Solve this simple math problem: 48/2(9+3)

[CalBoy]

And now we have resulting confusion because of math semantics. So it's easy to see how you can get both answers, depending on how you approach the problem.

Math is not a field where approaches, opinions or flights of fancy count for anything.

http://www.wolframalpha.com/input/?i=48/2(9+3)


http://www.google.com/#hl=en&sugexp....,cf.osb&fp=70c243f1a9371f44&biw=1040&bih=703

 

[dukebound85]

False. If it was written correctly for you to do order of operations (basic math level) than it should have been written:

48÷2*(9+3)

not 48/2(9+3) which is:

48
_____

2(9+3)

In calculus you don't write equations like 48/x+6(9+45) or anything like that, you write it as

48
_____

x+6(9+45)

I've already pointed out that it is very easy to interpret this either way, and it's just semantics. But the problem was written as I've shown in the second and third example, not the first. What's obvious to you is unfortunately incorrect.

False. It is written correctly as is.

I have never used a % sign since elementary school. / is the same as %. In fact, I never see the % symbol past elementary math teachings or applications.

What's next, are you going to say that "x" is not the same as *?

For one being in calculus, I thought this was obvious

If you want 2, you need those extra (). Otherwise, one is incorrectly applying the OOO

Intended fractions need to be explicitly written with ()'s when writing single line expressions. That is the purpose of ()'s... to give clarity to the expression. If one ever writes code, this is ingrained behavior. Also, if you wanted to evaluate that expression as you suggest (to get 2) in a calculator, how do you type it? With the (). If you type it in verbatim, you get 288.

From Wiki also (if Wolfram, schooling, experience haven't convinced one yet..)

A second way to show division is to use the obelus (or division sign), common in arithmetic, in this manner:

This form is infrequent except in elementary arithmetic.

http://en.wikipedia.org/wiki/Division_(mathematics)

 

[balamw]

http://www.wolframalpha.com/input/?i=48/2(9+3)

Math is not a field where approaches, opinions or flights of fancy count for anything.

http://www.wolframalpha.com/input/?i=48/2(9+3)

Wow. I would have thought for sure that "Camp 2" would have managed to convince Wolfram otherwise in the 8 months since I last posted that link.

B

 

[Heynonny]

It isn't an equation. It isn't a mathematical expression. There is no "answer."

EDITED TO ADD: An "implied" multiplication between the 2 and the open parenthesis? Who would do that? But if you insist that is to be taken as a given then you could claim 288 with some tiny bit of validity. There is no argument at any level of validity that an additional set of parenthesis is implied, i.e. that the answer is 2.

 

[CalBoy]

Wow. I would have thought for sure that "Camp 2" would have managed to convince Wolfram otherwise in the 8 months since I last posted that link.

B

Isn't it amazing?

On the other hand, I have heard that if the expression is entered as 48/2(9+3)-246, Wolfram reduces to "everything."

 

[eric/]

I don't want to quote each individual response and state the same thing over so I'll just reiterate what I've said previously.

When typing it in, in this example, actually using the dividing signs would have been appropriate. Others may see it different, and that's fine, however you're incorrect from an order of operations standpoint as " / " denotes a fraction whereas ÷denotes division.

You can disagree all you want, but you're wrong. And citing Microsoft Excel doesn't really refute what I've said because it's programmed to use / as a dividing symbol. So what?

This is all I have to say. It's a semantics argument, and it should have been written using ÷ in order to not create confusion, but then if it had been this thread wouldn't have been created.

Also, internet credentials count for nothing. IE "I took 4 semesters of calc" etc...

I lol at each one of you trying to justify your answer of 288, when at any time had somebody said that you would have written the equation as follows:

48
__

2(whatever it was)

you don't write down equations as 48/x+2(39+8) and then solve. You're being dishonest.

 

[dukebound85]

Bang. Head. Wall

You would think that how productivity programs are coded would enlighten the proper use, as would be other science based sources provided.

But....I guess not

 

[eric/]

Bang. Head. Wall

Is going to give you a headache.

I understand ÷ isn't used outside of elementary school, but that's irrelevant.

Again I have to reinforce that if somebody verbally presented this equation to you you would have written it as a fraction, not as an OOO problems, unless you're an elementary math student.

 

[wordoflife]

48
____ or 48 ÷ 2(9+3) -> 48 ÷ 2 * 12

2(12)

Question is too ambiguous. We'd never see that in a standardized test due to how poorly it is written. Whenever I see a "/" I think of a fraction though.

 

[dukebound85]

Is going to give you a headache.

I understand ÷ isn't used outside of elementary school, but that's irrelevant.

Again I have to reinforce that if somebody verbally presented this equation to you you would have written it as a fraction, not as an OOO problems, unless you're an elementary math student.

I wouldn't. Those who aren't quite proficient at math would. There really is no debate as there is no ambiguity. The expression is clear and only yields one possible answer.

