What Is The Answer To This Math Problem?

48÷2x12 isnt being rewritten...thats what it is...if you wanted to you could put the 48 over the 2 (solve it) then proceed to multiply THAT answer by 12 if it makes it easier to understand. Still need to solve each (in this case basic) problem from left to right as it comes up before you can move on.

10 pages because some people see parentheses that aren't there? It's 288 deal with it.

http://www.purplemath.com/modules/orderops2.htm

Example 5

Know YOUR meme!! Haaaa

http://knowyourmeme.com/memes/48293

As far as I'm concerned the ONLY wrong answer is thinking there is only ONE answer.

This was taken from Dr.Math himself....hes a doctor...of MATH.

http://mathforum.org/library/drmath/view/54341.html

This paragraph makes it very clear.

"I don't know of a general rule among mathematicians that implied
multiplication should be done before explicit multiplication. As far
as I'm concerned, all multiplications fit in the same place in the
order of operations. It's not an unreasonable rule, though, since it
does seem that implied multiplication ties the operands together more
tightly, at least visually; but the idea of Order of Operations (or
precedence, as it is called in the computer world) is supposed to be
to ensure that everyone will interpret an otherwise ambiguous
expression the same way - so if some texts change the rules, or if
people do what feels natural, the purpose has been lost."

You read your bolded and must have skipped that bolded in your own post.

also Drac posted something that clearly states the following:

Honestly I had no clue that "implied multiplication" even existed but i'll accept it as a rule. That being said...I still feel that there needs to be a definite yes/no way of solving this and the math "powers that be" need to cement this once and for all.

I was taught the "implied multiplication" by several teachers in school. Maybe it's just different depending on what country you're in.

Both answers are correct as there is no accepted rule for how to handle this. Well more correctly put its a good example of starting a ridiculous amount of controversy over a poorly written statement. 10 pages of arguing and debating on this forum alone on no more deep an argument than this:

Does "it" refer to the cabinet, or the disc?

Is the divisor "2*(9+3)" or is the divisor 2 and the fraction multiplied by (9+3). Essentially the controversy boils down to understanding whether the resulting 12 is on the top or the bottom of the fraction.

The truth is without knowing the author's original intent, its impossible to know for sure.

As Dracondria points out the convention is to accept that the original intent of parentheses is to carry through the operation to the resolution of the parenthesis, but that's not something that is a hard and fast rule.


The reason PEMDAS/BOMDAS is a rule, and this isn't is because of two things.

Using the after learning what fractions are is silly, because the dividing process is really taking a part our of a whole. Also as mathematics become more complicated, it makes more sense to set problems with division up that way as things usually cancel out making a simpler division problem.

When people didn't have calculators (154/88) = 7/4 was more difficult to solve and more time consuming than (7(22))/(4(22)) = 7/4. When you start including variables in equations, canceling out variables in the top and bottom of a fraction becomes essential. When dividing, you should recognize you are making a fraction, and when making a fraction you are in a way dividing.

The reason that its still a big deal is because of the advent of calculators.
A)

B)

As we can see there are two different problems here that provide 2 different answers. It's very obvious how to do both of these problems, and they turn out differently. The problem with calculators and computers is that everything is entered on one line. If someone was doing the math by hand it should be clear if they meant A) or B), a calculator needs many more parenthesis to make the calculations clear, because without them you don't know if the resulting 12 is in the dividend or in the divisor.

My contention is there probably is a correct answer to this problem. This problem wasn't likely devised in a vacuum. It, or something like it, came up as a real life problem on someone's homework or test. They used a calculator to do several calculations at once and the calculator interpreted it one way or another. And they got the problem wrong based on how the calculator interpreted it. It then came up when people were reviewing the test/hw.

So essentially that makes the Dracondria unnecessary. While there may be conventions for how to handle a problem like this in isolation, the original problem this was derived from had either A) or B) in mind. Just be careful when doing problems by calculator and make sure you don't do 3 steps at once, you may have a calculator interpret your entry differently than you intended it to.

Just going to say the answer is 288 as per order of operations.
...and no...there is no other answer.

Personal interpretation to get the anwer 2 breaks the order of operations rule.

(9+3) first

then it is read 48 / 2 * 12 in that order.

Growing convention according to Dracondria's post suggests that you take the parenthesis multiplication more strongly than the dividing sign, however. If you're still arguing that there is some conclusive OOO rule that applies to this situation you are missing the point. OOO wasn't designed to handle calculations entered into a calculator, so there are no rules governing how to treat that problem.

I think the the implied multiplication is actually an older style of interpreting it rather than newer. The newer interpretation of doing purely left to right probably comes about from having to give hard and fast rules for math in programming. That's also why it seems to be that older calculators will have 2 but newer ones will have 288.

One example of this is you can see in the link I posted earlier (and got reposted again I think), the guy refers to his math textbook from 1969 as having this as an example.

(a / b) x (c / d) = a c / b d

Ya...well the problem is that in this day in age, nobody seems to be smart enough to do math on paper and the human brain is still technically more capable of doing calculations than any electronic device.

short answer : The calculator is wrong.

This is about where I stopped reading (*** reading 10 pages). In Aus we're actually taught BODMAS.

