48÷2(9+3)=?

[Thomas Rembrandt]

Some people's understanding of BIDMAS is shocking. When you take care of brackets, you do everything INSIDE the brackets. You don't expand them, you don't distribute them, you just do everything inside them. So you get:

48÷2(9+3) = 48÷2(12)

2(12) is EXACTLY THE SAME as 2x12. The brackets, at this point, are irrelevant. For people trying to subsitute x = 12 here, it doesn't work, as implied multiplication is a) ambiguous and b) works differently for variables.

Actually, I want to double check my work.

48/2(9+x)=2
48/(18+2x)=2
48=2(18+2x)
48=36+4x
48-36=4x
4x=12
x=3

Yup, still works.

/thread

No. You are completely missing the point of what everyone is saying. Even if you ignore the different rules for variables and constants, your maths is incorrect. Let's look at the first line:

48/2(9+x)=2

What you have done is distributed the 2 into the brackets. THIS IS INCORRECT. As this is multiplication, and not "part of the brackets", you have to do division and multiplication from left to right, as they have equal precedence. So rather than:

48/(18+2x)=2

you should have:

24(9+x)=2
216+24x = 2
24x = -214
x = -8.917

Which is not 3, obviously.

Despite your algebraic method, you are still falling for the trap that so many others are falling for, which is to assume that the 2 is part of the brackets, which is WRONG. Algebra does not make your answer more valid, especially when the core idea of the method, which happens to be what people have been trying to tell you is wrong, is completely overlooked.

So you're trying to tell me that

A ÷ BC

A
= -C
B

No.

If it were

A ÷ B * C

I might agree.

IT IS THE SAME! What do you think BC means for gods sake. It means B*C. Where did you hear otherwise??

A/ BC

A
= --- * C
B

or

A * 1 * C
= ---
B

Distributive law of multiplication states that BC cannot be separated on either side of the division sign. Thomas, you are saying that A/BC is the same as AC/B. And that is like saying A/B x C is the same as A/B x 1/C. Because by moving C from the bottom to the top, you are multiplying A/B by C's reciprocal and saying it equals the same. C does not equal 1/C, therefore A/B x C doesn't equal A/B x 1/C. And if you read left to right, like you are, that is what you are arguing for

Stupid formatation screwed it up. Maybe we were talking about the same thing the entire time *rolleyes*.

A/B = A * (1/B) that's what i'm saying. A * (B) * C can be arranged as you please.

 

[InfiniteSingularity]

Did you not read my post? I explained the logic. Let me give you another one of my many justifications as to why I am right:

BODMAS specifies brackets come before anything, right?

2(9+3) is one set of brackets. It is ONE TERM. You solve it ALL AT ONCE. And guess what? It equals 24.

I'm pretty sure we all agree on the simplification up to 48/2(12). Now tell me: Does 48/2(12) equal 48(12)/2? You are moving the 12 from the bottom to the top - you are, quite literally, changing the value of 1/12 into 12/1. You are saying 1/12 = 12. Does it? Because last time I checked it doesn't.

[EDITED typo]

See thar be the dragons... or rather there lies your problem.
You assume that 2(9+3) is single term. Assumptions are bad. Stop assuming. It's not one term.
48 is one term, 2 is other term (9+3) is third term. For 2(9+3) to be single term it has to be in brackets itself, that's what the brackets are for.

And yes. 48:2*12 = 48*12:2. Both return 288. Magick! You do not move anything from bottom to top however because you have no fractions here. If you want to write it as fraction you write it as
48
-- * (9+3) = 288
2

And as a final argument... Variables i choose you!
Solve x in:
48:2(x+3) = 2
and
48:2(x+3) = 288

2(9+3) is part of "Brackets" in BODMAS. Yes, even the 2 is part of it. So by definition, it is one term. Because the brackets are evaluated before anything else. And 2(9+3) = 24. You do not half-expand the brackets, by saying it equals 2 times 12, then moving the 2 to the other side of the division.

Remember that 2 is the coefficient of (9+3), so it is ALWAYS bound to (9+3). When you take it out in your fraction, you are separating it from it's coefficient. Or with the distributive law of multiplication, you are moving the 12 to the other side of the division sign, which doesn't work. So either way you are doing it wrong.

 

[ACman]

A coefficient is multiplied by a variable (i.e. (9+3) ). I don't understand where you learnt otherwise. Is that a new rule? "Coefficient goes first", that's nonsense. Multiplication and Division are equal and to be read left ro right.

