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J/c The answer is 288, as has been WELL ESTABLISHED.  Secondly, this thread stands as proof of many things, with the main one being "no wonder this group can't come to a consensus on anything." Even the simplest of things get parsed beyond belief. 
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Quote:
J/c
The answer is 288, as has been WELL ESTABLISHED.
Secondly, this thread stands as proof of many things, with the main one being "no wonder this group can't come to a consensus on anything." Even the simplest of things get parsed beyond belief.
This thread also proves that some people here shouldn't be on "are you smarter than a 5th grader"
It's supposed to be hard! If it wasn't hard, everyone would do it. The hard... is what makes it great!
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2nd String
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j/k
I have 48 apples that I have to give away. I see two groups of peolpe, 9 men and 3 women in each group. I gave the same number of apples to each person. How many apples did each person receive?
48 people are in a room, half of them leave. Those remaining received 9 red and 3 yellow apples each. How many total apples were handed out?
2 apples to each person.
Second question: 288 total apples. (I think?)
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I was just trying to see if either of these applied to the question at hand. I say the answer is 2. I may be wrong, math class was a long time ago. 
Last edited by RoosteR; 04/16/11 12:42 PM.
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Quote:
2. 48 / 2 * (9+3) = 288
But why did you add the asterisk? Is it needed, or, does it make a difference?
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Quote:
Quote:
2. 48 / 2 * (9+3) = 288
But why did you add the asterisk? Is it needed, or, does it make a difference?
It's not needed, it is implied. The problem is the same with or without the symbol
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It doesn't make a difference mathematically, although you can make a strong case that it's 'needed' in the sense that without it, a great many people misinterpret the problem as evidenced by how this problem has shown up on hundreds of internet boards and it usually ends up being something like a 50/50 split. In your second word problem, you can pretty much just say 24 people received 12 apples each.. I can't possibly see how there would ever be any confusion... 48/2*(9+3) simplifies to 24*12 But whether or not the * makes any difference seems to be the crux of the issue... I see 24*(12) as being identical in function to 24(12), and thats really how it should be... but for whatever reason some people are seeming to think that by omitting the *, that multiplication takes precedence over multiplication and division where really those should be done left-to-right as per the order of operations. I hope that made sense
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Totally agree hasugopher. Not having the * made me initially come up with the "2" answer. But then I thought about it before I moved on and came with the "288" answer.
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I have to admit, whoever came up with this problem did a pretty clever job in introducing a lot of things that could cause confusion. For example, ÷ would always be replaced by / in any problem that also included brackets/parentheses. I don't think any of us has seen a ÷ since elementary school probably.
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Ok, I get it now.  I guess I thought that 2(12) needed done first, because the parentheses were still there.
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To further go over what you said ... Quote:
In my humble opinion, because no multiplication sign was placed between the 2 and the (9+3) it is not implied.
But it is implied ... (yet it's not). The rule as I've always known it is that 3(12) = 3 * 12 ... as a simple multiplication. No preferential multiplication. Order of operations still apply
Quote:
Therefore the 2 multiplies the 12 as in 2x where x = (9+3) which = 24. Then you have 48 divided by 24 which = 2.
But it's not 2x ... it's 2(12). I think the problem stems from lazy algebra practices. When converting 2x to numbers, people/teachers/professors tend to write 2(12). Why? Two reasons ... One, it usually doesn't matter, as algebraic equations are already clearly written out with numerators and denominators clearly put above or below a division line, and most multiplications have already been added together, leaving only the lesser-order additions left. So when 2x + 3x = 2(12) + 3(12), the multiplication is going to come first anyway ... Two, it's much easier to write 2(12) than it is to write (2 * (12)), which is what 2x really means in proper notation.
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If it was written as 48 division sign (sorry don't know where that symbol is on my keyboard) 2 * (9+3) then the answer would be 288.
That's what it is written as. 2(9 + 3) is the exact same thing as 2 * (9 + 3). There is no implied preferential multiplication when you remove the *, meaning it doesn't suddenly become (2 * (9+3)).
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Just remember that everything you read on the internet is not necessarily true.
Most of this is based on what I've learned in school and college. (I was one credit away from a math minor). The stuff on the internet is just sort of corroborating what I thought was the case.
Quote:
anyone have one of those smart calculators where you can plug in the equation and get an answer? I would trust Texas Instruments long before I trusted google.
I think someone above mentioned that most modern calculators will give 288.
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Quote:
÷
I cant even find it on my keyboard. 
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Quote:
Quote:
÷
I cant even find it on my keyboard.
Highlight it in this post ... hit "cntl-c" ... then hit "cntl-v"
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Quote:
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÷
I cant even find it on my keyboard.
While I'm assuming that was a tongue-in-cheek comment, I think it speaks to the real-world practicality of the question. I mean, does anyone ever write a problem involving division using that symbol beyond the sixth grade? I've written division problems as fractions or ratios for 20 years now. Furthermore, writing "48/2(9+3)" would simply be considered lazy or sloppy by just about anybody.
