48

[satyr9]

It all seems to come down to whether you treat 2(9+3) as one term or two separate terms. To me, since there is no multiplication symbol separating the two, I treat it as one term. Not sure if that's the correct way to go about it, but from all the math classes I've taken, I've always been taught to treat it as such. To me, it's 48 divided by 2(9+3), not 48 divided by 2 multiplied by (9+3).

It's not. Just because you don't have to show the * symbol doesn't mean it isn't there and the order of operations is that multiplication and division have the same precedence so you work from left to right, therefore the 48 is divided by 2 before the 2 is multiplied by the (9 + 3).

It's the difference between:

48
--- (9 + 3)
2

and

48
---
2(9 + 3)

The equation in the OP represents the first fraction and to make the second fraction you need brackets around (2(9+3)) not a multiplication symbol between 2 and (9+3). If anyone still doesn't believe me, try:

http://www.wolframalpha.com

and put in 48/2(9+3), then 48/2*(9+3). Then try 48/(2(9+3)) and 48/2(2*(9+3)) and look at the input part for all four and see which difference actually matters.

I'm not trying to sound all know-it-all 'cause if you look to the first part of the thread I'm the first one to get it wrong, but there have been quite a few posts now that proved and explained this point. I do admit if you don't use math a lot, and I certainly don't, without a multiplication symbol between the 2 and the parenthesis, it certainly feels (maybe feels is the wrong word) that 2 should be the right answer, but it 100% no question is wrong.

[kwamebargnani]

4/2(12) and 4/2x12 are two comepletely different things.

People who claim the answer is 288 is basically saying the answer for 4/4A is A which is wrong.

[Parthenon]

I can't believe this thread has gone on for so long ...

[kwamebargnani]

I can't believe this thread has gone on for so long ...

I saw a 22 pager on Bulls board on this exact same topic.

[Raider917]

is there a right answer?

[kwamebargnani]

is there a right answer?

It's 2, as the question is 48÷2(9+3), not 48÷2 x (9+3)

[Mike Hunt]

4/2(12) and 4/2x12 are two comepletely different things.

People who claim the answer is 288 is basically saying the answer for 4/4A is A which is wrong.

Wrong. These are exactly the same thing. The opening bracket is the equivalent of a multiplication sign.

The people who are getting "2" as the answer are treating "2" as a coefficient of "9+3". It isn't. 2 is not the coefficient in this case because there is a bracket. People who are getting "2" are seeing 2(9+3) as 2X where X represents "9+3" and "2" is its coefficient. The problem is that the equation is actually formatted this way 2(X). Now, I hope no one disputes this as it is plainly visible that the formula has brackets around the variable. If you're solving an equation, you're solving for X, you're not solving for (X).

Here's a test for you so that you can see what I mean with regards to how the coefficient thing people are doing works:

In the link provided (http://www.wolframalpha.com) enter the following formula:

48/2x=24

You can enter any number after the equal sign for the purpose of this test. Look at how the formula is displayed. You'll see that because, in this scenario, 2 is the coefficient for X, the denominator will contain "2X".

Now enter this formula:

48/2(X)=24

Which my previous paragraph demonstrates is the actual formula format we're dealing with (I'm not sneaking in any multiplication signs. This is essentially a direct copy of the equation at hand except with the addition an answer (any answer) after the equal sign for demonstration purposes).

Look at the resultant break down of the equation. Note that the "X" remains in the brackets and is not included in the denominator. That's because the open bracket "(" in an equation is to be treated the same way as a multiplication sign. 2X is not the same as 2(X) when the order of operations is concerned. One is a coefficient of X (which would get priority), whereas the other is simply the number by which X is being multiplied.

In the case of this specific equation, 2 is clearly not a coefficienent of our variable. It's as plain as day (the brackets are clearly there). As such, 2(X) does not get priority over the 48/2 part of the equation.

In your example, you said that saying the answer is 288 is the equivalent of saying 4/4A = A. As I've explained, the problem with that is that nowhere in the equation is there anything resembling 4A, there is only something that looks like 4(A). On an island, they're the same. In an equation, they're vastly different.

[evilRyu]

4/2(12) and 4/2x12 are two comepletely different things.

People who claim the answer is 288 is basically saying the answer for 4/4A is A which is wrong.

Wrong. These are exactly the same thing. The opening bracket is the equivalent of a multiplication sign.

The people who are getting "2" as the answer are treating "2" as a coefficient of "9+3". It isn't. 2 is not the coefficient in this case because there is a bracket. People who are getting "2" are seeing 2(9+3) as 2X where X represents "9+3" and "2" is its coefficient. The problem is that the equation is actually formatted this way 2(X). Now, I hope no one disputes this as it is plainly visible that the formula has brackets around the variable. If you're solving an equation, you're solving for X, you're not solving for (X).

Exactly. The "2" is not the coefficient, unless there are brackets wrapping the "2" and the (9+3) term, which Mike Hunt explained.

It's 2, as the question is 48÷2(9+3), not 48÷2 x (9+3)

The two expressions you typed are indeed the same. How are they not? When two terms are next to each other with no sign, multiplication is implied, just like:

abc = a*b*c = ab*c = a*bc

[Modern_epic]

Can we just all agree this is a crappily formatted question, because no one over 12 should be using the ÷ sign?

I can more or less promise you that is the issue here. People (for good reason) think that sign is always matched by x for multiplication. If you want to leave multiplication implied by brackets, it is always matched with / for division. Mixing the two gives the apperance of a coefficient. Kthnx?