I don't add anything to the equation just by adding a * . Do you think that coefficient has some magical abilities? There already is a multiplication going on, the convenient notation simply does not show them.

Multiplication and Division are equal, yes, and do read left to right. But Brackets are before both. So you expand brackets first.

Why do you expand brackets, rather than evaluate them? Because when there is ambiguity with the latter, the former is a proven consistent rule which will always work no matter what.

Here extension you talk about: 2(x+y) = 2x+2y

But inside a formula you have to put brackets around the whole thing to be valid.

backwards this would be:

5/(2x +2y) can be written as 5/(2(x+y)). See the extra bracket? There is no magical bond between the bracket and its coefficient.

Yes there is.

How about this.

48 ÷ 7A

is it then equal to

48A ÷ 7

No.

A ÷ BC

doe not equal

AC ÷ B

 

[JoshGod]

you couldn't accept the draw could you? very well then, in a mathematical equation, a coefficient is a constant by which a variable is multiplied. Hence there is a multiplication between the 2 and the (9+3)... Also why do i get the feeling i'm being trolled?

Well then, if you admit that the (9+3) must be multiplied by the coefficient, which is 2, then you also admit that the answer is 2, correct? If the answer was 288 then the coefficient would have to be (48 ÷ 2), rather than the 48 ÷ 2.

I was arguing that there is a multiplication between the 2 and the 12 generating 48÷2*12.

 

[The Unworthy Gentleman]

I was arguing that there is a multiplication between the 2 and the 12 generating 48÷2*12.

You were right, we will never see eye to eye on this thing. I think we best call this one a draw.

 

[bliebblob]

I know what it is: TERRIBLE NOTATION. That's what it is.

There is no correct answer. The whole BEDMAS or Order of Operations thing is primarily based on custom and is taught differently in different parts of the world. The question uses that to be ambiguous, it is not a "real" mathematical question so much as hook to try and start semantical arguements based on pointless mathematical principles that nobody above the age of 12 should be bothering with.

TLR It's a troll thread.

Exactly what these two said folks. Not only is this a horrible math problem when it comes to putting it together, it's also the umpteenth time I've seen a thread like this on here just made to piss people off.

That's what I was gonna say at first too because it is clearly posted with the intention of starting an argument.
However, ambigious would mean it can be read in 2 ways and neither would be wrong. This isn't the case here: there IS a right way and a wrong way. The right way is just easily confused with the wrong way because of the way it is written.

 

[Thomas Rembrandt]

A coefficient is multiplied by a variable (i.e. (9+3) ). I don't understand where you learnt otherwise. Is that a new rule? "Coefficient goes first", that's nonsense. Multiplication and Division are equal and to be read left ro right.

I don't add anything to the equation just by adding a * . Do you think that coefficient has some magical abilities? There already is a multiplication going on, the convenient notation simply does not show them.

Multiplication and Division are equal, yes, and do read left to right. But Brackets are before both. So you expand brackets first.

Why do you expand brackets, rather than evaluate them? Because when there is ambiguity with the latter, the former is a proven consistent rule which will always work no matter what.

Here extension you talk about: 2(x+y) = 2x+2y

But inside a formula you have to put brackets around the whole thing to be valid.

backwards this would be:

5/(2x +2y) can be written as 5/(2(x+y)). See the extra bracket? There is no magical bond between the bracket and its coefficient.

Yes there is.

How about this.

48 ÷ 7A

is it then equal to

48A ÷ 7

No.

48 ÷ 7A

= 48 * (1/7)*A = 48A * (1/7)

Honestly and without any mean sprits: you are doing it wrong. Go ask your teacher or google "order of operations". There is no mention of some magical coefficients (because all they are are numbers who are multiplied by variables).

 

[InfiniteSingularity]

A coefficient is multiplied by a variable (i.e. (9+3) ). I don't understand where you learnt otherwise. Is that a new rule? "Coefficient goes first", that's nonsense. Multiplication and Division are equal and to be read left ro right.

I don't add anything to the equation just by adding a * . Do you think that coefficient has some magical abilities? There already is a multiplication going on, the convenient notation simply does not show them.

Multiplication and Division are equal, yes, and do read left to right. But Brackets are before both. So you expand brackets first.

Why do you expand brackets, rather than evaluate them? Because when there is ambiguity with the latter, the former is a proven consistent rule which will always work no matter what.

