48÷2(9+3) = ??

What is the answer?

  • 2

    Votes: 261 51.2%
  • 288

    Votes: 249 48.8%

  • Total voters
    510

Readers

Professional
No, it makes no sense. Being on the right side of 48/2 does not mean the (9+3) is in the numerator. But being to the right of / means the (9+3) is in the denominator, just like the 2 being on the right side of the / means it's in the denominator. There's no difference between the 2 and the (9+3) as far as which side of the / they are located.
OK, how are u going to do a/b/c/d then?
 

Hidious

Professional
purplemath.com



I wouldn't exactly take what she says as fact. As she herself states that she's never seen proof either way. Things getting even more blurry now.

She does have a M.A. in Math from Washington Univ at least.
How is it even possible to prove a convention?

I use this convention and i agree with her that it is the general consensus amongst mathematicians. I you don't use it, fine, but at least acknowledge that it exists, it's justified, and many people use it. You are not right or wrong.
 

Readers

Professional
And do you understand that 2011 is newer than 2009 and contains fixes to bugs and errors that were found in the 2009 version?
Can you really read or not?

did u see the a and b next to 2011 or 2009?

2011a is the most up to date version, just released this month.

2011b is not even out yet, won't be out for another half year.

Ag, do u understand what happens when u used an unfinsihed software?
 

BreakPoint

Bionic Poster
For the first point, it does not, else how u going to do a/b/c/d ????

Second, yes, but only when it's INSIDE the (), not next to it.
Easy, the answer is ad/cb. That is, the ad is the numerator and the cb is the denominator. Basic math.
 

BreakPoint

Bionic Poster
Can you really read or not?

did u see the a and b next to 2011 or 2009?

2011a is the most up to date version, just released this month.

2011b is not even out yet, won't be out for another half year.

Ag, do u understand what happens when u used an unfinsihed software?
Do you know what happens when you used old software full of errors they didn't know about when they made that version but now realize and have fixed with the new software?
 

Readers

Professional
btw the basic math for a/b/c/d = a/(b*c*d).

And no, don't argue with me on this, just do a/b/c and a/b/c/d/e and see how u do it, you might come to see the light.
 

subz

Rookie
Post deleted...

I am not commenting anymore...its not a big big issue. In ALL scientific journals, no one writes equations in this format: in them every equation is written in a very explicit manner with paranthesis and natural (hand written) format etc ...
 
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Steady Eddy

Legend
Numerator? Denominator? This is all on one line. Simply replace "÷2" with (1/2), (that's what the "÷" sign tells you to do, use the reciprocal of the number immediately after it.) Now it's all about multiplying! (Because dividing is simply multiplying by reciprocals.) We have (48 )(1/2)(12) which = 288.

Now order doesn't make a difference.

(48 )(12)(1/2) = (576)(1/2) = 288
(1/2)(48 )(12) = (24)(12) = 288
(1/2)(12)(48 ) = (6)(48 ) = 288
(12)(48 )(1/2) (576)(1/2) = 288
(12)(1/2)(48 ) = (6)(48 ) = 288

The "÷" is a bad symbol IMO. When you see one, use it to convert the number in question into a factor. Now, order won't matter, and you can hardly go wrong! :)
 

sureshs

Bionic Poster
btw the basic math for a/b/c/d = a/(b*c*d).

And no, don't argue with me on this, just do a/b/c and a/b/c/d/e and see how u do it, you might come to see the light.
That is correct. a/b/c/d = ((a/b)/c)/d = (a/(bc))/d = a/(bcd)

BP again followed the convention used in science and engineering books, where the first and third /s are regarded to be in the first and second lines of a fraction:

a/b
----
c/d

and he gets ad/(bc)

Notice he does not even write it this way but as ad/bc which is actually

((ad)/b)c = adc/b.
 