[Blair]

The problem with your coefficient theory is that you are talking about 2x, when what you're actually dealing with in this specific example is 2(x). While they look similar and, isolated, give you the same results, when they are part of a larger operation, they are not necessarily the same. In order of operations, we're taught to treat brackets as multiplication which is why, when we see 2(x), we don't treat as 2x but rather as 2 * x.

Theory wouldn't be the right word to use. I'm merely explaining where coefficients fall in the order of operations (I should've mentioned however that exponents also come before coefficients - don't know how that slipped my mind originally). There's really no potential for this problem to confuse anyone once that is realized. This very issue (multiplication via juxtaposition and the precedence it's given) is a familiar one among mathematicians, and is becoming increasingly familiar to manufacturers of calculators as most graphing calcs these days will evaluate this as 2. You can't ignore the fact that math simply breaks down if you use rather ambiguous expressions or poor mathematical notation to try and justify splitting up singular terms such as ax², or 2.7m (m being metres), or 185lbs. If math really did work the way you argue it does, we'd never be able to factor equations or anything of the like. Simplify the 2(9 + 3) by undoing the 2 that got factored out and you have 48 / (18 + 6). I trust there'd be no debate over the answer to that one, correct? Sometimes a little common sense can be beneficial, even when it comes to mathematics.

Brackets are not meant as an interchangeable substitution for a multiplication sign, rather they're a means to give priority to other operations. 8 - (1 + 5) has nothing to do with multiplication yet the brackets impact significantly on the answer. I stand by my original post.

It's definitely 288. 2(12) is the same as saying 2 * 12. Therefore you would do the division beforehand since it appears first.

No, you would extract the bracket first, as that will always take precedence as per order of operations. If you are getting 288, you're not properly extracting the bracket before working with other numbers in the expression. If it's actually possible to simplify the expression first to the point where the brackets are dealt with and removed, and still somehow find a way to make this into 288, then I'm not seeing it.

[DonYon]

that's exactly what i was trying to say.

/thread please

[Raps in 4]

What's so hard to understand about this?

48
---
2(9 + 3)

Obviously 288. No way around it.

[Raider917]

What's so hard to understand about this?

48
---
2(9 + 3)

Obviously 288. No way around it.

this is what i think but not eveyone does. using bemdas and doing multiplying and division from left to right comes up with 288 for me.

[Modern_epic]

What's so hard to understand about this?

48
---
2(9 + 3)

Obviously 288. No way around it.

Umm... what you wrote there is actualy obviously 2. The original question was 288, but it is was by no means obvious due to mixing of different sets of symbols.

[Raps in 4]

What's so hard to understand about this?

48
---
2(9 + 3)

Obviously 288. No way around it.

Umm... what you wrote there is actualy obviously 2. The original question was 288, but it is was by no means obvious due to mixing of different sets of symbols.

No, if I wrote it as:

48
---
(2(9 + 3))

it would be 2. Otherwise it's 288. The (9+3) is multiplied against the entire fraction. It's the same as:

48
--- (9 + 3)
2

just like like satyr9 said.

[xAIRNESSx]

48
---
2(9 + 3)

and

48
---
(2(9 + 3))

are the same thing. You made (9+3) part of the denominator.

[Modern_epic]

^^What he said^^

You've turned it into a fraction, and clearly put 3+9 on the bottom of it. You alwas resolve both sides first in those situations.

[Raps in 4]

^^What he said^^

You've turned it into a fraction, and clearly put 3+9 on the bottom of it. You alwas resolve both sides first in those situations.

Putting it on the bottom doesn't make a difference if it doesn't have brackets around it. Multiplication is always against the entire fraction. Go ahead and try it in a scientific calculator.

You can write it as:

48(9 + 3)
---
2

and the answer will still be 288 because it's the same question. Whether the term being multiplied is in the numerator or the denominator doesn't matter unless it's within a bracket.

[spykelee]

The answer is:



































Who cares, STFU already!

[Mike Hunt]

The problem with your coefficient theory is that you are talking about 2x, when what you're actually dealing with in this specific example is 2(x). While they look similar and, isolated, give you the same results, when they are part of a larger operation, they are not necessarily the same. In order of operations, we're taught to treat brackets as multiplication which is why, when we see 2(x), we don't treat as 2x but rather as 2 * x.

Theory wouldn't be the right word to use. I'm merely explaining where coefficients fall in the order of operations (I should've mentioned however that exponents also come before coefficients - don't know how that slipped my mind originally). There's really no potential for this problem to confuse anyone once that is realized. This very issue (multiplication via juxtaposition and the precedence it's given) is a familiar one among mathematicians, and is becoming increasingly familiar to manufacturers of calculators as most graphing calcs these days will evaluate this as 2. You can't ignore the fact that math simply breaks down if you use rather ambiguous expressions or poor mathematical notation to try and justify splitting up singular terms such as ax²,

I don't think there is anything ambiguous as far as a bracket is concerned. It's there. We know what it does (isolates a part of an equation). We also know how it's treated as part of an equation. Coefficients get priority. I wholeheartedly agree with you on that point. 2x is one term and must be treated as such. It gets priority over any of the operations. 2(x) is not the same thing unfortunately. It'd be great if it was, but it isn't. People are changing this equation using common sense as an excuse. If people can disregard brackets, why don't we add them in a manner that shouldn't change a thing:

48/(2)(9+3) =

I think everybody on this board would agree the answer to that equation is 288. Unfortunately, I can't ignore that this is not the equation at hand.

I implore people to run the test I recommended. It's the easiest visualization of the fact that the bracket takes away any notion that "2(X)", which is exactly what this formula has, is the same as 2X.