48/2(9+3)

= 24(9+3)

=216 + 72

= 288

Quoting einsteinboricua (Reply 148): Well, many, if not all math programs, have said that there is a multiplication in it

GIGO.

The equation itself is garbage, hence the confusion.

Doesn't change the fact that 2(9+3) is not the same as 2*(9+3), especially as part of a larger equation. The former implies a parenthetical operation, because it fails to separate the terms with any sort of operator. It's an outmoded way of doing things, and should never appear in a serious math problem, but it is what it is.

Quoting einsteinboricua (Reply 148): If 8 computer programs aren't enough to convince people that this is the answer

8 computer programs that either a) allow garbage like this to be computed using standard rules or b) change the equation according to what it thinks is the right way... which may not be the intent.

Oh, and:

Quoting XaraB (Reply 142): I have had several advanced theoretical mathematics courses during my education

I'll take someone who knows the rules over some program that just does what it's told to do.

48 ÷ 2(9+3) = 2 when written in this form.

And when I type 48 ÷ 2(9+3) into my Casio fx-83, what do I get? 2.

Oh, here is one more i just found on one of the other forums posting this...:

48/2 =/= (9+3) = 12
48÷2≠(9+3)=12

yaaaay! that one agrees!

Or another one

24 & 12, 2 equations?

[Edited 2011-04-14 15:47:27]

Quoting HAWK21M (Reply 150): 48/2(9+3) = 24(9+3) =216 + 72 = 288

48/2(9+3)

=48/(18+6)

=48/24

=2

Quoting Flighty (Reply 140): So, you made a bug report. Did you change the rules of math? No

wait, you do realize you reference mathematica to prove 288 when THEY THEMSELVES already corrected the error on their online plattform?

you can bet your behind that they would not have fixed alpha within 30 minutes from giving out 2 instead of the wrong 288 if they werent sure it was a mistake on the software interpretation of math

Quoting UAL747 (Reply 21): I got two as well. Always do stuff in parentheses first, then multiply, divide. Please Excuse My Dear Aunt Sally

Exactly right!
It's 2 everybody. My mom's best friend is a Calc teacher and was my SAT tutor and she was just over. End of discussion.

Quoting goblin211 (Reply 156):

Well my university's linear algebra professor said it's 288. What about that?    
PEMDAS applies to operations INSIDE the parenthesis. In such case, the answer would actually be 288.

48 ÷ 2(9+3).

48 ÷ 2(12) = 48 ÷ 2 * 12

24 * 12

288.

Cheers,
Cameron

Are my posts invisible or something?

For the thousandth time:

Quoting Longhornmaniac (Reply 157): 2 * 12

and

Quoting Longhornmaniac (Reply 157): 2(12)

Are not the same operation. The first is multiplication, the second involves multiplication but is really distribution.

Quoting Maverick623 (Reply 158): Are not the same operation. The first is multiplication, the second involves multiplication but is really distribution.

Sorry you think that.

Quoting zak (Reply 155): you can bet your behind that they would not have fixed alpha within 30 minutes from giving out 2 instead of the wrong 288 if they werent sure it was a mistake on the software interpretation of math

This is some misunderstanding on your part.

Quoting Flighty (Reply 159): Sorry you think that.

It's basic math. If you don't get it, that's not my problem.

Quoting Flighty (Reply 159): This is some misunderstanding on your part.

Now you're trolling.

Quoting einsteinboricua (Reply 102): Quoting CXfirst (Reply 101):48÷x(9+3) = 288 48/x*(9+3)=288 48/x=288/12 48/x=24 1/x=24/48 1/x=1/2 Inverse x=2

No. I did not say 48/x*(9+3) = 288

48/x(9+3) = 288
48/x(12) = 288 --> when x is coupled with the parenthesis, it is treated as one term, as it is one term.
48/12x = 288
12x = 48/288
x = 48/3456
x = (somebody calculate that for me, I don't have a calculator here)

-CXfirst

Quoting einsteinboricua (Reply 97): To be 100000000% sure, I'll ask a math professor and an engineering professor at my campus.

Don't be too confident they'll know better than some of the people on this thread...

Quoting StuckInCA (Reply 162): Don't be too confident they'll know better than some of the people on this thread...

I count 5 math professors who have said the best answer is 2. So you can knock it off with the patronizing.

Quoting CXfirst (Reply 161): x = (somebody calculate that for me, I don't have a calculator here)

.0138888888...

Quoting Maverick623 (Reply 163): I count 5 math professors who have said the best answer is 2. So you can knock it off with the patronizing.