Steady Eddy

Legend
That is correct. a/b/c/d = ((a/b)/c)/d = (a/(bc))/d = a/(bcd)
Like I said, if we think of it as a÷b÷c÷d and using the rule to replace "÷" with reciprocals, we get a(1/b)(1/c)(1/d) which equals a/(bcd). That's also how my TI-84 treated it.

BP again followed the convention used in science and engineering books, where the first and third /s are regarded to be in the first and second lines of a fraction:

a/b
----
c/d

and he gets ad/(bc)

Notice he does not even write it this way but as ad/bc which is actually

((ad)/b)c = adc/b.
I think that's it. Treat it like BP says if you're in an engineering class. But if you're in a beginning class that teaches the decimal system, they believe it's another answer. If I ever wind up in an advanced engineering course, (an unlikely event), I'll now be better prepared.
 

Hidious

Professional
Now order doesn't make a difference.

(48 )(12)(1/2) = (576)(1/2) = 288
(1/2)(48 )(12) = (24)(12) = 288
(1/2)(12)(48 ) = (6)(48 ) = 288
(12)(48 )(1/2) (576)(1/2) = 288
(12)(1/2)(48 ) = (6)(48 ) = 288
Oh man, all these example are irrelevant... This is about wheter implicit multiplication has priority over division. In all of those examples you changed /2 to 1/2 which means for you, it doesn't. Many people think like that, priority of operation should be left to right.

Many other people, like me, prioritize implicit multiplication. I can also give you a bunch of useless examples:

(48 )/2(12)=(48 )(1/24)=(1/24)(48 )=(48 )/(12)2=2
 

olliess

Semi-Pro
So it seems that the various positions expressed in this thread can be fully summarized:

1. Some people have seen both conventions and admit the possibility that other people use a different convention from themselves

2. Other people have seen only one convention but admit the possibility that other people use a different convention from themselves

3. Still other people have only seen one convention and do not admit the possibility that the alternative exists at all

4. A few people aren't sure about the conventions but can produce pictures from their calculators * ** ***

* Some people's calculators give different results

** Other people claim, incorrectly, that the expression can be evaluated in Maple and/or Matlab as specified

*** Still others seem to think that the version number of Matlab is more important than the doctoring that was applied to the picture

5. Certain individuals feel that their status as tutors, teachers, engineers, elite college students/graduates, math test whizzes, etc., renders any and all of the above arguments pointless -- they are just plain RIGHT!!!


Does this basically cover the bases? :D


P.S.: You guys go on having fun with this, I'm going to go play tennis now. :p
 
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cucio

Legend
BP again followed the convention used in science and engineering books, where the first and third /s are regarded to be in the first and second lines of a fraction:

a/b
----
c/d

and he gets ad/(bc)
I am an engineer, and I have never ever read a scientific or engineering book that used that contrived convention. Then again, I don't recall any such book that used single-line math expressions, so that is not saying much. But that method of prioritizing operators is ridiculously complex, and won't scale well for more sophisticated expressions.
 

ramseszerg

Professional
Does anyone know where this 48÷2(9+3) thing originated? I noticed the korean sites are talking about this too, it's really weird.
 

Claudius

Professional
That's because you 2ers are flat out wrong.

48/2(9+3) does not mean that the 9+3 is in the denominator.

48/2(9+3) = 48 x ½(9 + 3) = 288
 

Talker

Hall of Fame
Another way: :shock:

a = 48
b = 2
c = (9 + 3) = 12

So we have a/b*c

Left to right, use brackets for all but the last one to be clear.
(a/b)*c = (48/2)*12 = 131.

:(
 
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movdqa

Talk Tennis Guru
Amazing thread. I have a Masters of Science in Computer Science and you can find the rules for expression evaluation in Kernighan and Ritchie. It's 288.

If you want to be sure, just enter the expression in the Google box in your browser if you have one. Others can just go to the Google search engine and type it in there.
 

