48÷2(9+3) = ????

[mallorquin]

You're so corny that its beyond words. Get a life..... But wait, let me guess you have a wonderful life and any of us could only wish to trade places with you.

I dont have to lie to you about shit nigga. As I look back nigga even told me, "A few of these examples support your position".. How would could I have missed that?

Wish and could are two different things. What I said was couldn't, or could not. You probably did alright in junior high or high school math. You probably never made it to intermediate algebra or anything, if you did it was a long time ago.

If you only knew how obvious it is to see.

I also told you that some of the examples supported your conclusion. The irony of that situation is that you didn't even understand the logic behind, or in your words, "These examples have nothing to do with the original problem", even though we know later that you would lie about seeing them. You said this, even when they did support you.

You are so dumb, that you could not see the relationship between them and your conclusion.

This information was spoon-fed to your black ass, this morning, causing you to come to your more neutral stance.

And I agree, you had no reason to lie. But you sure did last night.

What is it going to take to get you to understand that you failed?

I won't stop.

How about some answers?

 

[Rick Spanish]

Wish and could are two different things. What I said was couldn't, or could not. You probably did alright in junior high or high school math. You probably never made it to intermediate algebra or anything, if you did it was a long time ago.

If you only knew how obvious it is to see.

I also told you that some of the examples supported your conclusion. The irony of that situation is that you didn't even understand the logic behind, or in your words, "These examples have nothing to do with the original problem", even though we know later that you would lie about seeing them. You said this, even when they did support you.

You are so dumb, that you could not see the relationship between them and your conclusion.

This information was spoon-fed to your black ass, this morning, causing you to come to your more neutral stance.

And I agree, you had no reason to lie. But you sure did last night.

What is it going to take to get you to understand that you failed?

I won't stop.

How about some answers?

I do not have a neutral stance. Its a conflicted stance. I stand by the way I was taught and the answer remains 2. I only said I understood the rationale that made people think otherwise.

What will make you understand that you're a petty, corny, pathetic, waste of life that should just go die immediately?

 

[mallorquin]

You're so corny that its beyond words. Get a life..... But wait, let me guess you have a wonderful life and any of us could only wish to trade places with you.

I dont have to lie to you about shit nigga. As I look back nigga even told me, "A few of these examples support your position".. How would could I have missed that?

You can call me corny and tell me to get a life, but the face of the matter is that your black ass is in here with me, going back and forth. I started in here on Sat. I'm almost certain that you were in here before me.

So coming here and going back and forth is that much of a waist of time for you, I would expect that you won't post anything else in here.

You will though because, it's really not about me getting a life. That is just something that you have been forced to say to me because you are not able really dispute any of the dumb shit that you have said in this post, that has been echoed and laughed at since 4:36 est from yesterday.

Your not on my level bro. Don't engage me anymore, and I will leave it alone.

Don't say anything else to me.

 

[mallorquin]

I do not have a neutral stance. Its a conflicted stance. I stand by the way I was taught and the answer remains 2. I only said I understood the rationale that made people think otherwise.

What will make you understand that you're a petty, corny, pathetic, waste of life that should just go die immediately?

If you read what I said, I said "More neutral", not neutral as in right in the middle. You started off, all the way in left field, now you are closer to center field.

Do you understand there is a difference?

Probably not...

 

[mallorquin]

You gonna go get that life yet? Probably not.

You will be back in 3,2,1....

 

[jam hunk]

arent you supposed to do whats in the parenthesis first, then whatever the squares or roots, then multiplication or division, the adding and subtracting?

i mean its been a LONG time since i did 6th grade math...and i NEED to relearn this shit now that i got a kid.

 

[Louis Koo]

damn you guys got too much time. i've stated my case and made some funny pshops. since then, i've been operating by this maxim.

 

[mallorquin]

Gonna call it a nite for today.

I will see what kinda bullshit the two dumbasses come up with in the morning. Or if they are still dancing around questions.

 

[WorldEX]

Common shorthand is B. E. D. M. A. S. which is: brackets, exponents, division & multiplication, addition & subtraction.


48÷2(9+3) =? Solving inside the bracket first
48÷2(12) = (following BEDMAS-we still have to get rid of brackets..the only way is by multiplying with the 2.
now you get this: 48÷24 = 2

 

[followup]

Follow up, once again you re cherry picking . In the example above you are confusing yourself.

