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» Hatrack River Forum » Active Forums » Books, Films, Food and Culture » 48÷2(9+3) (Page 1)

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Author Topic: 48÷2(9+3)
Samprimary
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what's the answer
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Misha McBride
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288
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Xavier
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I haven't seen ÷ in a math problem since elementary school, but my answer seems to match Misha's.
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King of Men
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Two your own homework.
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PSI Teleport
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2.
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PSI Teleport
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You know, I'm not positive whether the 2 multiplied by the contents of the parentheses takes precedence over the division problem that comes before it.

edit: I also totally missed KoM's "Two."

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scholarette
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PEMDAS! But remember M and D are tied as are A and S so do them in order from left to right (tied cause you can make a D an M and a S an A)
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Magson
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2
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kmbboots
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I thought 2 as well but I don't do math.
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scholarette
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2 is wrong. Unless it was written as a fraction originally and everything after the division sign was written in the denominator. If that was true though, an error was made in typing it out.
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Xavier
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48÷2(9+3)

First is parentheses, so:

48÷2(12)

Now the ambiguity is whether this is:

48 / (2*12) or 48 / 2 * 12

If it was the first, then it would be 2. If it was the second, it'd be 288.

I'm not familiar enough with the ÷ operator to say which, but the second makes more sense to me, in which case it'd be left to right like scholarette says. Is there some property of ÷ which takes the entire right hand side as the divisor?

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Samprimary
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quote:
Originally posted by King of Men:
Two your own homework.

two you say
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Lisa
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Order of operations says that if the equation read 48÷2×12, you'd just go from left to right, which would give you 288. The question is whether 2(12) is identical to 2×12. Is that just a convenient alternative representation, or does it have a different significance that might advance it in the order of operations. Personally, I think it's identical to 2×12.
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PSI Teleport
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I don't believe that it is.

[I have no evidence to back this up, however, I think of 2(12) as one term and treat it individually.]

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Xavier
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I've never seen it not be identical. Its just a short-hand notation.
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scholarette
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When you divide, you could instead multiply by the reciprocal if if make you happy. So 48/2 is the same as 48*1/2 or 48*0.5 to eliminate all signs of division. So if you were to convert 48/2*12 to all multiplication it would be 48*.5*12.
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MattP
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I would treat 2(12) as identical to 2×12.
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fugu13
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Juxtaposition means multiplication, yes.
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Glenn Arnold
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I see the ambiguity, but I see 2 as a coefficient of 12. The problem here isn't really order of operations, it is that the problem is one of pure arithmetic for arithmetic's sake.

So I have to ask: Is this question designed to demonstrate a flaw in the order of operations rules, or is there a real problem to be solved?

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PSI Teleport
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Step outside of "math" for a second and look at this realistically. If 12 is the number of eggs in a carton, and you want to know what 48 would be if you divided it by two cartons of eggs, you would write it:

48 divided by 2(12) = 2

Or, to put it a clearer way, if B = the number of eggs in a carton, you would use

48 / 2(b) or 48 / 2b

Does 48/2 take precedence is this instance? I find that hard to believe.

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Xavier
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Its a pretty banal order of operations question. Stepping outside of formal "order of operations" conventions to answer it seems like a square peg in a round hole.
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scholarette
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There is no ambiguity. 2 is wrong. 288 is right.
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PSI Teleport
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Except that math exists for a reason, Xavier.
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MattP
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Wolfram Alpha and Google both agree: 288
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MattP
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quote:
Originally posted by PSI Teleport:
Except that math exists for a reason, Xavier.

It also has rigorous rules. You can't look at an expression and intuit exceptions to those rules.
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Xavier
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quote:
48 / 2b

Does 48/2 take precedence is this instance? I find that hard to believe.

Yes, it absolutely does.

48 / 2(12) = 48 / 2 * 12 = 288

You can't just choose to ignore math conventions when it suits you. Or at least you can't if you want to actually pass a math class.

Just write it as 48 / (2 * 12) if you want to represent the english egg problem you have above in math notation.