Ease up there. I said long ago that I think the best answer is 2. I'm suggesting that there may be some math or engineering professors participating in this thread. I, myself, have several engineering degrees. Also, professors aren't always right.

Quoting Maverick623 (Reply 160): Now you're trolling.

So when I state my inarguable results about a 9th grade math topic (backed up with all major math environments, just for overkill) i am trolling.... And when people just make stuff up, they are not trolling, i am the bad guy. I see.

Quoting Longhornmaniac (Reply 157): 48 ÷ 2(12) = 48 ÷ 2 * 12 24 * 12 288.

There is no possible way to deny the above. It is 100% correct.

Keeping in mind that division and multiplication are binary operators, the expression 48 ÷ 2 * 12 should evaluate to 288.

I'll note that in spoken language, however, it is not at all clear whether it should be 288 or 2.

Well in my math class I was always told when solving equations to write out the details following the rule or multiplication division etc. then solve the equation.
So 2(9+3) would become 2(12) would become 2 * 12 it is a progression of an original equation not a change so

Quoting Maverick623 (Reply 158): For the thousandth time: Quoting Longhornmaniac (Reply 157): 2 * 12 and Quoting Longhornmaniac (Reply 157): 2(12) Are not the same operation.

For original euqations yes, but if one is attempting to solve an equation they naturally follow.

Now since this is an aviation forum and we have such a disagreement, why is it so hard for Airbus supporters to understand the doubt folks have on computerized a/c, imagine if the software uses a formula like this to determine whether to flar the a/c for landing on a hard touch down or initiate a go around, the difference between 2 and 288 is pretty huge.  

Quoting par13del (Reply 167): imagine if the software uses a formula like this to determine whether to flar the a/c for landing on a hard touch down or initiate a go around, the difference between 2 and 288 is pretty huge.

The software is using it's own order of operations. The result intended will be the way the software programmer writes the code.

Quoting ManuCH (Reply 126): If I enter 48/2*(9+3) it says 288. If I enter 48/2(9+3) it says 2. So there seems to be a difference if there's a multiplication sign before the brackets or not.

Quoting casinterest (Reply 168): The software is using it's own order of operations. The result intended will be the way the software programmer writes the code.

Seems so. Lotus will not accept the equation without the * between the 2 and the ( so "2*(" works and "2(" does not.

Quoting Baroque (Reply 169): Seems so. Lotus will not accept the equation without the * between the 2 and the ( so "2*(" works and "2(" does not.

So the folks who wrote Lotus use their rules which differ from the folks who wrote Excel and the folks who did some brands of calculators, it's a good thing math is such a pure science, its either right or its wrong as per the rules, which is what I learned from this thread, once we all use the same rule, we all get the same result.

I really enjoyed this thread, really.

I got 2.

48 divided by 2 (distribute to the 9 and the 3) so you get 18+6=24....48 divided by 24 equals 2.

Quoting par13del (Reply 170): Quoting Baroque (Reply 169): Seems so. Lotus will not accept the equation without the * between the 2 and the ( so "2*(" works and "2(" does not. So the folks who wrote Lotus use their rules which differ from the folks who wrote Excel and the folks who did some brands of calculators,

It does seem that early Excel versions were mostly copied from Lotus, or maybe some other spreadsheet I don't know about, but there are differences. However both Lotus and Excel demand the "*" before the "(". The demand from Excel to put the "=" before the argument always has me puzzled.

48 ÷ 2(9+3)=?

Wow. Lots of discussion (sadly)!

Sorry if I missed something in the 170+ arguments. I just despise discussions of how many angels can dance on the head of a pin. I can handle heated discussions over how and when zero is in fact not nothing but this?!

PEDMAS or as I learned it back in the dark ages: BODMAS:

Cut to the chase:

Open the Brackets (or parentheses) FIRST:

2(x+y) = [ (2 * x) + (2 * y) ] = [ 2x + 2y ] ∴ [ 2(9+3) ] = [ (2*9) + (2*3) ] = [ (18 + 6) ] = [ 24 ]

THEN:

[ 48 ÷ 24 ] or [ 48 / 24 ]

EQUALS

2

This left-to-right priority stuff is, a) for wimps; b) dexterocentric; and c) computercentric- irrespective of software.

Mathematics has no priority on left-right position in the equation. As for Excel- it's a spreadsheet software written by the same programmers as Windows 95, not an algebraic notation. Need one say more? As with all programs- and it too has been recently posted- GIGO.

