48÷2(9+3)=?

[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.

I'm not sure what you meant to write here, but I can guess. It's kind of tricky, as rules seem slightly different for variables, but I would hazard a guess at yes. It's ambiguous either way, although the original question is much less so.

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.

You too are completely missing the point. The coefficient is not "part of the brackets". The coefficient is just multiplication. That's it. It doesn't get priority because it's "attached" to the brackets, it's just more multiplication. The coefficient here is 48/2, because the division is written first.

Also, in BIDMAS, or BEMDAS, or whatever you want to call it, the B does not mean "get rid of the brackets". It does not mean "expand the brackets". It means "solve everything inside the brackets". That's not an opinion, or ambiguous, that's just what it means.

There is nothing in the Axioms of algebra that says anything about Bodmas, pemdas or whatever.

Order of ops is important for kids. Important for computers (And even in programming it seems to be applied patchily with distributivity being applied before and after on the TI-85 and the TI-86 respectively).

Pemdas is not relevent when doing algebra.

I'm not sure most would agree that

A ÷ BD

does not equal

AD ÷ B

There should be brackets after the division symbol but I think the distribution of the 2 into the brackets is implied here.

I lean towards the answer being 2 but I would accept 288.

Why is the distribution implied? It's just multiplication. With symbols or letters it is less clear, but when you have numbers, there is no reason to assume that the multiplication takes preference.

But there is not reason to assume that division takes preference apart from PEMDAS which doesn't appear in any serious Algebreic text.

Edit. And are you saying the laws of one part of mathematics do not apply to others?

I'm not saying it takes preference; they have equal precedence, as they are essentially the same function. Therefore you go from left to right.

I'm not entirely sure of the rules, but Wolfram Alpha, for example, uses implied multiplication with variables but not the question of this thread.

How do variables make it different?

The laws of algebra are the same as the laws of arithmetic.

If:

A = 48,
B = 2,
D = (9 + 3) = 12

Then: A ÷ BD = 2

It is somewhat ambiguous but PEDMAS et al don't exist unless you're teaching a child or a computer what to do.

Look up Laws/Axioms of Algebra/Arithmetic. No statements about order of operations there. And for myself the lack of a symbol between 2 and (9 + 3) implies that the 2 is distributed in first.

 

[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.

So you're trying to tell me that


.........AC
A ÷ BC = --
.........B

No.

If it were

A ÷ B * C

I might agree.

I'm not sure what you meant to write here, but I can guess. It's kind of tricky, as rules seem slightly different for variables, but I would hazard a guess at yes. It's ambiguous either way, although the original question is much less so.

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.

You too are completely missing the point. The coefficient is not "part of the brackets". The coefficient is just multiplication. That's it. It doesn't get priority because it's "attached" to the brackets, it's just more multiplication. The coefficient here is 48/2, because the division is written first.

Also, in BIDMAS, or BEMDAS, or whatever you want to call it, the B does not mean "get rid of the brackets". It does not mean "expand the brackets". It means "solve everything inside the brackets". That's not an opinion, or ambiguous, that's just what it means.

There is nothing in the Axioms of algebra that says anything about Bodmas, pemdas or whatever.

Order of ops is important for kids. Important for computers (And even in programming it seems to be applied patchily with distributivity being applied before and after on the TI-85 and the TI-86 respectively).

Pemdas is not relevent when doing algebra.

I'm not sure most would agree that

A ÷ BD

does not equal

AD ÷ B

There should be brackets after the division symbol but I think the distribution of the 2 into the brackets is implied here.

I lean towards the answer being 2 but I would accept 288.

Why is the distribution implied? It's just multiplication. With symbols or letters it is less clear, but when you have numbers, there is no reason to assume that the multiplication takes preference.

But there is not reason to assume that division takes preference apart from PEMDAS which doesn't appear in any serious Algebreic text.

Edit. And are you saying the laws of one part of mathematics do not apply to others?

I'm not saying it takes preference; they have equal precedence, as they are essentially the same function. Therefore you go from left to right.

I'm not entirely sure of the rules, but Wolfram Alpha, for example, uses implied multiplication with variables but not the question of this thread.

