48÷2(9+3)=?

[InfiniteSingularity]

48/2(12) =/= 48/2x12. The first one is dividing 48 by 2 x 12. The second one is multiplying 48/2 by 12. The first gives an answer of 2. The second gives an answer if 288.
However the question gave us brackets in the denominator - the answer is 2

Since when 48/2(12) is not equal to 48/2*12? What different mathematics they teach in your country? 2*2 is same as (2)(2).

Again. Let's try to make it simpler to understand the logic.

a=48 b=2 c=9+3

a:bc = a:b*c =/= abc)

Also, keep in mind that division is just multiplication by reverse. a:b = a(1/b) = a * (1/b)

so 48:2(9+3) = 48(1:2)(9+3) = 48*0.5*12 = 288

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]

 

[The Unworthy Gentleman]

Fine, if your interpretation of 2(x+y) is not the same as 2*(x+y) then you'r right, but the international standard is different. You see ÷2(9+3) as one function (apparently) while the standard is 48 op1 2 op2 (9 op3 3) meaning 3 functions, with multiplication and division beeing equal and to be read left to right.

You're right, my interpretation of 2(x+y) is not the same as my interpretation of 2*(x+y) and neither should yours, otherwise I doubt every other countries mathematics. 2(x+y) is all one number, unlike 2*(x+y) because that is two numbers separated by a function. While they produce the same result on their own, they produce wildly different numbers when applied. This is exactly why you never add functions to an equation willy nilly, like those who got 288 did.

The order of operations is right, but your application of functions is wrong. It should have went 48 op1 2(9 op2 3).

 

[InfiniteSingularity]

You are suggesting that 48/2(9+3) is the same as 48(9+3)/2.

Yes i do. 48*(9+3)/2 = 48 * (9+3)* 0.5 and equals 288 as well.

I don't know what you learnt, but i think you misunderstand what a coefficient is. Usually we have equations like 2x + 3y where it is clear what numbers are bound to which variables.

In the OP's equation we have to remember how the basic notations work. 3x/2 is just 3 * x * 0.5.

You are wrong, sorry.

48-----1---------48----(9+3)
---- x ----- =/= ------ x -----
2-----(9+3)------2------1

This is your fatal error, and i'm afraid it's pretty significant

EDIT: 2(x+y) is one term, is it not? Isn't 2 the coefficient of the bracket? And does it not equal 2x + 2y?

Now lets substitute x and y with, say, 9 and 3

2(9+3) = 2x9 + 2x3. This is 18 + 6 - which is 24.

That SINGLE TERMis the denominator - so quite clearly this is 48/24 which is 2

 

[The Unworthy Gentleman]

It is apparant to me that you think think 2(12) are grouped while I think that because there is no bracket around them and that you can rewrite 2(12) as 2*(12) that they must be considered seperately instead of a single entity. I doubt we will see eye to eye however i'm sure we can agree the question should be written as either (48÷2)(9+3) or 48÷(2(9+3)). lets just agree the question is stupid.

I'm afraid I can't do that Dave Josh. It is one number because the 2 is a coefficient and there is no operation between them, where x = 12 2x = 2(12)... c'mon, argue with me. Okay, I'll let you go, you were a worthy foe.

 

[Thomas Rembrandt]

You are suggesting that 48/2(9+3) is the same as 48(9+3)/2.

Yes i do. 48*(9+3)/2 = 48 * (9+3)* 0.5 and equals 288 as well.

I don't know what you learnt, but i think you misunderstand what a coefficient is. Usually we have equations like 2x + 3y where it is clear what numbers are bound to which variables.

In the OP's equation we have to remember how the basic notations work. 3x/2 is just 3 * x * 0.5.

You are wrong, sorry.

48-----1---------48----(9+3)
---- x ----- =/= ------ x -----
2-----(9+3)------2------1

This is your fatal error, and i'm afraid it's pretty significant

I don't know what you mean. That's like telling me 2+2 is not 2-2. I never said your strange equation there. (i use the star * as multiplication, maybe you misinterpreted my equation).

 

[InfiniteSingularity]

You are suggesting that 48/2(9+3) is the same as 48(9+3)/2.

Yes i do. 48*(9+3)/2 = 48 * (9+3)* 0.5 and equals 288 as well.

I don't know what you learnt, but i think you misunderstand what a coefficient is. Usually we have equations like 2x + 3y where it is clear what numbers are bound to which variables.

