(1/2)*(12) =
288

Or standard
48/2*(9+3) =
48/2*(12) =
24*(12) =
288

Or if you insist on moving the 2 in first, you have to bring the division operator along. First example should show why.
48/2*(9+3) =
48/2*(12) =
48*(12/2) =
48*(6) =
288

2) Alternatively, if you were taught that implicit multiplication (multiplication by juxtaposition) takes precedence over normal multiplication (which is apparently taught in some places) then
48÷2(9+3) =
48/2(12) =
48/24 =
2

3) Implicit multiplication having precedence shows up on random calculators, Google for the TI-8x series as an example, half of them seem to use one rule other half use the normal rule.

4) About a(b+c)=ab+ac, have you considered (48/2)*(9+3)=(48/2)*9+(48/2)*3? (48/2) is also known as the number 24.

5) PEMDAS:
Didn't know this mnemonic until I saw people using it while discussing this topic. Seems terrible since Google tells me it's supposed to be read P,E,MD,AS but lots of people just go from left to right.

I don't have a PhD in math though so it's all probably horribly wrong ^_^

Cracklepop
April 9th, 2011, 05:10 AM
How is this even a question? There's no ambiguity: 288
If you ever get confused about a question like this you can replace ''/x'' with ''*(1/x)''

48 * (1/2) * 12 = 288
No! The rule is PEMDAS Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction. Thus the result should be 2. See earlier post for more details.

Multiplication has no precedence over division, and addition has no precedence over subtraction.

a/b => a*(1/b)
a-b => a+(-b)

kio_http
April 9th, 2011, 05:21 AM
288

April 9th, 2011, 05:23 AM
How is this even a question? There's no ambiguity: 288
If you ever get confused about a question like this you can replace ''/x'' with ''*(1/x)''

48 * (1/2) * 12 = 288

this.

if you take it for what it is, its 288 without any question.

Division and multiplication goes left to right

its more like

P
E
MD
AS

hhh
April 9th, 2011, 05:25 AM
Concerning:
Please Excuse My Dear Aunt Sally (PEMDAS)

Most people remember this mnemonic, but the disadvantage of the acronym is it cannot convey the fact that M & D carry the SAME priority (along with A & S), carried out in order from left to right.
Except that it's not universal, I'm reading that in Australia and New Zealand they divide first.

How is this even a question? There's no ambiguity: 288
Because it's ambiguous. Again, this guy explains it nicely...
http://www.math.vanderbilt.edu/~schectex/commerrs/#Operations

Ambiguously written fractions. In certain common situations with fractions, there is a lack of consensus about what order to perform operations in. For instance, does "3/5x" mean "(3/5)x" or "3/(5x)" ?

For this confusion, teachers must share the blame. They certainly mean well -- most math teachers believe that they are following the conventional order of operations. They are not aware that several conventions are widely used, and no one of them is universally accepted. Students may learn one method from one teacher and then go on to another teacher who expects students to follow a different method. Both teacher and student may be unaware of the source of the problem.

pi3.1415926535...
April 9th, 2011, 05:27 AM
How is this even a question? There's no ambiguity: 288
If you ever get confused about a question like this you can replace ''/x'' with ''*(1/x)''

48 * (1/2) * 12 = 288

I fully agree with your solution, though I personally think that since it is being discussed by Linux users, especially those having mathematics degrees who are not in agreeance, it is a matter of at least some ambiguity.

Cracklepop
April 9th, 2011, 05:31 AM
Except that it's not universal, I'm reading that in Australia and New Zealand they divide first.
As an Australian, I can assure you we use the universal laws of mathematics. Division is just multiplication by a fraction. Neither has precedence over the other.

Because it's ambiguous. Again, this guy explains it nicely...
http://www.math.vanderbilt.edu/~schectex/commerrs/#OperationsThe student who wrote the equation may have intended to imply that ''a/b(c)'' should be ''a/(b(c))'', but he would have been wrong.

visitron
April 9th, 2011, 05:32 AM
I see part of the problem being the use of ÷ and parenthesis.

or even certain computer programs or calculators.

The division sign ÷ is never used in scientific formulas.

Also ultimately real math is done with a pencil.

For example let's say we are given;

y=1/2x

or what if we are given;

http://www.visitron.net/dp6.png

And then asked what is y when x = 2?

We might get confused.

But if we write;

http://www.visitron.net/dp5.png

Now we know for sure y = 1 when x = 2

So this was an artificial problem the whole confusion is this;

http://www.visitron.net/dp7.png

We would very rarely (if ever) use ÷ in a scientific formula or doing maths beyond arithmetic.

This whole discussion is meaningless if we accept that the problem should simply be;

http://www.visitron.net/dp8.png

In that case we know the answer is 288, however it was written ambiguosly and that was the whole reason behind it.

rJ~
April 9th, 2011, 05:36 AM
New rule: Teachers who say multiplication or division takes precedence over the other should be forced to use Windows ME :evil:

Cracklepop
April 9th, 2011, 05:39 AM
http://www.visitron.net/div2.png

http://www.visitron.net/div3.png

http://www.visitron.net/div1.png

a(b) = a*b = a.b = a.(b) = a*(b) = ab
You can replace any of these with any other, and the equation will not change.

jerenept
April 9th, 2011, 05:41 AM
New rule: Teachers who say multiplication or division takes precedence over the other should be forced to use Windows ME :evil:

or ubuntu 4.04 :P

pi3.1415926535...
April 9th, 2011, 06:05 AM
or ubuntu 4.04 :P

4.04 cannot be as bad as ME, because one could update much of the OS.

hhh
April 9th, 2011, 06:21 AM
As an Australian, I can assure you we use the universal laws of mathematics. Division is just multiplication by a fraction. Neither has precedence over the other.
Yes, I went back to check and the NZ site I have I got dyslexic on. Wikipedia cites Danica McKellar's new mnemonic "Pandas Eat: Mustard on Dumplings, and Apples with Spice." as a way to show that the two are interchangeable, and so should be carried out left to right. Also from Wikipedia...

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).

So I've come full circle, and my gut instinct was correct. First clear what's in the brackets, then do * and / as they appear from left to right.

earthpigg
April 9th, 2011, 06:23 AM
Most of the debate here is about juxtaposition. To remove the question of multiplication before division, consider this expression:

2(1+1)^2

Is this 8 or 16? gcalctool and Wolfram|Alpha disagree.

the one that returns 8 is correct, the other is wrong. i do not consider the question ambiguous.

in fact, questions exactly like that appear in college math books, and there is only considered to be one correct answer to the question.

exactly like the OP's question. this weekend, if i remember, i will bust out the cell camera and take some pictures for everyone.

earthpigg
April 9th, 2011, 06:25 AM
just to clarify:

i do not claim to be an expert in mathematics.

i do claim with confidence, however, that if anyone ever sees that math problem on a math test -- 2 will almost certainly be marked wrong, and 288 will almost certainly be marked right.

maybe all the math professors and math books are wrong, i am not qualified to say.