Photoshop

Professional
Does anyone know where this 48÷2(9+3) thing originated? I noticed the korean sites are talking about this too, it's really weird.
I think it was first posted on reddit. and that's really weird Koreans are arguing over such simple arithmetic problem. Even 8 year olds know 288 is the only acceptable answer over there.
 

pyrokid

Hall of Fame
Another way: :shock:

a = 48
b = 2
c = (9 + 3) = 12

So we have a/b*c

Left to right, use brackets for all but the last one to be clear.
(a/b)*c = (48/2)*12 = 131.

:(
Yes! it all makes sense now. But I think you made a typo, it should be 131i. When you multiply by using an asterisk it changes the possible solutions from real to imaginary. That's why most people just use a dot, but it's okay, not everyone knows this. Just warning you for next time.
 

jonnythan

Professional
BreakPoint knows better than Wolfram, Google, Texas Instruments, Matlab, Maple, Mathematica, licensed engineers, and math PhDs because he went to a good college and studied engineering.

End of thread.
 
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krz

Professional
BreakPoint knows better than Wolfram, Google, Texas Instruments, Matlab, Maple, Mathematica, licensed engineers, and math PhDs because he went to a good college and studied engineering.

End of thread.
aw but I went to a good college and studied engineering... well applied math which is basically the same and economics. I wish I knew better.

:(

btw
 
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aceX

Hall of Fame
It makes me laugh people taking pictures of calculators and software like they don't have a brain. Work it out yourself.



/thread
 

diredesire

Adjunct Moderator
It makes me laugh people taking pictures of calculators and software like they don't have a brain. Work it out yourself.



/thread
You realize this isn't even remotely close to the issue being discussed, right? It's obvious that these two are solved correctly, the math isn't the issue, its the convention. The /thread thing is getting kind of old. Posting this graphic doesn't solve anything or convince anyone :confused: :confused:

The problem is hardly people having trouble working it out ;)
 

aceX

Hall of Fame
You realize this isn't even remotely close to the issue being discussed, right? It's obvious that these two are solved correctly, the math isn't the issue, its the convention. The /thread thing is getting kind of old. Posting this graphic doesn't solve anything or convince anyone :confused: :confused:

The problem is hardly people having trouble working it out ;)
Hi there,

The discussion is about which of the following equations 48÷2(9+3) is:



Every single person who says the answer is 288 is saying that 48÷2(9+3) is the second equation, not the first.

Cheers,
aceX
 

Steady Eddy

Legend
Maybe I've got to change my mind? Here's what my research has turned up.

16 ÷ 2[8 – 3(4 – 2)] + 1
= 16 ÷ 2[8 – 3(2)] + 1
= 16 ÷ 2[8 – 6] + 1
= 16 ÷ 2[2] + 1 (**)
= 16 ÷ 4 + 1
= 4 + 1
= 5

The confusing part in the above calculation is how "16 divided by 2[2] + 1" (in the line marked with the double-star) becomes "16 divided by 4 + 1", instead of "8 times by 2 + 1". That's because, even though multiplication and division are at the same level (so the left-to-right rule should apply), parentheses outrank division, so the first 2 goes with the [2], rather than with the "16 divided by". That is, multiplication that is indicated by placement against parentheses (or brackets, etc) is "stronger" than "regular" multiplication. Typesetting the entire problem in a graphing calculator verifies this hierarchy:
http://www.purplemath.com/modules/orderops2.htm
 

Steady Eddy

Legend
I think I should add this from the website?



Note that different software will process this differently; even different models of Texas Instruments graphing calculators will process this differently. In cases of ambiguity, be very careful of your parentheses, and make your meaning clear. The general consensus among math people is that "multiplication by juxtaposition" (that is, multiplying by just putting things next to each other, rather than using the "×" sign) indicates that the juxtaposed values must be multiplied together before processing other operations. But not all software is programmed this way, and sometimes teachers view things differently. If in doubt, ask!

