Poll: What is the answer to 48/2(9+3)?

[doggie135]

If you wrote this as a fraction, not a division equation (same thing in terms of mathematical function), doesn't it become easier to see (at least in terms of the logic people are applying) how you can get 2? In a fraction, the core effect of it is to bracket the top and bottom, calculate and simplify.

Meh, why am I putting time into this?

 

[mjc0961]

My apologies then. But for what it is worth I agree, I just assumed left to right was another as I said regional quirk because of the debate. Going left to right with either bedmas or pemdas is 288. That is sure with the M and D holding equal weight.

48/2(9+3) is 48/2 x 12 which is 24 x 12 as many others have said.

Yeah. I made the same mistake; I haven't really seen any situations where multiplication and division were left alone like this, so I went "well multiplication is first in the list so you do that first". But then I looked it up on multiple sites and they ALL said that multiplication and division are equal, and if you have both, you go left to right.

So it's just that a lot of people made the same mistake I did, but aren't correcting themselves. If we were all on the same page of proper order of operations, we'd all get 288.

 

[Link_to_Future]

There are situations in which the rules of precedence are utterly unnecessary. For example, one could simply write an equation where any two operands (values) and a single operator are enclosed on parenthesis. This removes any ambiguity but has a nasty habit of making an equation more difficult to understand. There is even an a method of representing an equation in a similar way that is relatively common in computer science. Take the well known equation f = m * v (force is equivalent to the product of mass and velocity). In a different notation it is written as follows:

(= f (* m v)).

A slightly more complex example is d = vo * t + .5 * a * t^2 (the final position is equivalent to the sum of the product of velocity and time and the product of acceleration and time to the second power divided by 2) becomes:

(= v (+ (* vo t) (* .5 (* a (expt t 2)))))

There is absolutely no need to understand rules of precedence in such a case but the trouble is the equation is suddenly incredibly difficult to read unless you are used to workin in that format.

No kidding. I become more and more confident in my decision to avoid computer programming like plague when presented with issues like that. Suddenly my decision to stick with traditional paper and pencil methods sounds a lot more appealing when contrasted with the absolute ways of writing equations like that.

Sure, some of the more complex problems can take around an extra hour to solve. However, at least everything I'm doing makes sense in my brain spacy thing.

I have other points I could try to make but my bed is singing its siren song. I'll just let my end of the conversation trail off after this.

Thanks for humoring me. Hope to see you around.

 

[Atticus89]

To those people who say the answer is 2,
If 48/2(9+3)=2,
then 48/2/(9+3)=?

If I'm reading that right, you're asking was (48/2)/(9+3) is... which is still 2 because that whole thing simplifies down to 24/12 when using PEMDAS.

So you're saying that 48/2/(9+3) is equivalent to 48/2*(9+3)? They obviously can't have the same answer, you might as well be arguing that 1+3 is equal to 1-3.

I said no such thing. In fact, I came up with two different answers but you cut out the second half of my original post. In the part you quoted, I read the equation as (48/2)/(9+3), which makes the answer 2, because there were three slashes and no indication on what part to start with.

In the part you didn't quote, I re-read the equation as 48/(2/(9+3)), which simplifies down to 48/(1/6), the answer to that equation being 288.

My point was that how the equation is written can determine what the final outcome is. I also mentioned that I was a history major, which you also decided to leave out.

 

[flippedthebitch]

I don't know why you want us to do your homework for you, but I got 288... after you do the parentheses, you're supposed to do them from left to right. I think it's a poorly written problem, though.

Mathematics don't care about "left to right". You solve the parentheses first, and then in the order of multiply and divide. The answer is 2. Take it from the European guy.

Clearly a culture break has occurred because there seems to be no agreement on which should come first the multiplication or the division. The way I was taught was called "BEDMAS", which seems to be a Canadian thing according to a quick google search of the word. Other regions use other systems that are similar or different arrangements, which has resulted in this shift of multiply or divide first. For example I had never heard of PEMDAS before tonight, nor had a reason to seek out alternatives to what I was taught.

Parentheses (or brackets, even though they aren't actually brackets) do come first, that is a given. Afterwards, as I said, it is used both ways whether to utilize the M or the D. From what I can find there doesn't seem to be a concrete rule as to which is first. So if we are to ignore left-to-right as another regional quirk, there is no correct answer. It is 2 and 288, depending on which you solve first.