Let me break down this problem and set you straight.

62-2(5-1)^2+1

**random bullshit**

And once again, provide ANOTHER source, preferably two, that states implicit multiplication takes precedence over both explicit multiplication and division.

You came to the same conclusion as me. You have to realize that I have provided a source of someone who lists her credentials. The fact that you people keep asking for 'sources' when plenty have been provided shows that you will NEVER learn how to solve this problem. Just be thankful that you no longer have to take math classes because you will fail. You should have learned a decade or more ago that you finish all equations involving the parentheses (simplifyas some have called it) before you do anything else. You use PEMDAS until the parentheses are gone AND THEN you move on. Thanks. For those who would like to learn how to perform basic math calculations, keep learning. We are up to 60%, good job guys

 

[followup]

Common shorthand is B. E. D. M. A. S. which is: brackets, exponents, division & multiplication, addition & subtraction.


48÷2(9+3) =? Solving inside the bracket first
48÷2(12) = (following BEDMAS-we still have to get rid of brackets..the only way is by multiplying with the 2.
now you get this: 48÷24 = 2

Thank you.

Has been stated multiple times by multiple people. Doesn't matter what profession one is in, or how many degrees. if you did not learn this simple rule, you will get the wrong answer.

 

[followup]

To that i say this

48÷2(9+3)

is 48÷2*(9+3)

and that is exactly why you get the wrong answer. PEMDAS. Get rid of the parentheses first.

 

[Nobody]

You do not "get rid of" the brackets. You simply simplify or solve what's WITHIN the brackets first.

Similarly, care must be exercised when using the slash ('/') symbol. The string of characters "1/2x" is interpreted by the above conventions as (1/2)x. The contrary interpretation should be written explicitly as 1/(2x). Again, the use of brackets will clarify the meaning and should be used if there is any chance of misinterpretation.

consider x to be (9+3).

 

[Nobody]

You came to the same conclusion as me. You have to realize that I have provided a source of someone who lists her credentials. The fact that you people keep asking for 'sources' when plenty have been provided shows that you will NEVER learn how to solve this problem. Just be thankful that you no longer have to take math classes because you will fail. You should have learned a decade or more ago that you finish all equations involving the parentheses (simplifyas some have called it) before you do anything else. You use PEMDAS until the parentheses are gone AND THEN you move on. Thanks. For those who would like to learn how to perform basic math calculations, keep learning. We are up to 60%, good job guys

You don't realize the fundamental difference between

62-2(5-1)^2+1

and

48÷2(9+3)

Keep going with the condescending tone, it only makes you look like an complete fool.

 

[Nobody]

Now, arguing over whether implied multiplication takes precedence over multiplication and division is one thing

but to continue to argue (foolishly) that the goal of the order of operations is to "get rid of" the parentheses is a completely different thing.

It's a means of simplification.

So you know that the equation is 48÷2(9+3) and not 48÷2*9+3

THAT is what the order of operations sets out to clarify!

And to "get rid of" parentheses all you have to do is:

48÷2(9+3)

48÷2(12)

48÷2*12

VOILA!

 

[followup]

How the FUCK is this thread 53 PAGES!!!!!?????

even ELMO knnows the correct answer

If theres +50 pages about this on hundreds of websites wouldnt you think that confirms this as being ambiguous.

Nope. It means that 'people' do not know basic math.

The distributive property of multiplication CLEARLY states that the 2(9+3) is an entire statement and CANNOT be broken up. 2(9+3) follows the distributive entire statement and CANNOT be broken up. 2(9+3) follows the distributive entire statement and CANNOT be broken up. 2(9+3) follows the distributive property which can be rewritten as (2*9+2*3). Let me repeat the 2 outside of the parenthesis follows the distributive property of multiplication and must be factored and simplified before performing any other operations on it. You do NOT compute this expression from left to right until you use Algebra to simplify the statement 2(9+3). statement 2(9+3) So this can be rewritten as 48 / (2*9 + 2*3) Which leaves us with 48 / 24 = 2 Answer = 2 Lastly for those using Google or any other online calculator. These do not understand many theorems or properties so you must explicitly explain what you mean. There is a difference between 48 / 2 * (9+3) and 48 / 2(9+3). The first notation reads 48 / 2 * 1(9+3) while the second reads 48 / (2*9+2*3). Be very notation reads 48 / 2 * 1(9+3) while the second reads 48 / (2*9+2*3). Be very careful with your signs

This is how I learned it.