GWBouge
April 9th, 2011, 06:28 AM
a(b) = a*b = a.b = a.(b) = a*(b) = ab
You can replace any of these with any other, and the equation will not change.

Simply put, yeah, but distributed properties and implications dictate that ab is, more or less, a single entity. So, to throw some letters out there:

ab = (a * b)
a ÷ bc = a ÷ (b * c) != a ÷ b * c

I was taught PEMDAS as well, but my teacher also taught us that multiplication and division were the same, as are addition and subtraction, so that multiplication and division are done in the same pass. And I still come up with 2.

earthpigg
April 9th, 2011, 06:29 AM
i suspect beew is right about one thing, though: it is only the type of question you will see in pre-algebra and early algebra classes. for more advanced classes, there are bigger fish to fry and so additional parenthesis will be in place.

the question is indeed similar to the classic History question:

"When did World War I end?"

(hint: not on November 11, 1918!)

"When did the Korean War end?" (note the proper noun: Korean War.)

(hint: not in the 1950s!)

Neither of these questions are in any way ambigious, but all sorts of history nerds will still get them wrong. Including myself, if I am not paying close attention.

When I initially looked at the OP's question, I got two answers using two approaches and removed the least-cool one via process of elimination resulting in the one answer of 288. I may not be a mathematician, but I sure as hell am a good test taker. :)

jwbrase
April 9th, 2011, 06:44 AM
the problem is that the way it is written is ambiguous. It can be either (48/2)*(9+3) or 48/(2*(9+3)), which are not the same.

(48/2)*(9+3) = 288 whereas 48/(2*(9+3)) = 2.

No, it's not. If you follow the correct order of operations, it will always be (48/2)*(9+3).

Look those links have nothing to do with it. I teach University level math, ok? It is a poor way to write it like that. If you cannot communication your question clearly then it is not the fault that others give you confusing answers. The bottom line is none would be confused if the proper parentheses are inserted so the way the question is stated is problematic.

I will agree that using parentheses to make things extra clear even when the order of operations already gives you the interpretation you want is good for readability and error reduction, but the question *has* been communicated clearly so long as both the writer and the reader know the proper order of operations. The way the question is stated may not be optimal, but neither is it problematic.

If you can give a student that problem at the university level and they interpret it as 48 / (2 * (9 + 3)), then they need to review their order of operations. (Confession, even I got caught by this problem

I can see that too. If a teacher has to trap students like that he/she shouldn't be teaching math.

I absolutely disagree here. The purpose of running problems by students is to figure out if they understood what they were being taught. Part of that is testing for common mislearnings, and that's what trick questions are for. I'm grateful for the trick questions that my teachers threw at me.

Philsoki
April 9th, 2011, 06:49 AM
If it means anything I also got "2". This thread is 14 pages long... What am I missing here? :P

Cracklepop
April 9th, 2011, 06:53 AM
Simply put, yeah, but distributed properties and implications dictate that ab is, more or less, a single entity. So, to throw some letters out there:

ab = (a * b)
a ÷ bc = a ÷ (b * c) != a ÷ b * c

:P Ok, now I see the other side of the argument! I suppose people *do* use 'ab' to imply '(a*b)' rather than 'a*b'.

Still, strictly speaking they shouldn't do that. The correct answer can only be 288 (although I wouldn't mark a student wrong for writing '2=48/2(12)' unless it was code for a program).

The spaces you've put in your equations imply parentheses too: writing 'a/bc' instead removes those implications.

The question is not whether division has precedence over multiplication (neither has precedence, one operator is just the inverse of the other: '/a' => '*(1/a)' ), but rather it's whether 'a(b)' should be interpreted as 'a*(b)' or '(a*(b))'. You can't rely on implications in mathematics though. When there's any confusion you just have to use the strictest interpretation of the rules, so you get 288.

honeybear
April 9th, 2011, 06:56 AM
the one that returns 8 is correct, the other is wrong. i do not consider the question ambiguous.

in fact, questions exactly like that appear in college math books, and there is only considered to be one correct answer to the question.

exactly like the OP's question. this weekend, if i remember, i will bust out the cell camera and take some pictures for everyone.

If they gcalctool and Wolfram|Alpha disagree, please report them a bug immediately.

Because Mathematics never disagree. It is a precise science.
Brackets are always first ;)

GWBouge
April 9th, 2011, 07:06 AM
:P Ok, now I see the other side of the argument! I suppose people *do* use 'ab' to imply '(a*b)' rather than 'a*b'.

Still, strictly speaking they shouldn't do that. The correct answer can only be 288 (although I wouldn't mark a student wrong for writing '2=48/2(12)' unless it was code for a program).

The spaces you've put in your equations imply parentheses too: writing 'a/bc' instead removes the implications from the spaces.

Ah, bit of a habit. Spaces just make it easier on my eyes, lol. And I'm still up in the air about how it should be. A straight, order of operations method makes it a bit simpler, but to me just isn't logical. Supposed someone asked you: "What's ten divided by two pi?"

10÷2pi

What I'd calculate:
10÷(2pi)

To me, regardless of how you group it, that means ten divided by twice that of pi. Though I guess logic and math don't have any business being next to eachother in my head.

Shining Arcanine
April 9th, 2011, 07:10 AM
the problem is that the way it is written is ambiguous. It can be either (48/2)*(9+3) or 48/(2*(9+3)), which are not the same.

(48/2)*(9+3) = 288 whereas 48/(2*(9+3)) = 2.

Look those links have nothing to do with it. I teach University level math, ok? It is a poor way to write it like that. If you cannot communication your question clearly then it is not the fault that others give you confusing answers. The bottom line is none would be confused if the proper parentheses are inserted so the way the question is stated is problematic.

All operations are done either right to left or left to right, which is what permits cascading operations. Otherwise x = 3 * 4 * 5 would be an illegal equation. The numerical system is designed to be done left to right, which disambiguates this. This comes from compiler theory in computer science.

As for teaching university level math, that is not something about which you would want to brag in an open ended fashion. A safe bet with open ended things is to assume the worst case scenario. In the worst case, you teach remedial math classes that cover basic arithmetic at the university level. That is why I say that bragging about teaching university level math in an open ended manner is something that you should not do.

Cracklepop
April 9th, 2011, 07:19 AM
Supposed someone asked you: &quot;What's ten divided by two pi?&quot;

10÷2pi

I think most people would interpret their question as 10/(2pi), not just 10/2pi.
Is this 8 or 16? gcalctool and Wolfram|Alpha disagree.
? They both (correctly) give 8...
All operations are done either right to left or left to right, which is what permits cascading operations. Otherwise x = 3 * 4 * 5 would be an illegal equation. The numerical system is designed to be done left to right, which disambiguates this. This comes from compiler theory in computer science.

Only from a CS point of view ;). Outside of code, it doesn't make any difference what order you have the operators in.

GWBouge
April 9th, 2011, 07:25 AM
I think most people would interpret their question as 10/(2pi), not just 10/2pi.