In the OP's equation we have to remember how the basic notations work. 3x/2 is just 3 * x * 0.5.

You are wrong, sorry.

48-----1---------48----(9+3)
---- x ----- =/= ------ x -----
2-----(9+3)------2------1

This is your fatal error, and i'm afraid it's pretty significant

I don't know what you mean. That's like telling me 2+2 is not 2-2. I never said your strange equation there. (i use the star * as multiplication, maybe you misinterpreted my equation).

I'm pretty sure 4 isn't 0. And I understood the star * as multiplication. You just don't understand that multiplying something by 1/12 is not the same as multiplying it by 12/1.

Also read my edit to that post

2(x+y) is one term, is it not? Isn't 2 the coefficient of the bracket? And does it not equal 2x + 2y?

Now lets substitute x and y with, say, 9 and 3

2(9+3) = 2x9 + 2x3. This is 18 + 6 - which is 24.

That SINGLE TERM is the denominator - so quite clearly this is 48/24 which is 2

 

[RA92]

It's 2.

I'm Asian.

You're wrong.

 

[Magnatek]

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.

 

[InfiniteSingularity]

You are suggesting that 48/2(9+3) is the same as 48(9+3)/2.

Yes i do. 48*(9+3)/2 = 48 * (9+3)* 0.5 and equals 288 as well.

I don't know what you learnt, but i think you misunderstand what a coefficient is. Usually we have equations like 2x + 3y where it is clear what numbers are bound to which variables.

In the OP's equation we have to remember how the basic notations work. 3x/2 is just 3 * x * 0.5.

You are wrong, sorry.

48-----1---------48----(9+3)
---- x ----- =/= ------ x -----
2-----(9+3)------2------1

This is your fatal error, and i'm afraid it's pretty significant

I don't know what you mean. That's like telling me 2+2 is not 2-2. I never said your strange equation there. (i use the star * as multiplication, maybe you misinterpreted my equation).

I take no credit of this, but it explains it better than i can:

The distributive property of multiplication CLEARLY states that the 2(9+3) is an entire term 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.

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 careful with your signs.

 

[Cerdog]

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.

 

[Thomas Rembrandt]

You are suggesting that 48/2(9+3) is the same as 48(9+3)/2.

Yes i do. 48*(9+3)/2 = 48 * (9+3)* 0.5 and equals 288 as well.

I don't know what you learnt, but i think you misunderstand what a coefficient is. Usually we have equations like 2x + 3y where it is clear what numbers are bound to which variables.

In the OP's equation we have to remember how the basic notations work. 3x/2 is just 3 * x * 0.5.

You are wrong, sorry.

48-----1---------48----(9+3)
---- x ----- =/= ------ x -----
2-----(9+3)------2------1

This is your fatal error, and i'm afraid it's pretty significant

I don't know what you mean. That's like telling me 2+2 is not 2-2. I never said your strange equation there. (i use the star * as multiplication, maybe you misinterpreted my equation).

I'm pretty sure 4 isn't 0. And I understood the star * as multiplication. You just don't understand that multiplying something by 1/12 is not the same as multiplying it by 12/1.

Also read my edit to that post

2(x+y) is one term, is it not? Isn't 2 the coefficient of the bracket? And does it not equal 2x + 2y?

Now lets substitute x and y with, say, 9 and 3

2(9+3) = 2x9 + 2x3. This is 18 + 6 - which is 24.

That SINGLE TERM is the denominator - so quite clearly this is 48/24 which is 2

2(x+y) does equal 2x+2y, of course. But 0.5*4(x+y) equals 2x+2y as well, right? Regardless how you write it. Could be 4*0.5(x+y). Like in the OP equation.

What i am saying: Division by 2 EQUALS Multiplication by the half. I think this is pretty understandable. QED: 48/2(9+3) = 48*0.5*(9+3).

 

[JoshGod]

It is apparant to me that you think think 2(12) are grouped while I think that because there is no bracket around them and that you can rewrite 2(12) as 2*(12) that they must be considered seperately instead of a single entity. I doubt we will see eye to eye however i'm sure we can agree the question should be written as either (48÷2)(9+3) or 48÷(2(9+3)). lets just agree the question is stupid.

I'm afraid I can't do that Dave Josh. It is one number because the 2 is a coefficient and there is no operation between them, where x = 12 2x = 2(12)... c'mon, argue with me. Okay, I'll let you go, you were a worthy foe.