From yahoo

LS

THANKS AGAIN!!!

My Dear Aunt Sally is rolling over in her grave right about now.

Some people are taught differently.

You should be able to use PEMDAS as well

Typically, theres never a division sign in front of a implied multiplication problem

False. Some of us solved dozens, hundreds of problems just like this in our childhood. There is NO ambiguity in this problem. You and others are taking the route of defense attorneys and trying to introduce some sort of 'reasonable doubt' to save face. However, it is not working and BGOLers are learning to process the problem the correct way...

Also for the 288'ers

48÷a(9+3)=288
48÷a(9+3)=2

Please solve then come back here.

Equation 1. 48÷a(9+3)=288
Solve the parentheses: 48/a(12)=288-->48/12a=288
Multiply both sides by 12a: 48=288(12a)=3456a
Divide both sides by 3456: a=0.01388

Equation 2. 48÷a(9+3)=2
Solve the parentheses: 48/a(12)=2-->48/12a=2
Multiply both sides by 12a: 48=2(12a)=24a
Divide both sides by 24: 48/24=a
a=2
Thanks for this definitive answer to the original problem. Very creative way to show that there is no way that 288 can be the answer to the original problem.

What's especially embarrassing about this is that if you look up threads about this problem on predominantly white boards, most of the respondents arrived at the correct answer, 288.

Niggas.

A few things to note. In your world, 'white is right'. Unfortunately, white AMERICANS definitely should not be the standard to which you aspire when it comes to math and science. Maybe that's why you got the wrong solution. Lastly, because of your flawed way of thinking you are doubly incorrect: wrong answer to the problem and self hatred

THANK FUCKING YOU

HOW THE FUCK THIS THREAD GOT TO 53 PAGES

it's hilarious to me!!! people talking about how their career involves math and they are getting basic math wrong.

Wow. 54 pages. This thread needs to go down into the BGOL Hall of Fame.

Absolutely....people are thinking...however incorrect their thinking may be...

MAANNNN! i thank all you dumb mufuhs that picked 2. cause all of you made me realize that im smart as hell. fools still trying to come up with this answer wen it should take about 3 seconds CMON SON!

IRONY!!!!!

THIS IS SOO FUCKED UP

IT DOESN'T MATTER WHAT THE ANSWER IS!!!!!!

HOW HAS THIS EFFECTED YOUR LIFE?

CAN THE ANSWER TO THIS QUESTION SOLVE ANY OF THE WORLD PROBLEM

WILL THE NUCLEAR REACTORS IN JAPAN COOL ANY FASTER IF THE ANSWER IS 288

WILL KHADAFI LEAVE POWER IN LIBYA IF THE ANSWER IS 2

Ummmmm....and what has YOUR post contributed to anything? Why are you even on BGOL instead of fighting world wars? one of the most retarded questions asked on BGOL all the time.

 

[Rick Spanish]

What you did was apply Multiplication, and not use implied Multiplication to remove the Parentheses. When you simplify the × is never added to the problem. Its implied to simplify the Parentheses.

Now, arguing over whether implied multiplication takes precedence over multiplication and division is one thing

but to continue to argue (foolishly) that the goal of the order of operations is to "get rid of" the parentheses is a completely different thing.

It's a means of simplification.

So you know that the equation is 48÷2(9+3) and not 48÷2*9+3

THAT is what the order of operations sets out to clarify!

And to "get rid of" parentheses all you have to do is:

48÷2(9+3)

48÷2(12)

48÷2*12

VOILA!

 

[followup]

You do not "get rid of" the brackets. You simply simplify or solve what's WITHIN the brackets first.

consider x to be (9+3).

FAIL.

You don't realize the fundamental difference between

and

Keep going with the condescending tone, it only makes you look like an complete fool.

Riiiiiiight.

Now, arguing over whether implied multiplication takes precedence over multiplication and division is one thing

but to continue to argue (foolishly) that the goal of the order of operations is to "get rid of" the parentheses is a completely different thing.

It's a means of simplification.

