I can't believe this is still being talked about. Bottom line is it is a poorly written/organized math problem. Probably done intentionally to stir up arguments on the internet.
This is the issue here. Those of us who are getting 2 are rationalizing it incorrectly. We are taught f(x) in a segment of the equation, not in the full equation in itself. For example: f(x)=xy+xz which is also correct to say f(x)=x(y+z) But if you have: f(x)=a/xy+xz you can't rationalize it further. You can rationalize f(x)=a/(xy+xz), but it must read as f(x)=a/(x(y+z)) Those who are getting two are doing 48/(2(9+3)) and of course that is not the equation. When you simplify the equation by solving the parenthesis first as you're suppose to, you get 48/2(12). This is where poor expression of writing math gets in the way. In some minds, the parenthesis still exists, which is not the case.
Where do you work? I want to make sure I never get my taxes done there. I don't think so. It's pretty simple if you follow the rules and don't overthink it like the folks incorrectly getting 2 for the answer. Go back to this post for the correct way to use PERMDAS. Or start at 0:30 and go to 2:00 for another explanation: <iframe title="YouTube video player" width="480" height="390" src="http://www.youtube.com/embed/U9uS0orEMDo" frameborder="0" allowfullscreen></iframe>
I understand this methodology, I guess the confusion for me is when do you deal with parenthesis. Because as I was taught (many moons ago) you deal with them first. So you would deal with the 9+3 portion but the parenthesis are still there. And, I appreciate Hayes thoughts, she is on the frontlines of this... For me, and the way I was taught the order would be: (9+3) = 12 2(12) = 24 48/24 = 2 The reason that the multiplication would be done before the division even though they are equal and should be done left to right is that the parenthesis are still in play until that number is resolved. I can see 288, and I can see 2......whomever said it was a poorly conceived problem was right. LOL... DD
Keep in mind, in math, parenthesis can be used for two different things. It can be used for multiplication (12)(12)=144 or for functions (12+12). Once you solve (3+9), it is no longer a function. If you choose the keep the parenthesis, its is now multiplication. In PEMDAS, Parenthesis does not apply to the parenthesis used to express multiplication. Its not a poorly written problem. Its a simple problem that exposes those, like me, who do not have a concrete understanding of basic algebra.
And to Rezdawg: mid/late 70's. tehGLIDE, When I saw yours, I wasn't sure what you were getting at. In the case of the problem you posed, the parentheses do not matter, because it is preceded by a '+' , so the answer would be the same regardless. I don't know if that was your point or not. But it got me thinking, what if you had posed the problem as: 3 -5 -(2+4) = ? instead of 3 -5 +(2+4) = ? Now we are talking a whole different kettle of fish. In this case, the parentheses DO matter because the '-' must be applied to the entire contents of the set. In other words, it becomes 3 -5 -(2+4=6) or 3 -5 -6 = -8 So solving for the contents of the set, and then applying the '-' is correct, and necessary to properly solve the equation. If one ignored the parentheses and simply did 3 -5 -2 +4 = ? then you would end up with zero as the answer, which would be incorrect. In the case of your original problem, 3 -5 +(2+4) = ? you could remove the parentheses and the answer will remain 4. But, the thing which got my spinning around a bit is, why is this so? Well, in the original problem the +(2+4) is functionally actually (+1) * (2+4) .. in other words, multiply the contents of the set times 1. This does not alter the values inside the set, hence making the parentheses meaningless. However, in the second example, -(2+4) is functionally (-1) * (2+4) .. in other words, multiply the contents of the set by negative 1. Placing a '-' in front of a set changes the equation from being a simple addition/subtraction problem to multiplication, and therefore the necessity to solve the parenthesis set first. So then the equation could more accurately be written as 3 -5 + [-1*(2+4)] = ? So this is fine, because according to the order of operations, solve all parentheses first, then multiplication - any parenthesis sets preceded by a '-', and then all of the rest of the equation from left to right. It's all good. So kind of related back to the original problem, how would one write out an equation where you wanted to divide a number by a set of negative variables? For example, say I want to divide X by negative (A+B)? If that makes sense. It seems like it would have to be written out something like X / -(A+B) = ? Now I am not a mathematician, but if we go by the examples above, this would then be written as X / -1(A+B) = ? But since it seems to be firmly established standard now that, once the parenthesis is solved, you would NOT automatically then multiply the -1 * Y (where Y=A+B), but instead it would be done as X / (-1) * Y = ? which would yield an entirely different result from the one intended. So how would it have to be written? It seems like X / -(A+B) = ? is clear enough, but would it instead have to be written out as X / [-(A+B)] = ? or X / [(-1)*(A+B)] = ? in order to guarantee that the -1 is applied to (A+B) before anything else happens with the equation? Oh and yes, I realize I just spent an hour typing all this out, because it's a slow day at work, I am stuck at a desk, and... FML .
You gotta remember though, tax is a subset of Accounting, and Accounting is not math. Math is a science.......Accounting is (at best) an art. Math is the antithesis of Accounting. As long as your tax firm will sign off on their answer, make sure their E&O premiums are being paid, and will go to bat for you during an audit, it really doesn't matter what answer they get (just so long as it decreases your tax burden). BUT.........if we're looking at this in the context of an algerbra question, the answer is 288.
It doesn't matter in this case if you evaluate it as (X / -1) * Y or X / (-1 *Y), though maybe your point would be better illustrated if you had used 2 instead since there is a difference between (X / -2) * Y or X / (-2 * Y). As far as this general topic, I found this link interesting: History of the Order of Operations It talks about how parenthesis before exponents before M/D before A/S is a "natural" rule because it generally simplifies how we notate algebra and polynomials, whereas left-to-right evaluation for M/D and A/S is "artificial". Math is absolute in that if this problem were unambiguously written, there is only one correct answer. However, rules of interpreting notation like this aren't absolute. We could have just as easily said, evaluate M/D right-to-left (maybe if we were used to reading Hebrew, Arabic, or Chinese?), or, if you write a number next to parentheses, then that must be evaluated first. I hadn't thought about the fact that people could have been taught differently in the past than I was. I can see that we have created certain arbitrary/practical rules to interpret notation. The ones that are agreed upon now say the answer is 288 but they could have been different in the past.
Season seems over. Playoff hopes seem dim. This is what it has come to. On a more serious note, there are other forums in which this exact same topic has reached over 100 pages. It is an internet revolution.
Yeah I posted this about 20 pages back, and I'm sure others did as well - I guess the only value of it I guess is how extraordinarily popular arguing over it is, it seems to appeal to people (like the stupid airplane on a conveyor belt) on a some basic level that I don't get.
Actually this was my son's 6th grade math homework (GCCISD in Baytown) that he brought home Wednesday night. I posted it on facebook and it blew up. In less than 24 hours it was already being discussed in the UK and elsewhere. Pretty crazy that such a seemingly simple math question has sparked such vigorous debate. It inspired me to make this video. http://www.youtube.com/watch?v=wv19iAncrrQ
Got to page 3, realized what a stupid thread this is, skipped to the end. I apologize if someone else brought this up already. I was taught the 2 should be distributed through the parenthesis. 48÷(2(9))+(2(3)) 48÷(18+6) 48÷24 2 I agree, ÷ is a symbol for children. If / had been used instead, we wouldn't even be having this conversation. And if we were, it would be pretty clear who was wrong.
Love it! Well done! <iframe title="YouTube video player" width="640" height="390" src="http://www.youtube.com/embed/wv19iAncrrQ" frameborder="0" allowfullscreen></iframe>