Here extension you talk about: 2(x+y) = 2x+2y

But inside a formula you have to put brackets around the whole thing to be valid.

backwards this would be:

5/(2x +2y) can be written as 5/(2(x+y)). See the extra bracket? There is no magical bond between the bracket and its coefficient.

Um, there is, that is the definition of a coefficient. And as I said, Brackets are solved first. So when you see 2(9+3) ANYWHERE in ANY equation, by definition the 2 is multiplied by the bracket. And it will always be multiplied by the bracket. It doesn't matter in what context.

By separating the bracket from it's coefficient the question does not equate. But let's try another approach

Let (9+3) = x

48/2x = 2

48 = 4x

x = 12

x = (9+3)

Equation is true for solution 2

48/2x = 288

48 = 576x

1 = 12x (divided both sides by 48)

x = 1/12

Equation is NOT true for solution 288

So by reducing the equation to it's simplest algebraic for, by letting the bracket equal x, I have solved it. The answer can only be 2. And it cannot be disputed, as I have used simple, straightforward algebra. For the answer to be 288, the LHS would need to be (48/2)x. And this means the OP's question would need to be (48/2)(9+3)

 

[Morti]

Hmm, just thought I'd drop in what Wikipedia has to say on this (yes I know it's not the font of all knowledge).

"An expression like 1/2x is interpreted as 1/(2x) by TI-82, but as (1/2)x by TI-83.[2] While the first interpretation may be expected by some users, only the latter is in agreement with the standard rules stated above."

From http://en.wikipedia.org/wiki/BODMAS

 

[Keava]

2(9+3) is part of "Brackets" in BODMAS. Yes, even the 2 is part of it. So by definition, it is one term. Because the brackets are evaluated before anything else. And 2(9+3) = 24. You do not half-expand the brackets, by saying it equals 2 times 12, then moving the 2 to the other side of the division.

Remember that 2 is the coefficient of (9+3), so it is ALWAYS bound to (9+3). When you take it out in your fraction, you are separating it from it's coefficient. Or with the distributive law of multiplication, you are moving the 12 to the other side of the division sign, which doesn't work. So either way you are doing it wrong.

I have no damn idea what BODMAS is because in my times, in my country they didn't teach using mnemonics. Want to know why? Because mnemonics are not rules. They taught me, however, how to solve math problems.

2 is not part of any brackets. 2 is 2. Noting more, nothing less. Solve the x in my post and you will see.

Your way i guess you would do:
48:2(x+3) = 2
48:2x+6 = 2 | -6
48:2x = 2 - 6
48:2x = -4
and.. it would be that x has to be negative number.
The only way it would work is if 2(x+3) was written as [2(x+3)] since then you would have
482x+6) = 2 so 48 = 2(2x+6) so 48 = 4x + 12 so 4x = 36
When you drop brackets you can't suddenly create another set out of nowhere. It's not how mathematics work.

Now 48:2(x+3) = 288
24(x+3)=288
24x+72=288 | -72
24x=216 | :24
x = 9

Magick.

 

[bliebblob]

Did you not read my post? I explained the logic. Let me give you another one of my many justifications as to why I am right:

BODMAS specifies brackets come before anything, right?

2(9+3) is one set of brackets. It is ONE TERM. You solve it ALL AT ONCE. And guess what? It equals 24.

I'm pretty sure we all agree on the simplification up to 48/2(12). Now tell me: Does 48/2(12) equal 48(12)/2? You are moving the 12 from the bottom to the top - you are, quite literally, changing the value of 1/12 into 12/1. You are saying 1/12 = 12. Does it? Because last time I checked it doesn't.

[EDITED typo]

See thar be the dragons... or rather there lies your problem.
You assume that 2(9+3) is single term. Assumptions are bad. Stop assuming. It's not one term.
48 is one term, 2 is other term (9+3) is third term. For 2(9+3) to be single term it has to be in brackets itself, that's what the brackets are for.

And yes. 48:2*12 = 48*12:2. Both return 288. Magick! You do not move anything from bottom to top however because you have no fractions here. If you want to write it as fraction you write it as
48
-- * (9+3) = 288
2

And as a final argument... Variables i choose you!
Solve x in:
48:2(x+3) = 2
and
48:2(x+3) = 288

2(9+3) is part of "Brackets" in BODMAS. Yes, even the 2 is part of it. So by definition, it is one term. Because the brackets are evaluated before anything else. And 2(9+3) = 24. You do not half-expand the brackets, by saying it equals 2 times 12, then moving the 2 to the other side of the division.