To get 2, you violate the basic fundamentals of math. Not quite sure how you don't understand this...

/ is the inverse of multiple. That is the definition. Thus an equivalent expression is 48*2^-1*(9+3)

 

[wordoflife]

To get 2, it should read: 48/(2(9+3))

Actually, this true. You can't get 288 by doing 48/(2(9+3))

 

[dukebound85]

Actually, this true. You can't get 288 by doing 48/(2(9+3))

OOO is why. When applied to the original expression, using the same OOO, you get, and can only get, 288

When written with the extra(), you get, and can only get, 2

I have yet to see any application, proof or correct reason why it would ever be 2
http://thecorridortheory.blogspot.com/2011/05/ending-48293-debate.html

Matlab gives 288 as does every other piece of mathematical software

 

[eric/]

I wouldn't. Those who aren't quite proficient at math would. There really is no debate as there is no ambiguity. The expression is clear and only yields one possible answer.

To get 2, you violate the basic fundamentals of math. Not quite sure how you don't understand this...

/ is the inverse of multiple. That is the definition. Thus an equivalent expression is 48*2^-1*(9+3)

Except you're wrong. / is not the inverse of multiple. / denotes a fraction

÷ is the inverse of a multiple

When somebody states the problem verbally, you will always write it as:

48
___

2(9+3)

unless you're an elementary student in which case you will follow the OOO

and you will get 48(where you will actually be using ÷) 2(9+3)

 

[dukebound85]

Except you're wrong. / is not the inverse of multiple. / denotes a fraction

÷ is the inverse of a multiple

When somebody states the problem verbally, you will always write it as:

48
___

2(9+3)

unless you're an elementary student in which case you will follow the OOO

and you will get 48(where you will actually be using ÷) 2(9+3)

You ALWAYS follow the OOO
That is the point

The OOO is not there to use sometimes,and not other times

If you were correct, then every programmer,mathematical software, and mathematician is wrong. That should be telling

I mean c, matlab, excel, calculator, python, wolfram, google, IDL all give 288
Must be a conspiracy on a worldwide scale. Lol

 

[eric/]

You ALWAYS follow the OOO
That is the point

The OOO is not there to use sometimes,and not other times

If you were correct, then every programmer,mathematical software, and mathematician is wrong. That should be telling

I don't know any other way to explain it to you. You're wrong and I know that's hard to admit on the Internet, but it's simply the case. Had the problem been written with the division sign, it would have been a simple OOO. Since it was written as a fraction, you treat it as such. Bottom line. You can refute that, and that's fine as you automatically interpret / as a division sign, which is something typical of somebody that isn't accustomed to calculus or higher level math, but when spoken, or written, it's:

48
___

2(9+3) or whatever it was

if you would like to agree to disagree, as you interpret the problem differently, fine. But otherwise as far as I'm concerned you're simple incorrect.

 

[mobilehaathi]

Except you're wrong. / is not the inverse of multiple. / denotes a fraction

÷ is the inverse of a multiple

÷ and / are exactly the same. To get an answer of 2 you need an extra set of parentheses.

I can't believe I'm actually engaging in this thread.

 

[eric/]

÷ and / are exactly the same. To get an answer of 2 you need an extra set of parentheses.

I can't believe I'm actually engaging in this thread.

No they are not.

÷ denotes division

/ can denote division but usually denotes a fraction

 

[TEG]

÷ and / are exactly the same. To get an answer of 2 you need an extra set of parentheses.

I can't believe I'm actually engaging in this thread.

Exactly. In college we were taught that ÷ and / are the same. If you want it to read as 48 over 2 times 9 plus 3, you either need the extra parens, write it out like I did, or show it as an actual fraction.

TEG

 

[balamw]

I believe that the approach taken at Physics Forums is the only sane way to put an end to this

An issue of mathematical grammar circulating the internet lately has been how to read a mathematical expression like
48÷2(9+3)
that involves a combination of division and implied multiplication.

The standard way to read arithmetic expression (i.e. order of operations) involves dealing with parentheses first, then you do all division and multiplication operations from left to right, then all addition and subtraction operations from left to right.

So, this expression is computed as
48÷2(12)

24(12)

288

It doesn't matter whether or not the multiplication is made explicit, as in
48÷2×(9+3)=288
or if division is represented by a slash, as in
48/2(9+3)=288
all of these variations mean the same thing.

One thing to keep in mind is that not everybody follows the standard. Some people prefer to do implied multiplication before other multiplication and division operations. Some people prefer to do all multiplications before division with /. Some people even prefer to do addition before division with /.

So, when you are reading math from an unfamiliar source, make sure you know what convention they are adopting. And no matter what convention you prefer, you really ought to write things in an unambiguous fashion -- e.g. you should avoid
48/2(9+3)
and instead use the crystal clear
(48/2)(9+3)

If you actually think there is useful disscussion to be had here, please use the "Contact Us" link to have an admin unlock the thread.

B