(And please do not send me an e-mail either asking for or else proffering a definitive verdict on this issue. As far as I know, there is no such final verdict. And telling me to do this your way will not solve the issue!)
Should we call it a draw and enjoy what's left of the weekend? :)
 

Readers

Professional
That is correct. a/b/c/d = ((a/b)/c)/d = (a/(bc))/d = a/(bcd)

BP again followed the convention used in science and engineering books, where the first and third /s are regarded to be in the first and second lines of a fraction:

a/b
----
c/d

and he gets ad/(bc)

Notice he does not even write it this way but as ad/bc which is actually

((ad)/b)c = adc/b.
I get what you are saying, but....
how does his logic reacts to a/b/c/d/e ??? there is 5 of them now, you don't have a middle one, which 2 or 3 are you going to put on top?
 

dr325i

G.O.A.T.
Just as I thought. You can't explain your assertions. Why? Because they are erroneous. You can't explain why the (9+3) or 12 HAS TO BE in the numerator.
Read your signature!

I explained to you 25 times, the problem is you cannot understand it (my 9-yo can just fine). I posted the same problem at my 9-yo class. 50/50 got it right, for the same reason as people on this board. Then I explained them and reminded them what they learned in the last 1.5 years. ALL of them got the correct answer in the next 15 minutes...

12 HAS to be in the numerator because of the math rules, left to right. The division part only applies to the next term unless there re parenthesis.

Under ABSOLUTELY NO circumstances 12 is below the line here. Simply shown:
a*b = ab (ALWAYS!)
c/ab = c/a*b = (c/a)*b = c*b/a = cb/a ALWAYS!
 

dr325i

G.O.A.T.
Oh man, all these example are irrelevant... This is about wheter implicit multiplication has priority over division. In all of those examples you changed /2 to 1/2 which means for you, it doesn't. Many people think like that, priority of operation should be left to right.

Many other people, like me, prioritize implicit multiplication. I can also give you a bunch of useless examples:

(48 )/2(12)=(48 )(1/24)=(1/24)(48 )=(48 )/(12)2=2
But you made an error in the first step, those two are NOT equal!
a/bc != a/(bc) !!!
How can you randomly put the parenthesis where you want?!
a/bc = a/b *c = ac/b
left to right
no priority of division over multiplication and vice versa...
 

aceX

Hall of Fame


Every single person who says the answer is 288 is saying that 48÷2(9+3) is the second equation, not the first.
 

BobFL

Hall of Fame


Every single person who says the answer is 288 is saying that 48÷2(9+3) is the second equation, not the first.
And your point is? You are being super-redundant. Why are you repeating the same stuff over and over again?
 

pushing_wins

Hall of Fame
It was first posted on the bodybuilding.com forums i believe and spread from there
original question - posted by someone with 15000+ posts on bb forum. signature: CATZCREW BRAH ★281/713/832 Crew★ MISC Phaggotry Crew(ELITE)
--------------------------------------------------------

a couple of parents are having a debate over this...

i get 2?

edit - wolframalpha says 288? i thought PEMDAS says parentheses first?

------------------------------------------------------------------
 
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BreakPoint

Bionic Poster
That's because you 2ers are flat out wrong.

48/2(9+3) does not mean that the 9+3 is in the denominator.

48/2(9+3) = 48 x ½(9 + 3) = 288
And none of you 288ers have been able to explain why, if the (9+3) is in the numerator, the original equation wasn't 48(9+3)÷2.

And you guys also haven't explained why the (9+3) CAN ONLY be in the numerator and CANNOT possibly be in the denominator.

If the originator of this equation had wanted the (9+3) to be in the numerator, he or she would have written it: 48(9+3)÷2.

The fact that he or she specifically DID NOT write it 48(9+3)÷2, but specifically chose to write it 48÷2(9+3), is proof enough that he or she wanted the (9+3) in the denominator!
 