Right. Had they said "What's ten divided by two times pi?" it'd be different. Relating that to the original problem, what I see is: "What's forty-eight divided by two groups of nine plus three?" Again, Logic vs Math.

Hyporeal
April 9th, 2011, 07:26 AM
? They both (correctly) give 8...

gcalctool 5.32.0 (of Ubuntu 10.10) gives me 2(1+1)^2 = 16. Enter it exactly as written; there is no multiplication sign after the first numeral 2. gcalctool apparently puts juxtaposition (but not the times operator) at higher precedence than exponentiation.

Cracklepop
April 9th, 2011, 07:31 AM
gcalctool 5.32.0 (of Ubuntu 10.10) gives me 2(1+1)^2 = 16. Enter it exactly as written; there is no multiplication sign after the first numeral 2. gcalctool apparently puts juxtaposition (but not the times operator) at higher precedence than exponentiation.

Ah...I have 5.28.2
Right. Had they said &quot;What's ten divided by two times pi?&quot; it'd be different. Relating that to the original problem, what I see is: &quot;What's forty-eight divided by two groups of nine plus three?&quot; Again, Logic vs Math.

You're sneaking in another level of translation! ;)
You've gone written -> spoken -> written, to get the written version you want...
I think you mean mean your own commonsense, or instincts, rather than logic, because logic is as strictly defined as mathematics (although there are different schools/levels of logic).

GWBouge
April 9th, 2011, 07:44 AM
You're sneaking in another level of translation! ;)
You've gone written -> spoken -> written, to get the written version you want...
I think you mean mean your own commonsense, or instincts, rather than logic, because logic is as strictly defined as mathematics (although there are different schools/levels of logic).

Ha! =oD
Well, yes and no. I came up with 2 before I ever put it into words, so I didn't just 'get the version I want', that's just my way of thinking. Looking around the net, about half the people out there share it, so I wouldn't say that the logic is so strictly defined. =o)

Wow this problem has gotten a lot of attention the past couple days. I'm with the others that say the wording/format/syntax/whatever, while valid, is pretty crappy. You'd think something as precise and absolute as mathematics would be taught the same everywhere, lol.

ubuntu27
April 9th, 2011, 07:56 AM
48÷2(9+3)=X
48/2(12)=X
48/24=X
2=X

The answer is 2. First comes brackets or parenthesis. 2 is multiplying the numbers that are inside parenthesis. The parenthesis does not get eliminated when you finish the internal operation when it is multiplying.

A number next to the parenthesis means that it is multiplying.

This is elementary math.

Cracklepop
April 9th, 2011, 08:00 AM
This is elementary math.

What makes you think multiplication has precedence over division? It doesn't (they have equal precedence).
48/2*12 => 48*(1/2)*12

earthpigg
April 9th, 2011, 08:01 AM
A number next to the parenthesis means that it is multiplying.

This is elementary math.

2(12) = 2*12

always and forever. equals means exactly that --- exactly the same thing. if you disagree, then we need to re-evaluate and completely abandon the notion that 2x = 2*x. because i am certain that you do not disagree, that gives us...

48÷2*12

Hyporeal
April 9th, 2011, 08:05 AM
Ah...I have 5.28.2

That version complains of a "malformed expression". I guess it doesn't support juxtaposition at all.

Cracklepop
April 9th, 2011, 08:07 AM
That version complains of a &quot;malformed expression&quot;. I guess it doesn't support juxtaposition at all.

Yeah, it forces you to insert '*'.

ubuntu27
April 9th, 2011, 08:13 AM
What makes you think multiplication has precedence over division? It doesn't (they have equal precedence).
48/2*12 => 48*(1/2)*12

Yes, I know that.

But, parenthesis has precedence over any other operation.

Cracklepop
April 9th, 2011, 08:17 AM
Yes, I know that.

But, parenthesis has precedence over any other operation.

Er, whatever is *inside* the parentheses has precedence.

visitron
April 9th, 2011, 08:21 AM
We would very rarely (if ever) use ÷ in a scientific formula or doing maths beyond arithmetic.

Cracklepop
April 9th, 2011, 08:26 AM
For example let's say we are given;

y=1/2x

or what if we are given;

http://www.visitron.net/dp6.png

And then asked what is y when x = 2?

We might get confused.

True, but I think at the end of the day the people who are confused have to admit they are wrong.
It's just 1*(1/2)*x

earthpigg
April 9th, 2011, 08:27 AM
what tool are you folks using for the pretty expression of math?

do want.

ubuntu27
April 9th, 2011, 08:36 AM
Er, whatever is *inside* the parentheses has precedence.

Yes. But, as I said before, the parenthesis is not *yet* eliminated once we are done with the internal operation (what is inside the parentheses) if there is a number (without a operational symbol) next to it.

Example:

1)
10+2+8(3)
10+2+24
12+24
36

2)
10+3+5(4+2)
10+3+5(6)
10+3+30
13+30
43

Cracklepop
April 9th, 2011, 08:42 AM
Yes. But, as I said before, the parenthesis is not *yet* eliminated once we are done with the internal operation (what is inside the parentheses) if there is a number (without a operational symbol) next to it.

Example:

Parentheses have absolutely no effect on anything outside them.

1/2(3)
1/2*3
1*(1/2)*3
=1.5

ubuntu27
April 9th, 2011, 09:00 AM

Parentheses have absolutely no effect on anything outside them.

1/2(3)
1/2*3
1*(1/2)*3
=1.5

hhh, has a good quote:

Problem 2. In the following expression, how many terms are there? And each term has how many factors?

2a + 4ab + 5a(b + c)

There are three terms. 2a is the first term. It has two factors:
2 and a.
4ab is the second term. It has three factors: 4, a, and b.
And 5a(b + c) is all one term. It also has three factors: 5, a, and
(b + c). The parentheses mean that we should treat whatever is enclosed as one number.

http://www.themathpage.com/alg/algebraic-expressions.htm#parentheses

It's 2, and that's coming from the guy who insisted it was 288!

Cracklepop
April 9th, 2011, 09:03 AM
hhh, has a good quote:

2a + 4ab + 5a(b + c) ==> 2 * a + 4 * a * b + 5 * a * (b + c)

'terms' are operands separated by + or -
'factors' are operands separated by / or *
'(a+b)' is a factor (of '5a(b+c)'), which has two terms: 'a' and 'b'.

hhh interpreted his quote incorrectly.
You can NOT get two different results for an equation by exchanging a(b) with a*(b) or vice versa.

ubuntu27
April 9th, 2011, 09:10 AM
2a + 4ab + 5a(b + c) ==> 2 * a + 4 * a * b + 5 * a * (b + c)

2a + 4ab + 5a(b + c)

2*a + 4(a)(b) + (5a(b+c))

5a(b + c) is one term.

***************

2a + 4ab + 5a(b + c)

2a+4ab+5ab+5ac
2a+9ab+5ac

Cracklepop
April 9th, 2011, 09:15 AM
5a(b + c) is one term.