So you know that the equation is 48÷2(9+3) and not 48÷2*9+3

THAT is what the order of operations sets out to clarify!

And to "get rid of" parentheses all you have to do is:

48÷2(9+3)

48÷2(12)

48÷2*12

VOILA!

who said PEMDAS is a way of getting rid of the parentheses? I said you apply PEMDAS to parentheses. If you have a part of a problem that looks like this: 4(8)^2, do you perform the exponent first or the multiplication by 4 first? Don't try to twist what I typed, thanks

Secondly, if you STILL think that the times sign has the same priority as parentheses when you have more than 2 orders of operation, you will never learn. By simply removing the parentheses and adding in another sign, you are changing the problem. An equation is written the way it is supposed to be solved. To remove the parentheses, you must multiply the 2 throughout it.

 

[tre2k4]

Yeah I was posting facts instead of force feeding one particular answer. But no matter what I post, people will disregard it because it makes them wrong, even disagreeing with professors and texts, and other reputable sources.

 

[Nobody]

FAIL.

Riiiiiiight.

who said PEMDAS is a way of getting rid of the parentheses? I said you apply PEMDAS to parentheses. If you have a part of a problem that looks like this: 4(8)^2, do you perform the exponent first or the multiplication by 4 first? Don't try to twist what I typed, thanks

Secondly, if you STILL think that the times sign has the same priority as parentheses when you have more than 2 orders of operation, you will never learn. By simply removing the parentheses and adding in another sign, you are changing the problem. An equation is written the way it is supposed to be solved. To remove the parentheses, you must multiply the 2 throughout it.

the Parentheses in multiplication is simply the alternate of using "x" to avoid confusion in algebra.

The asterisk is another alternate, as well as the middle dot " • "you see sometimes.

It doesn't have a higher ranking than * or "x" or •

It's simply another way to write it.

This notation can also be used for quantities that are surrounded by parentheses (e.g. 5(2) or (5)(2) for five times two)

It's not "another sign" it's an alternate.

2*(9+3) = 2(9+3) = 2 x (9+3) = 2•(9+3)

In the end, the reality is the equation is written in a way that can be mis interpreted.

But the argument you're holding now about "getting rid of" parentheses is just ridiculous.

 

[misterX]

I was going to stay out of this but...

An example:

3 * ( 5 + 8 ) - 22 / 4 + 3

Parenthesis first: 5 + 8 = 13

3 * 13 - 22 / 4 + 3

Exponent next: square the 2 or 22 = 4

3 * 13 - 4 / 4 + 3

Multiplication and Division next (3 * 13) (4 / 4)
left to right:

39 - 1 + 3

Addition and Subtraction next
left to right:

39 - 1 + 3 = 41

Note that we first subtracted 1 from 39 (left to right!),
then added the 3 for the correct answer, 41.
from http://www.studygs.net/pemdas/

When expressions have more than one operation, we have to follow rules for the order of operations:

First do all operations that lie inside parentheses.
Next, do any work with exponents or radicals.
Working from left to right, do all multiplication and division.
Finally, working from left to right, do all addition and subtraction.

http://www.math.com/school/subject2/lessons/S2U1L2GL.html#sm1

Math expressions are evaluated from left to right and order of operations (PEMDAS) are used for hierarchy only. Thus...

48/2(9+3)

Parens are removed once the expression within has been evaluated

= 48/2*12

Working from left to right, do all multiplication and division

= 24*12 = 288.

 

[Rick Spanish]

It's not "another sign" it's an alternate.

2*(9+3) = 2(9+3) = 2 x (9+3) = 2•(9+3)

In the end, the reality is the equation is written in a way that can be mis interpreted.

But the argument you're holding now about "getting rid of" parentheses is just ridiculous.

"Getting rid of" the parentheses is basically simplifying. Now simplifying is ridiculous?

 

[followup]

Yeah I was posting facts instead of force feeding one particular answer. But no matter what I post, people will disregard it because it makes them wrong, even disagreeing with professors and texts, and other reputable sources.

Just like others have posted sources and you disagreed with them. The difference is that you are wrong to say that there is ambiguity in the original problem. There is none.

the Parentheses in multiplication is simply the alternate of using "x" to avoid confusion in algebra.

The asterisk is another alternate, as well as the middle dot " • "you see sometimes.