Remember that 2 is the coefficient of (9+3), so it is ALWAYS bound to (9+3). When you take it out in your fraction, you are separating it from it's coefficient. Or with the distributive law of multiplication, you are moving the 12 to the other side of the division sign, which doesn't work. So either way you are doing it wrong.

hear hear!
Like I said earlier: step one is getting rid of the brackets.And getting rid of them or only solving everything between them are not the same thing. In most cases they are, but in this case you have to apply the distributive law of multiplication or you will not have removed them properly.

Also:
48:2(x+3) = 2
48=2*2(x+3) why? because 2(x+3) is a single term, just as 3x is.
48/4=x+3
12=x+3
12-3=x
9=x

 

[Thomas Rembrandt]

A coefficient is multiplied by a variable (i.e. (9+3) ). I don't understand where you learnt otherwise. Is that a new rule? "Coefficient goes first", that's nonsense. Multiplication and Division are equal and to be read left ro right.

I don't add anything to the equation just by adding a * . Do you think that coefficient has some magical abilities? There already is a multiplication going on, the convenient notation simply does not show them.

Multiplication and Division are equal, yes, and do read left to right. But Brackets are before both. So you expand brackets first.

Why do you expand brackets, rather than evaluate them? Because when there is ambiguity with the latter, the former is a proven consistent rule which will always work no matter what.

Here extension you talk about: 2(x+y) = 2x+2y

But inside a formula you have to put brackets around the whole thing to be valid.

backwards this would be:

5/(2x +2y) can be written as 5/(2(x+y)). See the extra bracket? There is no magical bond between the bracket and its coefficient.

Um, there is, that is the definition of a coefficient. And as I said, Brackets are solved first. So when you see 2(9+3) ANYWHERE in ANY equation, by definition the 2 is multiplied by the bracket. And it will always be multiplied by the bracket. It doesn't matter in what context.

By separating the bracket from it's coefficient the question does not equate. But let's try another approach

Let (9+3) = x

48/2x = 2

48 = 4x

x = 12

x = (9+3)

Equation is true for solution 2

48/2x = 288

48 = 576x

1 = 12x (divided both sides by 48)

x = 1/12

Equation is NOT true for solution 288

So by reducing the equation to it's simplest algebraic for, by letting the bracket equal x, I have solved it. The answer can only be 2. And it cannot be disputed, as I have used simple, straightforward algebra. For the answer to be 288, the LHS would need to be (48/2)x. And this means the OP's question would need to be (48/2)(9+3)

48/2x = 288 |*2

48x = 576 | /48

x = 12


OK, lets end this, we obviously are victims of acii code here. You just see the formula as 48/(2x) while i see 48/2*x whith each operation done left to right (according to the rules).

 

[JoshGod]

I was arguing that there is a multiplication between the 2 and the 12 generating 48÷2*12.

You were right, we will never see eye to eye on this thing. I think we best call this one a draw.

I would have agreed to draw, but then i saw this XD

 

[ACman]

A coefficient is multiplied by a variable (i.e. (9+3) ). I don't understand where you learnt otherwise. Is that a new rule? "Coefficient goes first", that's nonsense. Multiplication and Division are equal and to be read left ro right.

I don't add anything to the equation just by adding a * . Do you think that coefficient has some magical abilities? There already is a multiplication going on, the convenient notation simply does not show them.

Multiplication and Division are equal, yes, and do read left to right. But Brackets are before both. So you expand brackets first.

Why do you expand brackets, rather than evaluate them? Because when there is ambiguity with the latter, the former is a proven consistent rule which will always work no matter what.

Here extension you talk about: 2(x+y) = 2x+2y

But inside a formula you have to put brackets around the whole thing to be valid.

backwards this would be:

5/(2x +2y) can be written as 5/(2(x+y)). See the extra bracket? There is no magical bond between the bracket and its coefficient.

Yes there is.

How about this.

48 ÷ 7A

is it then equal to

48A ÷ 7

No.

48 ÷ 7A

= 48 * (1/7)*A = 48A * (1/7)

Honestly and without any mean sprits: you are doing it wrong. Go ask your teacher or google "order of operations". There is no mention of some magical coefficients (because all they are are numbers who are multiplied by variables).

You're adding a multiplication sign.

48 ÷ 7A is the same as 48 ÷ (7A). The multiplication is implied to have already occured.