Absolutely it is. However, you misunderstand the (in)significance of that.
'term' is simply a piece of terminology. It means two operands separated by + or -. It has no significance or bearing on order of precedence.
Apply operators between factors first, then terms. (after parentheses, of course)
48/2(12) has no terms. It has three factors: 48, 0.5, 12
2a+9ab+5ac
You do realise that this is the the same as my answer?

mips
April 9th, 2011, 10:22 AM
I think this may turn into my longest thread ever, it's currently second :lolflag:

My answer is 288 in case anybody is wondering.

3Miro
April 9th, 2011, 11:01 AM
This is turning into a bogus discussion.

We should call the expression itself "wrong" and then move on with our lives.

koenn
April 9th, 2011, 11:04 AM
I think this may turn into my longest thread ever.
excellent thread to wake up with on a Saturday morning

machdohvah
April 9th, 2011, 11:27 AM
According to the rules of Algebra:

48 / 2 ( 9 + 3 ) =
48 / 2 ( 12 ) =
48 / 24 =
2

:D

koenn
April 9th, 2011, 12:35 PM
288

if you format the text a bit more clearly, you get this:
http://users.telenet.be/mydotcom/upub/pics/f1.png

one could be tempted to read the OP as
http://users.telenet.be/mydotcom/upub/pics/f2.png

but that would have to be written (*) as 48 ÷ ( 2 * (9+3) )

(*) rule #0 : add parentheses to avoid ambiguity

@ hhh : try your distributive property on those, and see how they work out

klytu
April 9th, 2011, 12:42 PM
48÷2(9+3)=48/2*(9+3)=48/2*12=48*1/2*12=24*12=288

If you don't believe me:
http://www.wolframalpha.com/input/?i=48%C3%B72%289%2B3%29

:)

Yes, 288 is the correct answer. The people getting an answer of 2 are really calculating 48/2/(9+3) instead of 48/2*(9+3)

features
April 9th, 2011, 12:44 PM
Lets look at it a different way. If we know it equals 288, then lets try and solve it for one of the numbers inside the parentheses:

48 / 2(x + 3) = 288
48 / (2x + 6) = 288 (multiply out the parentheses)
48 = 288(2x + 6) (multiply both sides by 2x + 6)
48 = 596x + 1728 (multiply out the parentheses again)
1680 = 596x (subtract 1728 from both sides)
x = 1680/596 (divide both sides by 596)
x = 105/36 (or 2.819 to 3dp)

which does not equal nine. So the original equation cannot equal 288.

I think thats right :D

rJ~
April 9th, 2011, 12:45 PM
Like Cracklepop said,
When numbers are added or subtracted, they are called terms.
When numbers are multiplied, they are called factors.

1+5a(b+c) = 1 + 5 * a * (b + c)

1+48/2(9+3) = 1 + 48 * 0.5 * (9 + 3)

Both examples have two terms, and three factors for the second term.

5a(b+c) = 5ab + 5ac
48*0.5*(9+3) = 48*0.5*9 + 48*0.5*3

EDIT:
@features

48/2*(x+3) = 288
24*(x+3) = 288
24*(x+3) = 288
24x+72 = 288
24x = 216
x = 9

Unless there are parentheses around 2(x+3) the division operator should be bound to 2.

Interesting how people read it as (48/2)*(9+3) or 48/(2*(9+3)). There was a 60/40 split in another post about this on a seperate forum.

~Plue
April 9th, 2011, 12:58 PM
48 / (2x + 6) = 288 (multiply out the parentheses)

thats exactly what you shouldn't do to find 288

48/2(x+3)=288
48x/2 + 144/2 =288 (multiply the entire (48/2) with the parenthesis)
48x/2 + 72 =288
48x/2=288-72
48x/2=216
48x=432
x=432/48
x=9

edit:// rj~ put it more simply ^

edm1
April 9th, 2011, 01:17 PM
People are only having a problem with this because mathematicians would usually write it in a different manner to avoid this type of confusion. If you think back to some of the first maths lessons you ever had, you divide before you multiply.

48/2(9+3)=48/2*12=(48/2)*12

nidzo732
April 9th, 2011, 01:23 PM
Multiplication and division have the same priority.
48÷2(9+3)=
48÷2*(9+3)=
24*(12)=
24*12=288

features
April 9th, 2011, 01:35 PM
Interesting how people read it as (48/2)*(9+3) or 48/(2*(9+3)). There was a 60/40 split in another post about this on a seperate forum.

I definitely read it as the latter, or more accurately as 48 over (2 * (9 + 3). Perhaps it's to do with the way we're trained here in New Zealand, or my ALU is faulty. I lost control of a negative in my working above as well, so I suspect it's the latter ;)

I maintain that the equation should be written in a clearer fashion though :D

mips
April 9th, 2011, 01:37 PM
I definitely read it as the latter, or more accurately as 48 over (2 * (9 + 3).

Adding brackets changes the equation, why not accept it as written without trying to change it?

tukuyomi
April 9th, 2011, 01:38 PM
48/2(9+3) = 2
48/2*(9+3) = 288
TI-82, Gcalctool says so too
Python does not seem to take implicit multiplication into consideration

mips
April 9th, 2011, 01:43 PM
Python does not seem to take implicit multiplication into consideration

That's the programmer or Python's problem.

features
April 9th, 2011, 01:51 PM
Adding brackets changes the equation, why not accept it as written without trying to change it?

In my head, I didn't change it. That's the way I saw it. Didn't even think there was another way until I saw 288 posted. Perception makes fools of us all at times I suppose :D

April 9th, 2011, 02:42 PM
The rules are very simple, as others have pointed out. Starting with 48 ÷ 2(9 + 3)...

Make assumptions explicit:
48 ÷ 2 x (9 + 3)
Evaluate parentheses first:
48 ÷ 2 x 12
Do higher priority items first. In this case, multiplication and division have equal priority, so no change:
48 ÷ 2 x 12
Where items have equal priority, go left to right (except for unary operators, of which we have none):
( 48 ÷ 2 ) x 12
Parentheses first:
24 x 12
Solve:
288

To those who say it should be 2, it would have been very different if the equation had a + instead of a ÷, because x has a higher priority than +:
48 + 2(9 + 3) = 48 + 2 x (9 + 3) = 48 + 2 x 12 = 48 + 24 = 72

That should make it clear.

ajackson
April 9th, 2011, 02:47 PM
The rules are very simple, as others have pointed out. Starting with 48 ÷ 2(9 + 3)...

Make assumptions explicit:

So which rule of maths did you pluck that one from or did you make it up to justify why you believe the answer is 288?

Edit: the solution is:
48÷2(9+3)
48÷2(12) -- note the brackets has not been completely dealt with yet
48÷24 -- now they have
2

Tigersmind
April 9th, 2011, 02:58 PM
http://www.wolframalpha.com/input/?i=48%C3%B72%289%2B3%29

sprocket10
April 9th, 2011, 03:00 PM
So which rule of maths did you pluck that one from or did you make it up to justify why you believe the answer is 288?