It doesn't have a higher ranking than * or "x" or •

It's simply another way to write it.

It's not "another sign" it's an alternate.

2*(9+3) = 2(9+3) = 2 x (9+3) = 2•(9+3)

In the end, the reality is the equation is written in a way that can be mis interpreted.

But the argument you're holding now about "getting rid of" parentheses is just ridiculous.

LOL!!! You thinking the 'argument' is ridiculous is why you are incorrect in solving the problem. #1. I am not making an argument. I am stating a fact. #2. Like, I said, there is a difference between multiplication next to a parenthesis and a times sign there. Hence, the term IMPLIED multiplication. These terms are not just there for convenience. Use them correctly and don't put signs in the equation that were not there to begin with and you will get the correct answer every time

 

[tre2k4]

the Parentheses in multiplication is simply the alternate of using "x" to avoid confusion in algebra.

The asterisk is another alternate, as well as the middle dot " • "you see sometimes.

It doesn't have a higher ranking than * or "x" or •

It's simply another way to write it.



It's not "another sign" it's an alternate.

2*(9+3) = 2(9+3) = 2 x (9+3) = 2•(9+3)

In the end, the reality is the equation is written in a way that can be mis interpreted.

But the argument you're holding now about "getting rid of" parentheses is just ridiculous.

Yeah and what Im posting below is legit as well

Distributive Property

The distributive property is actually a very simply concept to learn and apply. It will allow you to simplify something like 3(6x + 4), where you have a number being multiplied by a set of parenthesis. Let's start with a simple problem:

6(4 + 2)

Based on the order of operations, you know that anything inside parenthesis should be done first. Adding 4 + 2 is simple enough, resulting in this:

6(6)

When you see a number next to parenthesis like this, it means multiplication, so what we really have here is this (remember that * means multiplication):

6 * 6 = 36

That was easy enough, but what about a more difficult problem? Let's suppose that the 4 was really 4x, meaning 4 times the variable x. The distributive property allows you to simplify an expression like this, where you cannot just do the parenthesis and multiply.

6(4x + 2)

What this expression seems to say is that we want 6 times the sum of 4x + 2. It can also be expressed in a different way using the distributive property:

(6 * 4x) + (6 * 2)

We can do this because with 6(4x + 2), the 6 is distributed to the 4x and the 2. That expression can now be simplified to 24x + 12, which is easier to use that the original 6(4x + 2). Now try simplifying this expression:

-2(4y - 8)

This is no more difficult so simplify than the last one. Just distribute the -2 to the 4y and the -8:

(-2 * 4y) + (-2 * -8)
-8y + 16
16 - 8y

http://www.freemathhelp.com/distributive-property.html

 

[Nobody]

"Getting rid of" the parentheses is basically simplifying. Now simplifying is ridiculous?

It is not simplifying if you're breaking the basic rules of order of operations man.

 

[Rick Spanish]

You created Multiplication that wasn't there. You applied it, when the multiplication is implied in this equation.

I was going to stay out of this but...

An example:

3 * ( 5 + 8 ) - 22 / 4 + 3

Parenthesis first: 5 + 8 = 13

3 * 13 - 22 / 4 + 3

Exponent next: square the 2 or 22 = 4

3 * 13 - 4 / 4 + 3

Multiplication and Division next (3 * 13) (4 / 4)
left to right:

39 - 1 + 3

Addition and Subtraction next
left to right:

39 - 1 + 3 = 41

Note that we first subtracted 1 from 39 (left to right!),
then added the 3 for the correct answer, 41.
from http://www.studygs.net/pemdas/

When expressions have more than one operation, we have to follow rules for the order of operations:

First do all operations that lie inside parentheses.
Next, do any work with exponents or radicals.
Working from left to right, do all multiplication and division.
Finally, working from left to right, do all addition and subtraction.

http://www.math.com/school/subject2/lessons/S2U1L2GL.html#sm1

Math expressions are evaluated from left to right and order of operations (PEMDAS) are used for hierarchy only. Thus...

48/2(9+3)

Parens are removed once the expression within has been evaluated

= 48/2*12

Working from left to right, do all multiplication and division

= 24*12 = 288.

 

[followup]

I was going to stay out of this but...