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PSI Teleport
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I'm not "intuiting exceptions." I'm trying to show that there's a reason why so many mathematicians argue that juxtaposition takes precedence.
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scifibum
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PEMAL would be more useful than PEMDAS, IMO.

M = {M,D}
and
A = {A,S}

L = Left-to-right

Or, if we must, PEMDASL

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Xavier
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By the way, this is apparently a meme now:

http://www.youtube.com/watch?v=wv19iAncrrQ&feature=player_embedded#at=47

Added:

Which seems dumb to me that this is even a controversy. You can argue that it shouldn't be 288, but I don't see how you can argue that it actually isn't 288 by current mathematical conventions.

If you want to change it, I won't argue, but it's clearly the current standard.

Sources that give 288:

Google
WolphramAlpha
Matlab
Python
My TI-89 calculator

I haven't seen anything that gives 2 besides random people on the internet.

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rivka
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quote:
Originally posted by Xavier:
By the way, this is apparently a meme now

I knew THAT as soon as I saw who had posted the thread.
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mr_porteiro_head
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Bah. Whether in math or programming, if your expression is dependent on remembering whether operations are handled from left to right or right to left, it should probably be re-written to be clearer.

unambiguous != clear

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PSI Teleport
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Yeah, I think that video sums up my feelings pretty well. Namely that one answer is probably correct, but the fact that so many intelligent people have had such long, involved arguments about it makes me think that the silliest position one can take is "There's only one possibility, stupid."

Which, by the way, is not the position I'm taking. I lean toward 2, but I'm not arrogant enough to say that that's definitely, absolutely right.

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Xavier
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Teach the controversy!
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PSI Teleport
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That doesn't mean that everyone agrees on what that is.

[Oh, now you're just trying to make me look crazy. [Smile] ]

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Xavier
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I put it in an edit, so maybe you didn't see it:

Sources that say 288:
  • Google
  • WolphramAlpha
  • Matlab
  • Python
  • My TI-89 calculator

Where is the controversy exactly?

Edit: Yeah, sorry, I am edit crazy today.

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PSI Teleport
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quote:
Originally posted by Xavier:
quote:
48 / 2b

Does 48/2 take precedence is this instance? I find that hard to believe.

Yes, it absolutely does.

48 / 2(12) = 48 / 2 * 12 = 288

You can't just choose to ignore math conventions when it suits you. Or at least you can't if you want to actually pass a math class.

Just write it as 48 / (2 * 12) if you want to represent the english egg problem you have above in math notation.

Just to be clear, you're taking the position that 48 / 2b is the same as 24b?

BTW, I'm not ignoring the calculator references you've given. Everything I've read on this issue so far says that different software computes this problem differently. I'm interested in which software gives the answer as "2." Not that you know. I'm just musing.

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rivka
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quote:
Originally posted by mr_porteiro_head:
Whether in math or programming, if your expression is dependent on remembering whether operations are handled from left to right or right to left, it should probably be re-written to be clearer.

unambiguous != clear

Agreed.
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Xavier
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quote:
BTW, I'm not ignoring the calculator references you've given. Everything I've read on this issue so far says that different software computes this problem differently. I'm interested in which software gives the answer as "2." Not that you know. I'm just musing.
I'm interested in that as well, since so far I haven't heard of any software that says anything other than 288. If such exists (and is in wide use), then I will admit that a controversy exists and back away slowly [Wink] .

As something to get flustered over on the internet, its somewhat more fun than politics (as that depresses me more often than not) but still not something that will hold my interest for long.

For the record, I agree with Porter. When I am writing software, I always use parentheses when my order of operations isn't 100% clear at a casual glance.

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King of Men
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Yeah, ok, 288. But whoever wrote the expression that way should be shot for lack of clarity.
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mr_porteiro_head
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quote:
Everything I've read on this issue so far says that different software computes this problem differently.
It is language-dependent.

C/C++, for example, explicitly specify that the order of operations is from left to right. Python (which is written in C) does the same.

I cannot name any popular programming languages that go from right to left, but I know that obscure ones exist.

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mr_porteiro_head
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Just to be annoying to myself, here's an example of code that I would write and which is dependent on the order of operations:

code:
if(pointer && pointer->IsHappy())
{
.....
}


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PSI Teleport
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I wasn't referring to a language that performs the operations from right to left, but rather one that simplifies by applying the distributive property first.