Edit: the solution is:
48÷2(9+3)
48÷2(12) -- note the brackets has not been completely dealt with yet
48÷24 -- now they have
2

Incorrect Sir. The parentheses HAVE been dealt with as ONLY the stuff INSIDE parenthesis has priority. Once you have (12), you have 12:

48÷2(9+3)
48÷2*(12)
48÷2*12
24*12
288

Every time

klytu
April 9th, 2011, 03:08 PM
So which rule of maths did you pluck that one from or did you make it up to justify why you believe the answer is 288?

It's a convention from algebra notation that 2(a+b) is another way of writing 2*(a+b).

Edit: the solution is:
48÷2(9+3)
48÷2(12)
Correct so far ...

-- note the brackets has not been completely dealt with yet
Incorrect. You've already handled the brackets. Which rule of maths did you pluck that one from or did you make it up to justify why you believe the answer is 2. :-)

April 9th, 2011, 03:12 PM
So which rule of maths did you pluck that one from or did you make it up to justify why you believe the answer is 288?
That is the standard that mathematicians use (http://en.wikipedia.org/wiki/Order_of_operations) unless explicitly stated otherwise, known variously (http://en.wikipedia.org/wiki/Order_of_operations#Mnemonics) as BODMAS, BEDMAS and other variations.

48÷2(12) -- note the brackets has not been completely dealt with yet
Yes, they have. The parentheses are not "linked" to the 2; the assumption is a multiplication, giving
48÷2x(12)
which is the same as
48÷2x12
And now, you go left-to-right because the priorities of ÷ and x are equal.

Of course, if you were to explicitly state different rules, then the result would change.

Cracklepop
April 9th, 2011, 03:14 PM
So which rule of maths did you pluck that one from or did you make it up to justify why you believe the answer is 288?

Edit: the solution is:
48÷2(9+3)
48÷2(12) -- note the brackets has not been completely dealt with yet
48÷24 -- now they have
2

As soon as you get to '(12)', the brackets are 'dealt with'. Brackets don't have any effect on anything outside them.

By your reasoning, the following two identical equations would not be equal:

Eqn1: 48/2(12)
Eqn2: 48/2*(12)

...and you would be wrong.

red_Marvin
April 9th, 2011, 03:19 PM
I put the equation into octave matlab and maple and neither octave nor matlab allowed the notation, while maple to my surprise gave the answer 2.

So while I give that there are some ambiguousness in the notation, I still maintain that the answer 288 is the only reasonable interpretation.

ajackson
April 9th, 2011, 03:20 PM
That is the standard that mathematicians use (http://en.wikipedia.org/wiki/Order_of_operations) unless explicitly stated otherwise, known variously (http://en.wikipedia.org/wiki/Order_of_operations#Mnemonics) as BODMAS, BEDMAS and other variations.
Ahem you states Make assumptions explicit, where in your links does it state that?

cgroza
April 9th, 2011, 03:22 PM
Gcalculator says it is 2.

randyklein99
April 9th, 2011, 03:23 PM
Parentheses
Exponents
Multiplication/Division

x = 48÷2(9+3)

x = 48/2*(12)

x = 24*(12)

x = 288

I just typed "48÷2(9+3)" verbatim into my sci. calculator and got "288". So I am pretty sure I am right.

edit: Python agrees:

kevin@kevin-desktop:~\$ python
Python 2.6.5 (r265:79063, Apr 16 2010, 13:09:56)
[GCC 4.4.3] on linux2
>>> 48/2*(9+3)
288

Python3 is slightly different....:D

Python 3.1.2 (release31-maint, Sep 17 2010, 20:34:23)
[GCC 4.4.5] on linux2
>>> 48/2*(9+3)
288.0

April 9th, 2011, 03:24 PM
Ahem you states Make assumptions explicit, where in your links does it state that?
LOL, very good, thank you for calling me out on that.

The convention is that a(b) = a x (b).

Reword what I said as make conventions explicit in order to clarify the situation.

ajackson
April 9th, 2011, 03:24 PM
As soon as you get to '(12)', the brackets are 'dealt with'. Brackets don't have any effect on anything outside them.

By your reasoning, the following two identical equations would not be equal:

Eqn1: 48/2(12)
Eqn2: 48/2*(12)

...and you would be wrong.
Except equation 2 equates to 48/2 * 1(12). so isn't the same equation.

I'll stick with 2 as my answer, I'm sure others will stick with 288.

sprocket10
April 9th, 2011, 03:25 PM
It is shocking how many people immediately resort to a calculator. Calculators are only as smart as their operators. It's more shocking that different calculators give different answers... :confused:

sprocket10
April 9th, 2011, 03:26 PM
Except equation 2 equates to 48/2 * 1(12). so isn't the same equation.

I'll stick with 2 as my answer, I'm sure others will stick with 288.

which is the same as:
48/2*1*12
24*1*12
24*12
288

April 9th, 2011, 03:26 PM
Gcalculator says it is 2.
I don't have gcalculator, but I do have gcalctool. It does not like the implied calculation, so putting "48/2*(9+3)" gives 288.

ajackson
April 9th, 2011, 03:29 PM
LOL, very good, thank you for calling me out on that.

The convention is that a(b) = a x (b).

Reword what I said as make conventions explicit in order to clarify the situation.

Nope sorry that also doesn't seem to be part of BODMAS (or one of it's other names).

Cracklepop
April 9th, 2011, 03:29 PM
Except equation 2 equates to 48/2 * 1(12). so isn't the same equation.

I'll stick with 2 as my answer, I'm sure others will stick with 288.

?! Yes, #2 does equal that, and it's still exactly the same equation...

ajackson
April 9th, 2011, 03:31 PM
which is the same as:
48/2*1*12
24*1*12
24*12
288

And where exactly did I say that 48÷2*1(12) was the same equation as 48÷2(12)?

ajackson
April 9th, 2011, 03:32 PM
?! Yes, #2 does equal that, and it's still exactly the same equation...
If you say so. Might want to look up the inferred uses of ÷ and /

mcduck
April 9th, 2011, 03:33 PM
If you ask me, then the answer is 2 and there's no question about it. I was taught to handle implicit multiplication first, before other multiplications and divisions.

So it's not even a question of if the brackets have been handled or not when you've calculated the 9+3 part (they are), but simply of that if implicit multiplications have higher priority or not. It seems some calculators and math programs do this like I do, others can't handle implicit multiplications at all, and some even threat it in the same order as normal multiplications.