Today's computer programmers are obsessed with making round pegs fit into square holes. For them it's in how you program software to do what you want it to do. To get the answer you want, you have to create the formula in a way for the program to understand clearly what it is intended to do.

This is why high-school math teachers used to expect you to do all the work without a calculator- so you'd actually understand what you are wanting to accomplish.

Hence:

Quoting Longhornmaniac (Reply 157): 48 ÷ 2(9+3). 48 ÷ 2(12) = 48 ÷ 2 * 12 24 * 12 288.

Here is the kink in this fallacious argument:

Distributive or multiplactive or not (Thanks for that, Maverick!), for it to be 288, the parentheses would have to read like this:

(48 ÷ 2) (9 + 3) -OR- (9 + 3) (48 ÷ 2) ...It doesn't matter the order...

= (24) * (12)

= 288

Quoting Maverick623 (Reply 151): I'll take someone who knows the rules over some program that just does what it's told to do.

  

Quoting czbbflier (Reply 173): Open the Brackets (or parentheses) FIRST:

It's "terms inside the brackets first".

Well, what a fascinating discussion.


I've just typed it in as it comes on a Casio CFX9850G and get 2.
Exactly the same in a Casio FX83 and get 288.

I have to say at first glance I worked it out as 2.

Quoting cgnnrw (Reply 124): also he played a lot of "pocket pool".

My 8th grade science teacher had all the same qualities. I had completely forgotten about that.

Quoting Maverick623 (Reply 144): For a second, I thought you meant "Sorry, the answer is 288, people".

Great. Now we have to have a long, drawn out thread on diagraming sentences? 

Quoting HAWK21M (Reply 150): 48/2(9+3) = 24(9+3) =216 + 72 = 288

Yes, except parenthases come first. Making it:

48/2(9+3)

=48/2x12

=48/24

=2

Quoting Maverick623 (Reply 158):

You're not invisible, but I don't agree with you.

If you search google for "mathematical order of operations," every single link on the first page says to carry out the expression INSIDE the parenthesis. None of them identify distribution across a parenthesis as a part of the parenthetical priority. In such case, 2(12) and 2 * (12) are exactly the same thing.

Quoting czbbflier (Reply 173): but this?!

You'd do well to go back and actually read the thread, because it's obvious there's something you're missing if you think it's so cut and dry.

Quoting czbbflier (Reply 173): Open the Brackets (or parentheses) FIRST

  

Quoting czbbflier (Reply 173): This left-to-right priority stuff is

accepted mathematical process.

Quoting czbbflier (Reply 173): Mathematics has no priority on left-right position in the equation.

  

Quoting czbbflier (Reply 173): for it to be 288, the parentheses would have to read like this:

Actually, no. If the answer were 2, than the parenthesis should read 48 ÷ (2 (9+3)).

Quoting Ralphski (Reply 174): It's "terms inside the brackets first".

  

Quoting Maverick623 (Reply 151): I'll take someone who knows the rules over some program that just does what it's told to do.

Just goes to show that it's not that cut and dry, if a professor with a PhD in linear algebra says it's 288.

Cheers,
Cameron

Quoting seb146 (Reply 176): =48/2x12 =48/24

That does not equal 2.

You solve left to right, and division and multiplication have the same priority.

48/2 = 24

24*12= 288.

Cheers,
Cameron

Quoting czbbflier (Reply 173): This left-to-right priority stuff is, a) for wimps; b) dexterocentric; and c) computercentric- irrespective of software. Mathematics has no priority on left-right position in the equation.

   Yes it does. How else do programs solve equations? Unless you put terms inside parentheses (giving them further priority), the order to solve operations like multiplication and division which have equal priority, like addition and subtraction do afterwards, goes from left to right.

Please solve this equation then:

15 ÷ 3 × 4, where "÷" denotes division as in 15/3*4

If your answer is 15/12, you're wrong. Division comes first followed by multiplication. Left to right. If you want it to be 15/12, use parenthesis so that the multiplication goes first. Therefore, you would have 15/(3*4). Otherwise, the answer is 20.

Solve this other equation:
10-3+2

If your answer is 5, you are mistaken since addition and subtraction have the same priority. How to distinguish which one to do first? left to right. That's standard in ALL math operations. Ask ANY professor. The answer here is 9.

The left->right rule applies only when you encounter operations of equal priority. Parentheses are solved inside out. Once done, the term reverts to a number with the operation that precedes it if any. (EG. 3(3+4)=3(12)=3*12)

And by the way, those wimps, dexterocentric, computercentricirrespective of software people (you know that kinda describes engineers...computer people...those that work with software) are the very people that have enabled you to travel via airplane, designed your house, your car, and everything else that you have. I would treat them with more respect.