 

[bliebblob]

Your way i guess you would do:
48:2(x+3) = 2
48:2x+6 = 2 | -6
48:2x = 2 - 6
48:2x = -4
and.. it would be that x has to be negative number.
The only way it would work is if 2(x+3) was written as [2(x+3)] since then you would have
482x+6) = 2 so 48 = 2(2x+6) so 48 = 4x + 12 so 4x = 36
When you drop brackets you can't suddenly create another set out of nowhere. It's not how mathematics work.

the third line is wrong
This would be clear if you wrote above and below lines instead of everything in one line so I'll try to do so as best as I can in this texthingy:

48:2(x+3)=2 is the same as
48
-------- = 2 because 2(x+3) is a single term, just as 3x
2(x+3)

48
-------- = 2
2x+6

Hopefully now you see you cannot move the 6 to the other side as -6. You have to move the entire lower part to the other side as *(2x+6)

 

[InfiniteSingularity]

2(9+3) is part of "Brackets" in BODMAS. Yes, even the 2 is part of it. So by definition, it is one term. Because the brackets are evaluated before anything else. And 2(9+3) = 24. You do not half-expand the brackets, by saying it equals 2 times 12, then moving the 2 to the other side of the division.

Remember that 2 is the coefficient of (9+3), so it is ALWAYS bound to (9+3). When you take it out in your fraction, you are separating it from it's coefficient. Or with the distributive law of multiplication, you are moving the 12 to the other side of the division sign, which doesn't work. So either way you are doing it wrong.

I have no damn idea what BODMAS is because in my times, in my country they didn't teach using mnemonics. Want to know why? Because mnemonics are not rules. They taught me, however, how to solve math problems.

2 is not part of any brackets. 2 is 2. Noting more, nothing less. Solve the x in my post and you will see.

Your way i guess you would do:
48:2(x+3) = 2
48:2x+6 = 2 | -6
48:2x = 2 - 6
48:2x = -4
and.. it would be that x has to be negative number.
The only way it would work is if 2(x+3) was written as [2(x+3)] since then you would have
482x+6) = 2 so 48 = 2(2x+6) so 48 = 4x + 12 so 4x = 36
When you drop brackets you can't suddenly create another set out of nowhere. It's not how mathematics work.

Now 48:2(x+3) = 288
24(x+3)=288
24x+72=288 | -72
24x=216 | :24
x = 9

Magick.

No, I would go

48:2(x+3) = 2
48:2x+6 = 2
2x+6:48 = 1:2 (note that when in an equation, taking the reciprocal of BOTH sides retains the equality. And i did use 2x+6 as one whole term)
2x+6 = 48:2
2x = 24 - 6
x = 18/2 = 9

The "extra set of brackets" you refer to is implied in the brackets - as 2 is multiplied by (x+3) by definition it is part of the bracket. So 2(x+3) is the denominator underneath 48.

And BODMAS is a fundamental rule for solving linear equations. So you solve the brackets first. Which means OP's question should be resolved to 48/24 which equals 2.

 

[ACman]

Gentlemen we have been trolled.

http://knowyourmeme.com/memes/48293

 

[Keava]

No, I would go

48:2(x+3) = 2
48:2x+6 = 2
2x+6:48 = 1:2 (note that when in an equation, taking the reciprocal of BOTH sides retains the equality. And i did use 2x+6 as one whole term)
2x+6 = 48:2
2x = 24 - 6
x = 18/2 = 9

But it's not a whole term. That's the point. It's not 482x+6) it's 48:2x+6. There is a huge difference between the two, difference that the brackets are used for. You pretty much added those brackets despite them not existing in original calculation.

What you did was taking 2*2+1 and turning it into 2(2+1). See the difference?

 

[bliebblob]

Gentlemen we have been trolled.

http://knowyourmeme.com/memes/48293

I knew it was a troll question from the start but like I told the other guy who said so:
I'm pretty sure it IS correct form. Just really easily confused. A few extra brackets would have been nice to avoid confusion though.
It's like in chemistry where you can (for example) leave out the number that indicates where the Cl atom is located on a molecule because it can't be in any other spot anyway. ( because of certain properties of the molecule etc.)
It is correct form but you have to be pretty good at chemisty to just instantly see the H atom can only be in that spot. So not leaving the number out is just best to avoid confusion.
It's the same story here (I think): they left out some brackets in a way that is legit, because it can still only be interpreted in one way, but it makes confusion much more likely.

 

[ACman]

I still think that the multiplication is implied.

So 2.