Brackets
Of (nfi what that means now)
Divide
Multiply
Add
Subtract

IN THAT ORDER, so I got 288

Ten *** pages and people are still going on about PEMDAS/BEMDAS/BOMDAS when that has nothing to do with it.

Ya'll *** suck at math.

EDIT: And reading comprehension, for that matter.

Actually, in a way it does. OOO, PEMDAS/BEMDAS/BOMDAS whatever you want to call it will influence how you read the problem, whether you read the problem as

A)

or

B)

OOO doesn't give a rule describing exactly how to handle this problem. If you assume in some way it does, it can influence how you see the problem play out, as A) or B). So no, the key to understanding the problem does not lie in OOO, but understanding OOO is essential to understanding why there is so much rage about this problem. To those who say OOO says something about the problem, there are conventions, but nothing that can't be interpreted another way depending on where you reference.

In any event, it has nothing to do with strict mathematics. OOO is a semantics systems that says when we say "a*b+c-d) we mean ((ab)+c)-d. We could just as easily have SADMEP. Math wouldn't change, just how we wrote math would.

In the same vein, that's what this problem boils down to. Its not clear what the original author intended. People (mistakenly or not) interpret it one way or the other.

If the original author had wrote his problem well as
A)

or

B) ,
we wouldn't be arguing about this in the first place.

I wasn't talking to you lol, you know why the question is ambiguous. It will certainly influence how you read the problem, but it does not eliminate the ambiguity (yet so many people apparently think it does) which was my point.

Fair enough, I'm glad we agree.

I don't think it's an ambiguous question at all, from what I can see, anyone that followed the rules of whichever system they're used to came up with 288. After all, that's the entire point of these rule systems. If the person writing the question was expecting 2 as an answer, then they've written their question incorrectly, not ambiguously. Unless it was written as forty-eight divided by two times nine plus three, then I really don't see the ambiguity, as it would then be unclear as to whether any brackets were to be used and where.

As the question stands though, it's clear, and the answer is 288.

Except according to older convention, you're doing it wrong. Calculators will use differing conventions as well. You can quote what you think the OOO says all you want, there is reason to believe that 2 is the answer as well.

Should there be ambiguities? No, but then again math, and these conventions, were made prior to the use of the modern calculators when structure of the way the problem was written aided in the way a problem was solved as well.

Its a question of how far the divisor line extends more than a question of what is done in what order. Think of it as if OOO is semantics, and the proper use of symbols is punctuation. Improperly using punctuation can mess with the meaning of a sentence as well.

O.O 10 pages because of a math problem...?

Hmm, okay I just read that purplemath link above, that's *** up lol. I find it really odd that math, which is so strictly governed by rules, has no definitive answer for such a simple issue.

Maybe if I'd bothered to read the 10 pages I'd have seen that earlier, but I guess it really is true that either answer is acceptable... which kinda goes against everything maths stands for no?

145±143

I helped my Uncle Jack off a horse.

vs

I helped my uncle jack off a horse.

Big difference, good point.

/thread

Not really, the problem is not with the equation but simply with how the equation's written down. There's another quote from the mathforum site which I could see as being true. Math people don't care about stuff like this because they know how to write it properly in the first place.

Damn 10 pages

No because the problem is is that there aren't two answers to a single problem. There are two ways to read that problem. Someone using those numbers practically has a purpose behind it, namely either problem A) or problem B). They don't mean both, they mean one or the other, they're just posing the problem poorly.


I guess the simplest analogy I could offer would be something like me saying: "I put my phone and my wallet on the table, bring it to me." If I wanted my phone and you brought me my wallet (or even the table), I shouldn't be upset with you because I haven't made my intentions clear.

But that's a simple statement made in a void. In a conversation I might have been talking about calling our friend up for tea later, and then say "I put my phone and my wallet on the table, bring it to me." Given the wider context of the conversation you should probably assume I want my phone. If there was a larger problem or series of steps guiding my actions, I'd have more information to solve the problem.

Or I could just reword the problem. "I put my phone and my wallet on the table, bring my phone to me." Using more information, proper punctuation, more detail, you can appropriately read what I meant to say. Using appropriate length lines to show what I meant to be in the numerator, and what I meant to be in the denominator would make the problem unambiguous.

When doing math by hand, if you're doing it correctly you'll supply the appropriate length line. But when all symbols are only one symbol big (in a calculator or computer), you have to use other ways of getting your message across (appropriate parentheses, or the correct calculations at once).

I know its a horrid analogy, but its late.

Another way to avoid confusion is to use the appropriate length segments of calculation.


If you enter into a calculator 48/2 = (revealing 24) * (9+3) = 288. its different if you enter into a calculator 48/(2*(9+3)) revealing 2. Neither of these two calculations are ambiguous.

Math itself is constant. The rules guiding semantics is just how we understand and interpret math. Its a question of being ambiguous (human error) rather than a faulty system.

http://mathforum.org/library/drmath/view/72166.html

http://www.physicsforums.com/showthread.php?p=3242786

Some more stuff on implied multiplication. My book was fairly new (2003+ iirc, was in 07 or so too) and it had the implied ones which worked with the calculators we used.

There's no real point in arguing this anymore because there's no definitive answer. Teachers teach different methods and it seems to vary depending on country too.