Since there clearly are two commonly used but different ways of dealing with implicit multiplications (+ the possibility of not actually handling it at all) links to Google calculator or output from some random program are not going to prove anything here. However since there are plenty of such links, I'll be happy to tell you that Qalculate handles implicit multiplications, and does it exactly in the order I would do them:
48/2(9+3)=2
48/2*(9+3)=288

So perhaps it might be a good idea to stop calling one answer correct and other wrong and instead just agree that the equations could really use some more parentheses to clear things up... :D

Cracklepop
April 9th, 2011, 03:33 PM
I don't have gcalculator, but I do have gcalctool. It does not like the implied calculation, so putting &quot;48/2*(9+3)&quot; gives 288.

This is a long thread, I can understand there is a lot of tl:dr... ;)

gcalctool in 10.04 gives 288, gcalctool in 10.10 gives 2.

Also, for others: if you get confused about this stuff just replace all divisions with an inverse multiplication, ie. '/x' => '*(1/x)' and you'll never get anything wrong.

So the equation in question would be '48*(1/2)(9+3)', which is of course 288.

April 9th, 2011, 03:34 PM
Except equation 2 equates to 48/2 * 1(12). so isn't the same equation.
Yes it is. Multiplying a number by 1 makes no change.
48/2 * 1(12) = 48/2 * (12) = 48/2(12)
also = 48/2 * 1 * (12)
and = 1 * 48 / (1 * 2) * 1 * (12)

Are you going to tell me that the following is true?
48 / 2 = 48 / (2) = 48 / 1(2)
In fact, 48 / (2) = 48 / 2 = 24
But 48 / 1(2) = 48 / 1 * 2 = 96

sprocket10
April 9th, 2011, 03:40 PM
If you say so. Might want to look up the inferred uses of ÷ and /

People are INFERRING that those symbols mean more than than they really do. If you approach the expression based on order of operations:

48÷2(9+3)=?
48÷2(12)=?
48÷2*12=?
24*12
288

Anything else if ASSUMING that proximity multiplication like 2(12) has priority over regular multiplication, which it does not

ajackson
April 9th, 2011, 03:42 PM
Are you going to tell me that the following is true?
48 / 2 = 48 / (2) = 48 / 1(2)
In fact, 48 / (2) = 48 / 2 = 24
But 48 / 1(2) = 48 / 1 * 2 = 96
And this is why you don't understand what the 2 brigade are saying.

48÷2 = 48÷(2) = 48÷1(2) algebra rules still apply so 48÷a = 48÷(a) = 48÷1(a)

sprocket10
April 9th, 2011, 03:45 PM
And this is why you don't understand what the 2 brigade are saying.

48÷2 = 48÷(2) = 48÷1(2) algebra rules still apply so 48÷a = 48÷(a) = 48÷1(a)

I would do:
48÷2
48÷(1*2)

same thing to me

ajackson
April 9th, 2011, 03:45 PM
People are INFERRING that those symbols mean more than than they really do. If you approach the expression based on order of operations:

48÷2(9+3)=?
48÷2(12)=?
48÷2*12=?
24*12
288

Anything else if ASSUMING that proximity multiplication like 2(12) has priority over regular multiplication, which it does not

All I'll say is algebra.

Would you say that x=48÷2(9+3) and x=48÷a(9+3) are different or the same (assuming a=2 of course)?

mcduck
April 9th, 2011, 03:46 PM
Anything else if ASSUMING that proximity multiplication like 2(12) has priority over regular multiplication, which it does not

It does! It does not! Yes it does! No it doesn't! :D

Clearly, both ways of handling implicit multiplications are common, perhaps depending on where you live, or who happened to teach you, or if you are following some mnemonic which doesn't include implicit multiplications at all and is missing some other special cases as well. ;)

ajackson
April 9th, 2011, 03:47 PM
I would do:
48÷2
48÷(1*2)

same thing to me
Where did I even suggest that those two equations are different?

sprocket10
April 9th, 2011, 03:50 PM
All I'll say is algebra.

Would you say that x=48÷2(9+3) and x=48÷a(9+3) are different or the same (assuming a=2 of course)?

They are the same

x=48÷2(9+3)
x=48÷2*(9+3)
x=48÷2*(12)
x=48÷2*12
x=24*12
x=288

x=48÷a(9+3)
x=48÷a*(9+3)
x=48÷a*(12)
x=48÷a*12
x=48÷2*12 <- sub in a=2
x=24*12
x=288

April 9th, 2011, 03:51 PM
@ajackson: I get where you're coming from.

You are saying that an implied multiplication has a higher priority than an explicit one (which has the same priority as a division).

I have never seen such a rule; but I think that mcduck is correct in saying that it may be location-dependent -- or, perhaps, education-dependent.

Therefore, I think we'll have to say that it equals either 2 or 288, depending on whether you consider implied multiplication to have higher priority than explicit.

Interestingly, this is unique to multiplication, as that is the only implied operator.

alaukikyo
April 9th, 2011, 03:54 PM
48÷2(9+3)=48/2*(9+3)=48/2*12=48*1/2*12=24*12=288

If you don't believe me:
http://www.wolframalpha.com/input/?i=48%C3%B72%289%2B3%29

:)

you should search for http://duckduckgo.com/?q=48%C3%B7%282%289%2B3%29%29%3D

ajackson
April 9th, 2011, 03:55 PM
They are the same

So if x=48÷2(9+3) and x=48÷a(9+3) are the same

x=48÷a(9+3) = x=48÷(9a+3a) following the rules of algebra
x=48÷(18+6)
x=48÷24
x=2

If those equations are the same why is the answer not 288?

a(9+3) can be a(12) as well as (9a+3a), again using the rules of algebra, your method gets two different results depending on how you expand a(9+3) which defies all logic.

Pogeymanz
April 9th, 2011, 03:56 PM
@ajackson: I get where you're coming from.

You are saying that an implied multiplication has a higher priority than an explicit one (which has the same priority as a division).

I have never seen such a rule; but I think that mcduck is correct in saying that it may be location-dependent -- or, perhaps, education-dependent.

Therefore, I think we'll have to say that it equals either 2 or 288, depending on whether you consider implied multiplication to have higher priority than explicit.

Interestingly, this is unique to multiplication, as that is the only implied operator.

This thread blew my mind! I'm a physics grad student and was pretty sure the answer was 2, but I don't know where I ever "learned" that implied multiplication has a higher priority than explicit multiplication, I just felt like it does...

sprocket10
April 9th, 2011, 03:57 PM
@ajackson: I get where you're coming from.

You are saying that an implied multiplication has a higher priority than an explicit one (which has the same priority as a division).

I have never seen such a rule; but I think that mcduck is correct in saying that it may be location-dependent -- or, perhaps, education-dependent.

Therefore, I think we'll have to say that it equals either 2 or 288, depending on whether you consider implied multiplication to have higher priority than explicit.

Interestingly, this is unique to multiplication, as that is the only implied operator.

I just can't understand HOW you can add in additional orders of operations :confused: It seems to me that, if another country teaches a mathematical method allowing these implied operators and their different orders, then wouldn't they also have to basically isolate their math style from the people who do not use implied operators? I don't see how they could work together at all :confused:

ajackson
April 9th, 2011, 04:01 PM
@ajackson: I get where you're coming from.
To be fair the BODMAS stuff (or whichever name you call it) is taught to kids just starting their 11 and onwards maths education so it does miss out some of the more odd things that would just confuse a child that age.