And here is why I always disliked math classes in school (even though I am actually quite proficient with math): All this discussion over a meaningless equation, the answer to which will solve nothing.

IF it mattered, then I can stand it, then I can do the problem (I understand the reason for math class and that it is trying to teach processes but that fact that the answers seldom actually lead to any real work just made it boring to me). In reality, in "real life", mathematics has an automatic double check mechanism that determines if the calculations and answer are correct: Does it match, does it agree with what is actually observed (figuring out the speed/acceleration of a falling apple, does it match the real world observations)?

Otherwise there is no use for mathematics, it is supposed to be backed up by something that has an effect in the real world (whether the dimensions of a black hole or the balance of an account after a few years) all math should be able to be tested.

I realize that there are many things that math is used for in place of being able to do or observe it in reality (testing nuclear blasts or that black hole or determining how many quarks can dance on the head of a pin...) but then it is simply up to the person presenting/using the equation to be clear on what they are intending. All the discussion in this thread is very interesting (I have read the thread since it started) but in truth the arguments are meaningless as the answer does not mean anything. If it meant something then we would know exactly how the answer should read and it would mean something. Math may have rules but the most important thing is that the solution, however it is reached, is accurate.

Just my 2 cents (or should that be 288 cents?   )

Tugg

Quoting einsteinboricua (Reply 179): Yes it does.

Upon further research, I do see that I am incorrect on this point.

Quoting einsteinboricua (Reply 179): 15 ÷ 3 × 4, where "÷" denotes division as in 15/3*4 If your answer is 15/12, you're wrong. Division comes first followed by multiplication.

However, here I am not wrong. If division comes first (and indeed it does) then let's play fractions:

15
-------------
3 x 4

= 15
-------------
12

∴ 15/12


Hence:

48 ÷ 2(9+3)

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

= 48
---------
2(12)

= 48
--------
24

= 2

Quoting einsteinboricua (Reply 179): And by the way, those wimps, dexterocentric, computercentricirrespective of software people (you know that kinda describes engineers...computer people...those that work with software) are the very people that have enabled you to travel via airplane, designed your house, your car, and everything else that you have. I would treat them with more respect.

I see I came across a bit strong but it was actually meant to be a strain to humour to lighten the note. I see it backfired. My apologies.

Quoting tugger (Reply 180): And here is why I always disliked math classes in school (even though I am actually quite proficient with math): All this discussion over a meaningless equation, the answer to which will solve nothing.

Alas, Tugg, on your point about whether these sorts of exercies are useful, I must say I agree with you.

However, these sorts of 'pedantic' discussions in mathematics amount to the same as the discussions we wordsmiths have from time to time. Mathematics is a 'language' of sorts and sometimes there is a need to sort out convention and grammar. There is a surprising amount of imprecision in mathematics (this thread notwithstanding) and hence there are whole journals devoted to such ponderings.

Fractals, a purely mathematical function rendered into graphic form, are some of the most beautiful works of 'art' I know.

Also, your observation regarding mathematics and 'the real world' assumes that there is only inductive reasoning at play. However, where mathematics becomes really handy is in deductive reasoning. You have a mathematical hypothesis... now go out there and disprove it. That is the key to progress. It is exactly that which upset my engineer friend, Einsteinboricua a couple of entries back.

As an example, you're driving a truck. F=MV² is a very important formula. Sure, it was derived through observation in the distant past but it goes through your head every time you start down on a 12% grade with a full load. But there was a long period of time where that was first figured out by trial and error. An awful lot of error.

New generations have to learn this stuff and so as it gets passed on, it gets redefined. Conventions change as we can see here. And then suddenly, one day someone invents cold fusion. And everything changes again.

Quoting czbbflier (Reply 181): However, here I am not wrong. If division comes first (and indeed it does) then let's play fractions:

Your game of fractions would be correct if it were based on the following: 15 ÷ (3 x 4). But division is a binary operation! If you have 15 ÷ 3 x 4 then you can't consider the 4 until after you divide 15 by 3.

I think you are translating from the spoken form: "Fifteen divided by 3 times 4" where the correct translation from English into mathematics would be 15 ÷ (3 x 4), because this is what is usually meant (though admittedly this depends on the context and hence still is not entirely clear.)

If you are still not convinced then do the calculation using reverse Polish notation (also known as postfix notation): 15,3,÷,4,x = 20. Note that postfix notation does not need brackets.