I feel like I bring something to this conversation being a 3rd mathematics major at the university of alberta. When we think of BEDMAS or PEDMAS its important to recognize that this perticulair method of remembering order of operations implies that you always do division before multiplication when this is obviously not the case. The proper order is B for everything inside of your brackets, then E for exponents, then we are supposed to think of D and M not as seperate steps, but rather that all multiplication and division needs to be completed before addition and subtraction. When faced with a problem like this with both a division and a multiplication the proper way to interpret the order, and indeed the way that a calculator interprets the order, is to do the operations from left to right, not all divison then all multiplication. So in this perticular problem:

48/2(9+3) our first step is the 9+3
48/2(12) then we continue onto our multiplication and division step, moving left to right
24(12)
228

If the intention was for the (9+3) to be multiplied to the denominator then we would have to include this step in brackets, making it occur before our regular division and multiplication step. So it would have to look like this:

48/(2(9+3)) again our first step is 9+3
48/(2(12)) then because our 2*12 is in brackets, it occurs before our division
48/24
2

so the way the question is written in the original post the answer is 228. Now if only I could do my 300 level number theory algebra this easily......

 

[Sprinal]

The layout of the question would suggest that the writer has asked for 12 to be multiplied by the denominator. Thus the answer would be 2.

yet as you are giving me the option of 288. It would then appear that you gut this by multiplying the fraction by the brackets. This I struggle with as if I had tried this wit either my Graphics or scientific calculators. It would give me 2 from the way the design has been set.

 

[Lim3]

Poorly written.

If its 48/(2(9+3)) then it is definitely 2. As it is 48/2(9+3) I wouldn't multiply the 2 by 12.

 

[Bearjing]

I said no such thing. In fact, I came up with two different answers but you cut out the second half of my original post. In the part you quoted, I read the equation as (48/2)/(9+3), which makes the answer 2, because there were three slashes and no indication on what part to start with.

In the part you didn't quote, I re-read the equation as 48/(2/(9+3)), which simplifies down to 48/(1/6), the answer to that equation being 288.

My point was that how the equation is written can determine what the final outcome is.

You aren't reading it differently, you are changing it.

 

[Choppaduel]

depends how you parse it.

 

[Dair1]

I say 2, though you can get 288.

 

[thahat]

Well this has been an entertaining read. I forget how passionately people can argue about something so banal.

I'll just repeat what has been said before because there really isn't a lot to say. The problem is poorly presented. When I first looked at it I saw 2 because I always make it a point to separate individual fractions by parenthesis as so:

(48/2)*(9+3)

It's clear and unambiguous. There is no argument about how it can be perceived. Without the first set of parenthesis or the multiplication sign, I see it as being in the denominator. Is that wrong? Apparently, and since I'm wrong I'm a bad person and a terrible student who should just flip burgers for the rest of my life. That's how it works, right?

If this were a math problem of any actual bearing to any situation then it would be framed slightly better. Yes, all of you who say its 288 are correct. Technically. But why this sense of superiority that I'm sensing from some of you? What good is it doing honestly?

/preachyrant

good explanation, exept for one part. whats so unclear about it?
X and / before - and +, always.basic rule, right?
stuff of the same class go from left to right.
if you jsut stick to that, rigerously. its not unclear at all. exept for the not actually putting down an x or a . ( multlipication = x = . )

But don't you see that at a glance it could be seen the other way? Can't you acknowledge the possibility that someone would just work it in their head real quickly without following that basic rule simply because they failed to see it in that manner?

On simple set of parenthesis would make it so that there was absolutely no way to argue it either way. That there was no way to perceive it incorrectly.

I realize that technically you are correct. I never denied that. I'm just saying that it would be just as easy to make this undeniably one way or the other.

Also, that really wasn't the main point of my post. I was more curious about why people were acting so...smug. I was really trying to figure out why that was necessary.

Oh wait...internet. Right.

yes, i do agree to the fact that on a quick glance one could easily make a an error, and that that would be easily corrected with an extra pair of brackets.
also, spot on there, with the internet and smug comments //is wrong// remark. seems to be the truth most of the times, lol. any psychologists in the house who can explane as to why we seem to want to go into such discussions XD?

 

[Dair1]

It does tell you, the 2 is after the '1-over' sign (/) so the 2 is part of the denominator so it is 48/(2(9+3))

 

[FluxCapacitor]

...*sighs for anyone getting a 2*...

Folks, this is a compsci problem msaquerading as a math problem, and it's all about the "/" operator. The key here is that we're looking at a formula represented strictly in ASCII characters, so we have to use the rules that coders use - if a mathematician were writing this with a pen and paper, or any of the wealth of formula tools they can use to compose papers on a computer, they would make it explicitly clear what expression to use as the denominator by representing the division by a horizontal line.

This isn't that - it's ASCII, which is how programmers would represent an equation, so we have to interpret it the way a computer would parse the data. For any programming language you care to name, the "/" operator divides only by the next token in the code string unless that next token is a grouping token like "(". Thus, it's 24 divided by 2 times 12 - read left to right. If you wanted to do the multiplication before the division, you'd have to explicitly say so with brackets. This is why EVERY piece of software is reading the answer as 288 - they are better at interpreting ASCII equations than the untrained eye.