Cracklepop
April 9th, 2011, 04:04 PM
If you ask me, then the answer is 2 and there's no question about it. I was taught to handle implicit multiplication first, before other multiplications and divisions.

You have an extra rule for determining precedence then: a(b) is higher than a*(b).

There are several problems with that:
- I doubt you can find it published (widely accepted by academics)
- if 'a(b)' = 'a*(b)', which it does, then they cannot have different levels of precedence
- exactly how high is the new rule? eg. 2(3)^2= ?

There is no such existing rule. All multiplications have equal precedence.

ajackson
April 9th, 2011, 04:04 PM
This thread blew my mind! I'm a physics grad student and was pretty sure the answer was 2, but I don't know where I ever "learned" that implied multiplication has a higher priority than explicit multiplication, I just felt like it does...

Probably somewhere in your first year (if not in a course you did between school and university).

mcduck
April 9th, 2011, 04:09 PM
You have an extra rule for determining precedence then: a(b) is higher than a*(b).

There are several problems with that:
- I doubt you can find it published (widely accepted by academics)
- if 'a(b)' = 'a*(b)', which it does, then they cannot have different levels of precedence
- exactly how high is the new rule? eg. 2(3)^2= ?

There is no such existing rule. All multiplications have equal precedence.

Like I said, there seems to be two rules about this, and both are commonly used, by mathematicians and programs and calculators. So your answer is more about the "yes it is! no it isn't!" part of my post. :)

Anyway, the fact that this is and extra rule is exactly what I'm saying. And so are many others, including my calculator. And also what I've learned to do in school. (if you are one of those following the PEDMAS mnemonic, that's missing many other things as well so it's only really a useful menmonic for kids, not any actual standard)

sprocket10
April 9th, 2011, 04:09 PM
You have an extra rule for determining precedence then: a(b) is higher than a*(b).

There are several problems with that:
- I doubt you can find it published (widely accepted by academics)
- if 'a(b)' = 'a*(b)', which it does, then they cannot have different levels of precedence
- exactly how high is the new rule? eg. 2(3)^2= ?

There is no such existing rule. All multiplications have equal precedence.

I believe this guy is saying what I believe with better clarity. I wouldn't know HOW to incorporate that rule into the order of operations I learned: PEMDAS

Cracklepop
April 9th, 2011, 04:11 PM
So if x=48÷2(9+3) and x=48÷a(9+3) are the same

1: x=48÷a(9+3) = x=48÷(9a+3a) following the rules of algebra
2: x=48÷(18+6)
3: x=48÷24
4: x=2

If those equations are the same why is the answer not 288?

You went wrong in step 1.
You have gone ahead and implied parentheses: 48÷(a(9+3))
You cannot do this. a(12) is multiplication, and has *the*same* precedence as division. You have decided for yourself that the division here should be lower precedence, which is wrong.

Rewrite all divisions as inverse multiplications to avoid all confusion, and prevent all related mistakes: 48*(1/2)(12)

ajackson
April 9th, 2011, 04:12 PM
- exactly how high is the new rule? eg. 2(3)^2= ?
2(3)^2 = 2(3*3) = 18

Don't forget exponents come before multiplication.

hhh
April 9th, 2011, 04:14 PM
hhh, has a good quote:
<snip>And 5a(b + c) is all one term. It also has three factors: 5, a, and
(b + c). The parentheses mean that we should treat whatever is enclosed as one number.
Now hang on, you missed where I realized my mistake and went back to my original answer of 288. Let's go back to the order of operations...

The standard order of operations, or precedence, is expressed in the following chart.

terms inside brackets
exponents and roots
multiplication and division
And the definition of a term...
In elementary mathematics, a term is either a single number or variable, or the product of several numbers or variables separated from another term by a + or - sign in an overall expression.
Now look at the expression... 48÷2(9+3)=?

Crap, ÷ isn't a + or - sign, is it?
If the equation was 48+2(9+3)=? there would be no argument, the answer would be 72. As there is no +, - or other term in between 2(9+3) and the rest of the equation, sprocket correctly identified this equation as all one term, there is no justification for separating 48 as another term. So after doing the addition, you multiply from left to right, as Cracklepop absolutely correctly wrote...
48*(1/2)*12 =?
...or as Dennis wrote...
48/2*12=?

...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).

http://en.wikipedia.org/wiki/Order_of_operations
http://en.wikipedia.org/wiki/Term_%28mathematics%29

288

ajackson
April 9th, 2011, 04:15 PM
You went wrong in step 1.
You have gone ahead and implied parentheses: 48÷(a(9+3))
You cannot do this. a(12) is multiplication, and has *the*same* precedence as division. You have decided for yourself that the division here should be lower precedence, which is wrong.

Rewrite all divisions like this to avoid all confusion, and prevent all related mistakes: 48*(1/2)(12)
I followed the rules of algebra or are you really arguing that a(9+3) and (9a+3a) are different.

klytu
April 9th, 2011, 04:18 PM
Here's an old post from a math forum that's related:

http://mathforum.org/library/drmath/view/54341.html

Cracklepop
April 9th, 2011, 04:20 PM
Like I said, there seems to be two rules about this, and both are commonly used, by mathematicians and programs and calculators. So your answer is more about the &quot;yes it is! no it isn't!&quot; part of my post. :)

If you could address the three issues I raised then your argument would be stronger...
2(3)^2 = 2(3*3) = 18

Don't forget exponents come before multiplication.

I know what the answer is of course, you only need to follow the rules to never be wrong.
I take it you want to insert the new rule above ''normal'' multiplication, and below exponents?
...
exponents
implied multiplication
other multiplication, and division
...

Yes?

In that case, could you please state for the record that 2(3) does not equal 2*(3).

Cracklepop
April 9th, 2011, 04:22 PM
I followed the rules of algebra or are you really arguing that a(9+3) and (9a+3a) are different.

Not at all. The coefficient in front of the brackets isn't a, it's 48/a (or more specifically: 48/a => 48*(1/a), so the coefficient is (1/a)). You CAN NOT just arbitrarily make division a lower precedence.

ajackson
April 9th, 2011, 04:24 PM
Here's an old post from a math forum that's related:

http://mathforum.org/library/drmath/view/54341.html
That explains it quite well as if written the equation in question would be:

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

The ÷ is often used instead of / to try to avoid the confusion but the better way is to add the implied brackets 48/(2(9+3)).

hhh
April 9th, 2011, 04:25 PM
"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)."

@ajackson, I agree with Cracklepop that you are expressing the contrary interpretation and adding extra brackets that are not implied by the equation.

mips
April 9th, 2011, 04:27 PM
I followed the rules of algebra or are you really arguing that a(9+3) and (9a+3a) are different.

Why don't you just apply the equation from left right where priorities are equal?