If 2(a + b) = 2a + 2b, then it stands to reason that 2(9 + 3) should equal 2(9) + 2(3), or 24.

But, yes, in the end it seems like the problem was written in order to get one answer, but done so poorly that it got another.

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mr_porteiro_head
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I can't imagine why a programming languages would by default take 2*(3+4) and solve it by first converting it to 2*3+2*4 instead of 2*7. It's more work for the computer, more work for the person writing the language, and it ends up giving you the same answer.

[ April 08, 2011, 08:34 PM: Message edited by: mr_porteiro_head ]

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Glenn Arnold
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quote:
You can't just choose to ignore math conventions when it suits you.
Really? What's "i" then?

How about Tau vs. Pi?

Or assuming that parallel lines will cross eventually?

If following mathematical conventions is just a lock step habit, then we might as well just accept that pi is 3.

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mr_porteiro_head
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What? I really don't understand your post, Glenn.
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xtownaga
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quote:
Originally posted by mr_porteiro_head:
[QUOTE]
C/C++, for example, explicitly specify that the order of operations is from left to right. Python (which is written in C) does the same.

Well, for operations with the same precedence level this is true (which multiplication and division are, of course, so for this case yes I'll grant that this objection is something of a side note). The precedence levels are set up such that multiplication and division are equal, with addition and subtraction equal to each other but lower precedence (just like these operations are handled in math done outside a computer).

Wikipedia tells me that APL and Smalltalk have no precedence levels, and that operators in these languages are evaluated strictly right to left and left to right, respectively.

I would love to move to a postfix (or, I suppose, prefix) system for writing math to get rid of the need for an explicit order of operations, but I really never see it happening.

ETA: I don't mean to imply that you didn't know about precedence levels and whatnot, just including this as a note to people who aren't familiar with programming languages.


Edited also to add in responce to Glenn:

Except this is completely different than the topic at hand. We can prove that pi =/= 3. Proving that something previously thought to be correct is not correct will cause mathematical conventions to change, but that's not ignoring something "when it suits you", it's ignoring something because it's wrong. You can't prove that the arbitrary ordering of operations generally agreed upon is somehow incorrect, it's really no more correct or incorrect than any other ordering would be.

It is, however, standardized. Sure you can reject the standard, but that would be pretty similar to saying 288 is not the correct value of the expression in the subject because you're choosing to disregard the fact that + commonly means addition and instead think it should mean subtraction. Sure there's no provable reason that '+' is a better symbol for addition than subtraction, but if you want to throw that out whenever you feel like without specifically noting that you're doing so math is going to get a lot harder for you to communicate.

[ April 08, 2011, 08:58 PM: Message edited by: xtownaga ]

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Samprimary
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quote:
Originally posted by Xavier:
I put it in an edit, so maybe you didn't see it:

Sources that say 288:
  • Google
  • WolphramAlpha
  • Matlab
  • Python
  • My TI-89 calculator


Where is the controversy exactly?

it is a weird controversy to be sure, but it's neat to me. How it gets worked out and all that.

In some places it's gotten as acrimonious as the point nine nine nine repeating equals one debate, and there's a lot of surprising processes like having google settle it.

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Samprimary
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quote:
Originally posted by King of Men:
Yeah, ok, 288. But whoever wrote the expression that way should be shot for lack of clarity.

if I can find them, i'll shoot them for you
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mr_porteiro_head
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quote:
Wikipedia tells me that APL and Smalltalk have no precedence levels, and that operators in these languages are evaluated strictly right to left and left to right, respectively.
IIRC, Lisp has no precedence levels, and operations must be explicitly ordered with parentheses.

[ April 08, 2011, 11:39 PM: Message edited by: mr_porteiro_head ]

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happymann
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At first read I saw the answer as 2 with reservations because I couldn't remember where "÷" fell in the order of operations. After reading that so many different places agree that the answer is 288, I will have to trust them since I haven't taken a math course in 10 years (even if it was college calculus). So consider me convinced.
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