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?

 

[ACman]

You are suggesting that 48/2(9+3) is the same as 48(9+3)/2.

Yes i do. 48*(9+3)/2 = 48 * (9+3)* 0.5 and equals 288 as well.

I don't know what you learnt, but i think you misunderstand what a coefficient is. Usually we have equations like 2x + 3y where it is clear what numbers are bound to which variables.

In the OP's equation we have to remember how the basic notations work. 3x/2 is just 3 * x * 0.5.

You are wrong, sorry.

48-----1---------48----(9+3)
---- x ----- =/= ------ x -----
2-----(9+3)------2------1

This is your fatal error, and i'm afraid it's pretty significant

I don't know what you mean. That's like telling me 2+2 is not 2-2. I never said your strange equation there. (i use the star * as multiplication, maybe you misinterpreted my equation).

Thomas, you're confusing

A ÷ BC

= A * 1/BC
=A/BC

with

A ÷ B * C

=A * 1/B * C
=AC/B

Here 2 is the coefficient of the brackets so 48 is divided by the 2(9 + 3)

The 2 is a coefficient, it goes first. You can even process it before adding the 9 and the 3.

48 ÷ 2(9 + 3)
=48 ÷ (18 + 6)
=48 ÷ 24
=2

You're changing the equation by adding a multiplication operator.

 

[Glademaster_v1legacy]

Right so it can be read as 48/2*(9+3) which is 48/2*12 then with order of operations taking / as standard division symbol and not a fraction line it is 288. You are taking it as though it would be a fraction line so we have 48 over 2*12 which does give 2. So yes it is ambiguous. You can chop and change it whatever way you like but standard order does not favour you but algebra shows you as right. What we need is more brackets and stop this shit everytime someone rehashes this flamebaiting thread.

My issue is not with the division symbol at all. My issue is that people are dismissing coefficients altogether. The 2 is a coefficient of (9+3) and not as something to divide the 48 by.

2x
It's plain to see that the coefficient of x is 2, correct? And that 2x can be rewritten as 2(x)? Because 2*x is 2x. So:

20 ÷ 2x can be rewritten as 20 ÷ 2(x)
So, with the same principle you applied to before you could say that

20 ÷ 2x = (20 ÷ 2)(x)
If x = 4 then

20 ÷ 2(4) = (20 ÷ 2)(4)
2.5 =/= 40

So you can't separate the coefficient from it's partner because they are very much glued together.

This is why the answer must be 2. If the coefficient is disregarded and a function is added in like dividing the 48 by 2 then the answer will be changed drastically.

No see you're just not getting it yes your answer is perfectly fine but if you go with order of operations you end up with 288. Regardless of how you see it in your mind this what you are doing and it is the same as think it is under a fraction line. Now you can quote me all you like after this I don't care but I refuse to add another post in the mountain of crap and epeen stroking that becomes every iteration of this thread.

Last thing I will say is another pair of brackets are needed to rule out ambiguity. There are so many different ways of looking at the damn thing I can't believe people bite on this troll topic every damn time. For fuck sake is being right on the internet of all places so damn important? You people are making me a sad panda.

 

[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.

 

[Morti]

Also why do i get the feeling i'm being trolled?

Because you are. The best answer to this problem is to slap the OP and tell it to come back when it can express the equation in a way which cannot be misinterpreted.

 

[ACman]

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


.........AC
A ÷ BC = --
.........B

No.

If it were

A ÷ B * C

I might agree.

 

[InfiniteSingularity]

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 what you're saying is that expanding brackets doesn't work...right? Because I'm pretty sure that's what you're saying.

48/2(9+x)=2

Yes, when you have multiplication and division you read it left to right. But brackets trumps all. Why? Because that is the whole point of brackets. So you do solve the brackets first. And when you have a pronumeral in the brackets (WHICH INCLUDES THE COEFFICIENT) what do you do? You expand.

48/x(9+3)=2
48/9x+3x=2
48/12x=2
48=24x
2=x

x/2(9+3) = 2
x/24 = 2
x = 48

See, everytime I solved the brackets first. And I got 2 as the final result to OPs question. Because brackets comes before division and multiplication, and so when you have brackets like that you cannot read left to right.

With fractions you do not read left to right, or top to bottom - you solve whatever comes first.

 

[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

1
--- * A * C
B

EDIT: FORMATATION was screwed up.

 

[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.