Cracklepop
April 9th, 2011, 04:29 PM
That explains it quite well as if written the equation in question would be:

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

The ÷ is often used instead of / to try to avoid the confusion but the better way is to add the implied brackets 48/(2(9+3)).

÷ is 100% exactly, precisely the same as /.
And btw, as an aside, in my last six years of university (CS, maths, physics) I have never once seen the ÷ symbol used.

ajackson
April 9th, 2011, 04:29 PM
in that case, could you please state for the record that 2(3) does not equal 2*(3).
2(3) = 2*(3)

ajackson
April 9th, 2011, 04:31 PM
Why don't you just apply the equation from left right where priorities are equal?
I was trying, and failing it seems, to get across the confusion another way. Good job I'm not a teacher :)

Cracklepop
April 9th, 2011, 04:31 PM
2(3) = 2*(3)

In that case the operators in both must have the same precedence. It is not possible to be otherwise.

If they are equal then any two equations which differ only by replacing one of these two with the other, MUST ALWAYS give the same result.
But that is not always going to happen if they have different precedences.

Eg: x/2(3) equals x/2*(3) ---> you said so yourself in the quote.

fela
April 9th, 2011, 04:34 PM
48 ÷ 2(9 + 3) =
48 ÷ (18 + 6) =
48 ÷ 24 =
2

--- EDIT ---
or is it:

48 ÷ 2(9 + 3) =
24(9 + 3) =
216 + 72 =
288

ajackson
April 9th, 2011, 04:34 PM
In that case the operators in both must have the same precedence. It is not possible to be otherwise.

If they are equal then any two equation which differences only by replacing one of these two with the other MUST give the same result, but that is not always the case if they have different precedences.

Sigh 2(3) = 2*3 = 6, 2*(3) = 2*1*3 = 6.

Edit: funnily enough 2+2+2=2(3)=1+2+3=5+1=7-1=12/2

All those equations are identical.

giddyup306
April 9th, 2011, 04:38 PM
Yeah the answer is 288. Someone might have already said this, but you always do parentheses or brackets first. So 9+3 = 12, then do division. So 12 X24 is 288.

Cracklepop
April 9th, 2011, 04:38 PM
Sigh 2(3) = 2*3 = 6, 2*(3) = 2*1*3 = 6.

Exactly 100% correct.

2(3) = 2*(3)
Therefore:
a(b) = a*(b)
x/a(b) = x/a*(b)

Telengard C64
April 9th, 2011, 04:41 PM
And btw, as an aside, in my last six years of university (CS, maths, physics) I have never once seen the ÷ symbol used.

That is because physicists are smart enough to avoid any potential ambiguity. My college profs rejected the ÷ symbol in my work and insisted that I craft my expressions unambiguously. Depending on the intended meaning, I would have to write one of these.

42
-- x (9+3)
2

or

42
------
2(9+3)

ajackson
April 9th, 2011, 04:42 PM
Exactly 100% correct.

2(3) = 2*(3)
Therefore:
a(b) = a*(b)
x/a(b) = x/a*(b)
Nope.

hhh
April 9th, 2011, 04:43 PM
or is it:

48 ÷ 2(9 + 3) =
24(9 + 3) =
216 + 72 =
288
This. ajackson keeps saying implied brackets, but there are none implied, they have to be explicitly expressed.

sprocket10
April 9th, 2011, 04:44 PM
Nope.

Order of operations doesn't not allow for an elevated priority on implied multiplication.

Cracklepop
April 9th, 2011, 04:45 PM
That is because physicists are smart enough to avoid any potential ambiguity.

I always thought it was just because / was easier ;)
Anyway, and confusion caused is because the equation is displayed in one dimension (which can happen with either symbol) instead of two, not by the symbol itself.

ajackson
April 9th, 2011, 04:46 PM
This. ajackson keeps saying implied brackets, but there are none implied, they have to be explicitly expressed.

The implied brackets surround 2(9+3).

Cracklepop
April 9th, 2011, 04:46 PM
Exactly 100% correct.

2(3) = 2*(3)
Therefore:
a(b) = a*(b)
x/a(b) = x/a*(b)Nope.

Ohhh, ok.....????????????? Now I'm just feeling the laughs coming on...

Care to elaborate?

If 2(3) = 2*(3)
then if c = 2(3), it must follow that c = 2*(3), agreed?

Now tell me what 4/c = ?

ajackson
April 9th, 2011, 04:51 PM
Ohhh, ok.....????????????? Now I'm just feeling the laughs coming on...
I've been at that stage for ages.

Care to elaborate?
x
-
a(b)

vs

x
-b
a

hhh
April 9th, 2011, 04:52 PM
@ajackson...

48÷2(9+3) = 48÷2(12) = 48(1/2)(12) = 288

...but you've convinced yourself that 48 is a separate term.

mips
April 9th, 2011, 04:52 PM
2(3) = 2*(3)
Therefore:
a(b) = a*(b)
x/a(b) = x/a*(b)

This is how I would approach it.
Equal precedence for / and * and apply the equation from left to right.

Cracklepop
April 9th, 2011, 04:55 PM
I've been at that stage for ages.

x
-
a(b)

vs

x
-b
a

Not much of an elaboration...which line of mine do you disagree with, and why?
I have no idea what the second equation you've written is.

Do this for us:
If 2(3) = 2*(3)
then if c = 2(3), it must follow that c = 2*(3), agreed?

Now tell me what 4/c = ? And which one of these does *not* equal 4/c: 4/2(3) or 4/2*(3)?

ajackson
April 9th, 2011, 04:55 PM
Ohhh, ok.....????????????? Now I'm just feeling the laughs coming on...

Care to elaborate?

If 2(3) = 2*(3)
then if c = 2(3), it must follow that c = 2*(3), agreed?

Now tell me what 4/c = ?
By the gods he's got it.

c=6 so 4/c = two thirds.

By pulling the 2(3) out to c you have more or less explicity shown the implied brackets but 4/2(3) is not the same as 4/2*(3) as 4/2*(3) is actually 4/2 * 1*3 or 6.

mips
April 9th, 2011, 04:56 PM
The implied brackets surround 2(9+3).

By doing that you change the equation.

ajackson
April 9th, 2011, 04:58 PM
@ajackson...

48÷2(9+3) = 48÷2(12) = 48(1/2)(12) = 288

...but you've convinced yourself that 48 is a separate term.

If you say so. The answer is still 2.

Cracklepop
April 9th, 2011, 04:59 PM
If 2(3) = 2*(3)
then if c = 2(3), it must follow that c = 2*(3), agreed?

By the gods he's got it.

c=6 so 4/c = two thirds.

By pulling the 2(3) out to c you have more or less explicity shown the implied brackets but 4/2(3) is not the same as 4/2*(3) as 4/2*(3) is actually 4/2 * 1*3 or 6.

Hohoho, not so fast my friend...
Now tell us which of these is NOT equal to 4/c: 4/2(3) or 4/2*(3)?