posted
I haven't seen ÷ in a math problem since elementary school, but my answer seems to match Misha's.
Posts: 5656 | Registered: Oct 1999
| IP: Logged |

posted
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."
Posts: 6328 | Registered: Aug 2003
| IP: Logged |

posted
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)
Posts: 2223 | Registered: Mar 2008
| IP: Logged |

posted
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.
Posts: 2223 | Registered: Mar 2008
| IP: Logged |

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?
Posts: 5656 | Registered: Oct 1999
| IP: Logged |

posted
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.
Posts: 12266 | Registered: Jul 2005
| IP: Logged |

[I have no evidence to back this up, however, I think of 2(12) as one term and treat it individually.]
Posts: 6328 | Registered: Aug 2003
| IP: Logged |

posted
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.
Posts: 2223 | Registered: Mar 2008
| IP: Logged |

posted
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?
Posts: 3683 | Registered: Mar 2002
| IP: Logged |

posted
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.
Posts: 6328 | Registered: Aug 2003
| IP: Logged |

posted
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.
Posts: 5656 | Registered: Oct 1999
| IP: Logged |

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.
Posts: 5656 | Registered: Oct 1999
| IP: Logged |

posted
I'm not "intuiting exceptions." I'm trying to show that there's a reason why so many mathematicians argue that juxtaposition takes precedence.
Posts: 6328 | Registered: Aug 2003
| IP: Logged |

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.
Posts: 5656 | Registered: Oct 1999
| IP: Logged |

posted
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.

posted
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.
Posts: 6328 | Registered: Aug 2003
| IP: Logged |

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.
Posts: 6328 | Registered: Aug 2003
| IP: Logged |

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.

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 .

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.
Posts: 5656 | Registered: Oct 1999
| IP: Logged |

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.
Posts: 16551 | Registered: Feb 2003
| IP: Logged |

posted
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.
Posts: 6328 | Registered: Aug 2003
| IP: Logged |

posted
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.

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.
Posts: 3683 | Registered: Mar 2002
| IP: Logged |

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.

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.
Posts: 14920 | Registered: Aug 2005
| IP: Logged |

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.

posted
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.
Posts: 256 | Registered: Jul 2006
| IP: Logged |