BreakPoint

Bionic Poster
BreakPoint knows better than Wolfram, Google, Texas Instruments, Matlab, Maple, Mathematica, licensed engineers, and math PhDs because he went to a good college and studied engineering.

End of thread.
What I know is that there is no basis for believing that the (9+3) in the equation 48÷2(9+3) MUST be in the numerator and CANNOT be in the denominator. So far, no one has been able to explain this.
 

BreakPoint

Bionic Poster
Read your signature!

I explained to you 25 times, the problem is you cannot understand it (my 9-yo can just fine). I posted the same problem at my 9-yo class. 50/50 got it right, for the same reason as people on this board. Then I explained them and reminded them what they learned in the last 1.5 years. ALL of them got the correct answer in the next 15 minutes...

12 HAS to be in the numerator because of the math rules, left to right. The division part only applies to the next term unless there re parenthesis.

Under ABSOLUTELY NO circumstances 12 is below the line here. Simply shown:
a*b = ab (ALWAYS!)
c/ab = c/a*b = (c/a)*b = c*b/a = cb/a ALWAYS!
Wrong! If bc is the denominator, many books will write it a/bc. The / is nothing but a substitute for the horizontal divide line since it can't be easily typed with a computer keyboard with the a above the horizontal divide line and the bc below the horizontal divide line. NO PARENTHESES AROUND THE bc IS REQUIRED!

Example, if 3x is the denominator, you will see many equations written as 1/3x or y/3x or 456a/3x. The x is NOT in the numerator in any of these examples! We are NOT talking about programming a computer here. We are talking about solving an equation by hand.

1/3x is NOT x/3. It is 1 in the numerator and 3x in the denominator.
 

dr325i

G.O.A.T.
And none of you 288ers have been able to explain why, if the (9+3) is in the numerator, the original equation wasn't 48(9+3)÷2.

And you guys also haven't explained why the (9+3) CAN ONLY be in the numerator and CANNOT possibly be in the denominator.

If the originator of this equation had wanted the (9+3) to be in the numerator, he or she would have written it: 48(9+3)÷2.

The fact that he or she specifically DID NOT write it 48(9+3)÷2, but specifically chose to write it 48÷2(9+3), is proof enough that he or she wanted the (9+3) in the denominator!
ARE YOU SERIOUSSSSSSSSSSSSSSSSSSSS????!!!

You call yourself an Engineer or an Engineering Student?!

Run away from Engineering, it is NOT for you!!!

That is the Proof for you?!

"Proof Enough"?

Really, you would fail in the middle school with this conclusion, not in College, especially some kick-*** college as you would call it...

I have seen thousands of tricky equations that if you simply re-write them following the rules, they become very simple, just like this one.

And stop saying that none of you provided you the reasoning and PROOF of why 12 is NOT a denominator. It is clear why it is not and why it cannot be, simple left to right rules with no priority operations.

Stay away from Engineering, you will mess up some real-life things...
 

Bartelby

Bionic Poster
'When you have a bunch of operations of the same rank, you just operate from left to right. For instance, 15 ÷ 3 × 4 is not 15 ÷ 12, but is rather 5 × 4, because, going from left to right, you get to the division first.'



The answer is obviously 2 ;)

solve within the () first, then Multiply then divide 48/24
 
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dr325i

G.O.A.T.
Wrong! If bc is the denominator, many books will write it a/bc. The / is nothing but a substitute for the horizontal divide line since it can't be easily typed with a computer keyboard with the a above the horizontal divide line and the bc below the horizontal divide line. NO PARENTHESES AROUND THE bc IS REQUIRED!

Example, if 3x is the denominator, you will see many equations written as 1/3x or y/3x or 456a/3x. The x is NOT in the numerator in any of these examples! We are NOT talking about programming a computer here. We are talking about solving an equation by hand.

1/3x is NOT x/3. It is 1 in the numerator and 3x in the denominator.
please scan the page of the (engineering) book where 1/3x means 1/(3x) rather than x/3.
 
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