[Edited 2011-04-19 22:37:30]

Quoting einsteinboricua (Reply 179): Division comes first followed by multiplication. Left to right.

Hopefully you mean "in our equation" the division is first, so you do it first. Generally, division and multiplication have the same priority (despite "BEDMAS"; note the similar "PEMDAS"). The convention (correct way) to evaluate that is left to right, as you said.

But I guess, if people draw an actual fraction (which wasn't true here), the typical rules of operation don't apply.


For example, we will grant that conventionally:

2
-----
3+5

evaluates to 0.25, if you encounter a fraction like that. Does this mean 2 / 3 + 5 = 0.25, of course no.

Quoting czbbflier (Reply 181): If division comes first (and indeed it does) then let's play fractions:

   Nop. Division and multiplication have equal order of precedence.

Quoting Flighty (Reply 183): Hopefully you mean "in our equation" the division is first, so you do it first.

I meant in the equation I wrote first, though in this thread's scenario, division does indeed go first.

48 / 2 (9+3) = ?

The problem is incomplete; should be EITHER;

48 / [2*(9+3)]= 2

or

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

The point of consternation is the lack of appropriate use of brackets in the right places, but standard mathematical convention dictates the first interpretation and answer of 2 should be the correct one.

This is what google thinks;

http://tinyurl.com/3r3fzxw

http://tinyurl.com/6ffynxe

[Edited 2011-04-24 11:02:39]

whoever started this must be very clever. I love how after 100 posts after the suspect equation is pointed out posters are still arguing whether the answer is 2 or 288.

Just for the record before opening the thread I treated it as such:


48/2(9+3)

Brackets get done first

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

When their isn't a sign separating the brackets it automatically becomes multiplication

so 48/2(12) = 48/2*12

48/2 = 24

24*12 = 288

It appears Apple is also confused about the equation just for kicks I tried several of their programs and got different answers

Spotlight says 2
Numbers says the answer is Red Triangle (Syntax Error)
Calculator (Mac) won't let me put in the bracket after 48/2
Calulator (iphone) says the answer is FOUR!!!!!! (i'd like to know how it got that)


The correct answer is... NOTHING is because the equation isn't set out properly

the correct way would be either

48/2*(9+3)=288

or

48/2/(9+3)=2


or more simply

24*12=288 or 24/12=2

Quoting vhqpa (Reply 187): Numbers says the answer is Red Triangle (Syntax Error)

The only correct answer.   

Quoting vhqpa (Reply 187): Calulator (iphone) says the answer is FOUR!!!!!!

Must be something you're doing wrong.

Quoting vhqpa (Reply 187): Calulator (iphone) says the answer is FOUR!!!!!! (i'd like to know how it got that)

I knew I had seen the answer somewhere else. Apparently, neither the iPhone calculators nor Calculator in Windows accept parentheses without an operation preceding it. What the programs did was the following:

48/2(9+3)

Since there isn't a sign between the 2 and (, both programs assumed the 2 is misplaced, so it's taken out. You're left with

48/(9+3)=48/12=4

It seems my calculator and my girlfriend have conflicting issues with each other.

By inputting 48/2(9+3) into my TI-83 Graphing Calculator, I came up with 288.

HOWEVER, the girlfriend suggested using BEDMAS, the 'order of operations' acronym for Brackets, Exponents, Division, Multiplication, Addition, Subtraction.

By doing so:

48 ÷ 2(9+3)
48 ÷ 2(12)
48 ÷ 24
Answer: 2

Girlfriend: One. Calculator: Zero.

Nik

Quoting czbbflier (Reply 181):

Quoting casinterest (Reply 168):

Quoting Maverick623 (Reply 158):

I repeat my stand from my previous post: All these guys has it correct, and the correct answer is 2.

All the arguments about how computers, calculators or software solve problems are moot, as they only do what they are told to do. Exact and theoretical mathematics are all solvable by hand if using the correct definitions and rules, and in mathematical science this "ancient" manual way of solving equations has precedence over "quick-and-dirty", sometimes elaborate, solutions by machines.

Take a pen and paper, write down the equation EXACTLY as given in the original post, use the rule provided by Casinterest in post #118 before anything else, and the only possible answer is TWO. End of story, double lines under the answer.

The rule a(b+c) = ab + ac is one of the basic arithmetic rules for multiplication provided by Dr. Karl Rottman in his university level mathematics rulebook "Matematische Formelsammlung" (I only have a Norwegian translation, so cannot provide the correct ISBN). The context a(b+c) defines "a" as a prefix to the parenthesis, and should not be treated separately.