(Frankly, folks who are claiming some kind of special 'single entity' status for a term and its coefficient are also just plain wrong - the only reason they think this is that in a standard general form polynomial the coefficient is more strongly associated with each term because every other operator is additive or subtractive, but I'll argue this from my strengths...)

 

[Supernatural Girl]

It is my belief that if you were to get the "24*12" section of the sum, then the equation would be written (48/2)*(9+3).

Instead the brackets are referring the the number immediately adjacent to the brackets/parenthesis, leading the answer 2.

You're not finished with the bracket until there isn't one. To get the answer 288, you'd be leaving the sum as 48/2(12). So the remove the bracket completely, you have to multiply the 2 and 12 together. Continue from there.

 

[Merkavar]

apparently this is a popular question if you google it.

 

[flippedthebitch]

So I guess the boiled-down question I pose to you is what would a possible real-world situation be where a question framed in this manner would become a hindrance to those not abiding by the strict left-to-right operations?

There are situations in which the rules of precedence are utterly unnecessary. For example, one could simply write an equation where any two operands (values) and a single operator are enclosed on parenthesis. This removes any ambiguity but has a nasty habit of making an equation more difficult to understand. There is even an a method of representing an equation in a similar way that is relatively common in computer science. Take the well known equation f = m * v (force is equivalent to the product of mass and velocity). In a different notation it is written as follows:

(= f (* m v)).

A slightly more complex example is d = vo * t + .5 * a * t^2 (the final position is equivalent to the sum of the product of velocity and time and the product of acceleration and time to the second power divided by 2) becomes:

(= v (+ (* vo t) (* .5 (* a (expt t 2)))))

There is absolutely no need to understand rules of precedence in such a case but the trouble is the equation is suddenly incredibly difficult to read unless you are used to workin in that format.

I am struggling a touch with your interpretations. To take your equation f=m*v and rearrange your equation so our force ends up on the right hand side, we would need to do a division of the force to both sides of the equation. so it looks like this:

(f/f)=(m*v)/f the f/f is simply 1, so your equations should look like
1=(m*v)/f

Unless your computer science requires a completely different method of imput specific to your programs, which I understand it very well could be. your manipluation of that equation is flawed. So would be your comment that the rules of procedence are unnessessary. In fact if you want to mantain the equality of these equaltions the procedure of equation manipulation is utterly important to the whole process. The second equation has similair flaws, your manipulation loses the equality of the equation making, as far as I can interprete, the two sides of your equation no longer equal and totally useless to solving for any kind of variable.

 

[Quazimofo]

I don't know why you want us to do your homework for you, but I got 288... after you do the parentheses, you're supposed to do them from left to right. I think it's a poorly written problem, though.

lol it's not a homework problem man, I'm not in middle school. This question is blowing up other forums and reddit.

48/2(12) = 2

Yeah, that's how I did it. But the way it's written, it doesn't specify if the only the 2 is being multiplied by 12 or if the entire fraction is. If the first, then it's 2. If the second, then it's 288.

So, as Professor Layton wisely pointed out, the problem is poorly written.

not really. due to the limitations of computers, we cant write fractions on forums quite as well as by hand, so one must assume that since the whole fraction was not in parenthesis to be multiplied, the multiplication by 12 only applies to the denominator of the fraction. and so, by adding (9+3) to get 12, then 12*2 to get 24, 48/24=2. simple

yay high school freshman pre calc class!

 

[Henkwich]

I'm pressed for time so I'll do this as fast as possible and I think a lot of people already said this but here's my 2 cents as they say.

48/2(9+3) the way I was thought works out like so

You start out with the parenthesis getting 9+3 = 12

Then you procceed with the multiplication and division going from left to right

coming to the conclusion that the full equation would be something like 48/2(9+3) = 48/2(12) = 24(12) = 24x12 = 288

THAT. IS. HOW. YOU. DO. IT!

If anyone thinks different, they don't know math or their teachers didn't get through to 'em.

Incidentally I think that while you might say the the multiplicatin symbol should be added before the parenthesis I believe that when I was doing this level of math they started out doing that to put emphasiz on the fact that it's supposed to be there, but in the end if there's a parenthesis in an equation you're supposed to know that the numbers preceeding it are supposed to be multiplied by it. After the parenthesis is calculated mind you. And either way it doesn't matter if a multiplication sign is there or not because if we follow the calculate from left-to-right rule and the equation looked like this

48/2x(9+3) we'd still end up with
48/2x(12) paranthesis done
24x(12) Division done - 48/2<<this one first cause, left to right remember?
288 - Final multiplication of the two sets of numbers.




Now. Is that bloody clear enough for you?!

Edit: wow.. keyboard kind of got away from me there. Anyway. I stand by this.

 

[Hashime]

The answer is 288.

 

[Goldeneye1989]

BOMDAS
Brackets pOwer Multiplication Division Addition Subtraction