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I know when I program ... I constantly abuse the use of parenthesis, to ensure the correct order of operation.. That equation would look something like: ((48 / 2) * ((9 + 3))) 
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Me too when I put problems into my TI-89, or when I was programming in MATLAB for a school course a couple years ago. I don't leave anything up to chance. Nice thing about the TI-89 is that it displays your input on the screen after you enter it so you can visually check to make sure that nothing was entered incorrectly.
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Quote:
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Just remember that everything you read on the internet is not necessarily true. anyone have one of those smart calculators where you can plug in the equation and get an answer? I would trust Texas Instruments long before I trusted google.
Found that at the link Excl posted.
This actually is ambiguous, and it depends on whether you view this as 48/[2(9*3)] or 48/2*(9*3).
My interpretation is the former because of the parenthesis and the implied multiplication. 2(9*3) becomes the divisor and 48 is the dividend. That makes the answer 2.
My interpretation was the same, I got 2. Pretty interesting though I must admit
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Most programming languages (all of the ones I am aware of) used would force you to put an asterisk in order to compile:
48/2*(9+3)
So there are no interpretations. I did it in C#, VB.NET, Clarion for Windows, Python, and C - all came up with 288 and needed the * between the 2 and (9+3) to compile.
#gmstrong
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Isn't there another punch-bowl where you can drop your magic?
Sure. Have you started another thread?
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If this was written out in proper form then the (9+3) would be identified in the denominator or numerator for order of operations.
48/2(9+3) like so.. therefore = 2
Since its uses the dividend symbol I believe the summation is still first before dividing because the 2 is attached to the (9+3) therefore its still 48/24=2
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Quote:
Most programming languages (all of the ones I am aware of) used would force you to put an asterisk in order to compile:
48/2*(9+3)
So there are no interpretations. I did it in C#, VB.NET, Clarion for Windows, Python, and C - all came up with 288 and needed the * between the 2 and (9+3) to compile.
Your adding things to change the question
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Quote:
If this was written out in proper form then the (9+3) would be identified in the denominator or numerator for order of operations.
48/2(9+3) like so.. therefore = 2
Since its uses the dividend symbol I believe the summation is still first before dividing because the 2 is attached to the (9+3) therefore its still 48/24=2
No.
Summation is done first. You have 48/2*12. All you have left is multiplication and division. Order of operations states you work from left to right. 48/2 = 24, then 24*12 = 288.
It's supposed to be hard! If it wasn't hard, everyone would do it. The hard... is what makes it great!
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But,
if you write it this way:
48
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2(9+3)
The answer is 2. No?
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The reason the calculators ring up a 288 is because when entered into a calculator, you need to add an extra set of parentheses. The calculator needs the parentheses. A human should just know better. That's my stance.
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And into the forest I go, to lose my mind and find my soul.
- John Muir
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Quote:
But,
if you write it this way:
48
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2(9+3)
The answer is 2. No?
Correct ... but it wasn't written that way. A "/" does not imply a division line where everything after it is under the numerator. It is simply an operator, meaning divide the number to the left by the number on the right. Since there are no parenthesis or higher orders of operation to the right that would be forced to multiply the 2 and the 12 first, then only the 2 is used as the denominator.
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If I put it into a calculator, the answer is 288. Plus you could always use the saying PEMDAS, .If it were me writing it and I wanted it to be 2, I'd put the numerator and denominator in complete () so there could be no confusion at all. meaning....either way I think their way of writing it is crap.
(48)/(2(9+3))
OR you could do this, (48/2)(9+3).
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I understand that. But you cannot compile anything in any language that I am aware of without adding the "*". I understand that part of the fun of debating this is due to the fact that the "*" isn't there, but in order to make sure there is no doubt as to what the operations are, a programming language is going to want the multiplication sign.
I still think the answer is 288 regardless as the multiplication is assumed next to the parenthesis.
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An observation I've made, currently taking my final (thank god) math class I'll ever need in my life, is that the way we are being taught now leads us to the answer of 2. Every one of my classmates I showed this problem to came to the conclusion the answer was 2, and so did my professor.
Its an interpretation of the way the problem is being presented, its that "new math" that "kids these days" are being taught I guess.
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Quote:
I understand that. But you cannot compile anything in any language that I am aware of without adding the "*". I understand that part of the fun of debating this is due to the fact that the "*" isn't there, but in order to make sure there is no doubt as to what the operations are, a programming language is going to want the multiplication sign.
I still think the answer is 288 regardless as the multiplication is assumed next to the parenthesis.
For written math, you do not need to put in the "*", it is implied. With the way the problem is written, you are to automatically assume that there is a multiplication operator present; you don't need to see one; it's shorthand mathematics.
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Yes, I know that - I was just explaining to Paco why I put it that way in my first response as I was showing how a programming language would want it in order to compile, but I know you know that I agree that it is implied which is why the answer is 288. To me it wasn't confusing at all, but apparently there is some question about it due to the lack of the multiplication symbol - math really was not my strong point anyhow.
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Bottom line: if you format the problem like so 48/2(9+3), you're going to get confusion. It's poorly typed. (48/2)(9+3) is obviously 288, and (48/(2(9+3))) is 2. Parentheses are your friend in math. A poorly formatted mathematical expression is like a sentence with awful grammar. It makes for confusion.
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Forums DawgTalk Tailgate Forum 48÷2(9+3) = ????
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