An example:

3 * ( 5 + 8 ) - 22 / 4 + 3

PAUSE. we have stated multiple times that a times sign being there DEPRIORITIZES multiplying something by the parentheses. You simply solve what's inside and then go left to right. This is not a good problem to compare to the original problem.

 

[followup]

Yeah and what Im posting below is legit as well

hard headed

 

[Nobody]

Just like others have posted sources and you disagreed with them. The difference is that you are wrong to say that there is ambiguity in the original problem. There is none.

LOL!!! You thinking the 'argument' is ridiculous is why you are incorrect in solving the problem. #1. I am not making an argument. I am stating a fact. #2. Like, I said, there is a difference between multiplication next to a parenthesis and a times sign there. Hence, the term IMPLIED multiplication. These terms are not just there for convenience. Use them correctly and don't put signs in the equation that were not there to begin with and you will get the correct answer every time

Find me more sources where it states that implied multiplication takes precedence over multiplication and division besides that picture posted.

If it was a fact, then this shouldn't be difficult at all. Back up your stance with further proof beyond what you claim, and you will have proved it.

Also, you're constantly talking PEMDAS, but note it doesn't account for implied multiplication. Funny how that would be left out, eh?

 

[Rick Spanish]

It is not simplifying if you're breaking the basic rules of order of operations man.

No one is breaking the rules of the Order of Operations. You're just creating something that's not there.


Its right in front of your eyes fam. Read this carefully...

 

[tre2k4]

Im not against any source. I even posted information that supported both answers. Heres so more info.

As written, your expression

ax/by

should be evaluated left to right: a times x, divided by b, times y.
The multiplication is not done before the division, but both are done
in the order they appear. Your first solution is right.

Some texts make a rule, as in your second solution, that
multiplication without a symbol ("implied multiplication") should be
done before any other operations in an expression, including "explicit
multiplication" using a symbol. Following this rule, you would
multiply a by x, then multiply b and y, then divide one by the other.
Some (probably most) texts don't mention such a rule - but some of
those may use it without saying so, which is far worse.

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.

The problem here is that the expression looks as if it were meant to
be

ax
----
by

In the Dr. Math FAQ about writing math in e-mail, one of our
recommendations is to use parentheses wherever possible to avoid
ambiguity, even where the rules should make it clear, because it can
be easy to forget them in some situations

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

 

[followup]

Find me more sources where it states that implied multiplication takes precedence over multiplication and division besides that picture posted.

If it was a fact, then this shouldn't be difficult at all. Back up your stance with further proof beyond what you claim, and you will have proved it.

Also, you're constantly talking PEMDAS, but note it doesn't account for implied multiplication. Funny how that would be left out, eh?

Once again, I have posted LOTS of sources in this thread and will not do it any more. From now on, I am only teaching and solving problems.

The part of PEMDAS that deals with implied multiplication is the P: PARENTHESES. Thanks for making me state the obvious. I don't mind.

EDIT: all of the sources I posted showed that you get rid of the parentheses before you can solve the problems.

 

[misterX]

PAUSE. we have stated multiple times that a times sign being there DEPRIORITIZES multiplying something by the parentheses. You simply solve what's inside and then go left to right. This is not a good problem to compare to the original problem.

4*2 or 4(2) is still 4 multiplied by 2 ... you cannot use the distributive property on "2(9+3)" because you have not evaluated what is in the parens and therefore have defied PEMDAS. Once you have evaluated what is in the parens then it become multiplication and must be evaluated from left to right. Therefore the problem is simplified to 48/2*12 and from that to 24*12 which is 288.

 

[tre2k4]

Microcomputers and teachers

 

[followup]

4*2 or 4(2) is still 4 multiplied by 2 ... you cannot use the distributive property on "2(9+3)" because you have not evaluated what is in the parens and therefore have defied PEMDAS. Once you have evaluated what is in the parens then it become multiplication and must be evaluated from left to right. Therefore the problem is simplified to 48/2*12 and from that to 24*12 which is 288.

You may have missed it, but I have explained it several times.

In the examples you posted, there is only one operation. So they are the same problem. You most definitely CAN solve 2(9+3) with the distributive property:
2(9+3)
(18+6)
24...

EDIT: 2 multiplied by parentheses is an operation involving the parentheses, therefore you ARE using PEMDAS...