How do variables make it different?

The laws of algebra are the same as the laws of arithmetic.

If:

A = 48,
B = 2,
D = (9 + 3) = 12

Then: A ÷ BD = 2

It is somewhat ambiguous but PEDMAS et al don't exist unless you're teaching a child or a computer what to do.

Look up Laws/Axioms of Algebra/Arithmetic. No statements about order of operations there. And for myself the lack of a symbol between 2 and (9 + 3) implies that the 2 is distributed in first.

I'm not sure on the variables thing. Perhaps I'm wrong about it, but you can put things into Wolfram and it gives different answers depending on whether or not you use variables, and I tend to trust Wolfram on things like this.

The lack of a symbol doesn't mean anything, it just means multiplication. Furthermore, you shouldn't be distributing anyway if you can simplify the inside of the brackets more.

 

[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.

I'm not sure what you meant to write here, but I can guess. It's kind of tricky, as rules seem slightly different for variables, but I would hazard a guess at yes. It's ambiguous either way, although the original question is much less so.

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.

You too are completely missing the point. The coefficient is not "part of the brackets". The coefficient is just multiplication. That's it. It doesn't get priority because it's "attached" to the brackets, it's just more multiplication. The coefficient here is 48/2, because the division is written first.

Also, in BIDMAS, or BEMDAS, or whatever you want to call it, the B does not mean "get rid of the brackets". It does not mean "expand the brackets". It means "solve everything inside the brackets". That's not an opinion, or ambiguous, that's just what it means.

There is nothing in the Axioms of algebra that says anything about Bodmas, pemdas or whatever.

Order of ops is important for kids. Important for computers (And even in programming it seems to be applied patchily with distributivity being applied before and after on the TI-85 and the TI-86 respectively).

Pemdas is not relevent when doing algebra.

I'm not sure most would agree that

A ÷ BD

does not equal

AD ÷ B

There should be brackets after the division symbol but I think the distribution of the 2 into the brackets is implied here.

I lean towards the answer being 2 but I would accept 288.

Why is the distribution implied? It's just multiplication. With symbols or letters it is less clear, but when you have numbers, there is no reason to assume that the multiplication takes preference.

But there is not reason to assume that division takes preference apart from PEMDAS which doesn't appear in any serious Algebreic text.

Edit. And are you saying the laws of one part of mathematics do not apply to others?

I'm not saying it takes preference; they have equal precedence, as they are essentially the same function. Therefore you go from left to right.

I'm not entirely sure of the rules, but Wolfram Alpha, for example, uses implied multiplication with variables but not the question of this thread.

How do variables make it different?

The laws of algebra are the same as the laws of arithmetic.

If:

A = 48,
B = 2,
D = (9 + 3) = 12

Then: A ÷ BD = 2

It is somewhat ambiguous but PEDMAS et al don't exist unless you're teaching a child or a computer what to do.

Look up Laws/Axioms of Algebra/Arithmetic. No statements about order of operations there. And for myself the lack of a symbol between 2 and (9 + 3) implies that the 2 is distributed in first.

I'm not sure on the variables thing. Perhaps I'm wrong about it, but you can put things into Wolfram and it gives different answers depending on whether or not you use variables, and I tend to trust Wolfram on things like this.

The lack of a symbol doesn't mean anything, it just means multiplication. Furthermore, you shouldn't be distributing anyway if you can simplify the inside of the brackets more.

But thats how the distributive law works.

A(3 + 9)= 3A + 9A = A(12) = 12A

See here it doesn't matter whether you process the inside of the brackets first or distribute first.

If you want to do it left to right like some sort of robot just because some computer programs do it fine but there is nothing that stipulates left to right in the Laws of Algebra and Arithmetic. PEMDAS etc etc is just a convention useful for teaching children and computers to to process arithmetic.

And thus because the format in the question is A(x + y) I would suggest that that implies that it is a single term.

If you wanted it your way it would be written

48(3 + 9) ÷ 2

 

[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.

So you're trying to tell me that


.........AC
A ÷ BC = --
.........B

No.

If it were

A ÷ B * C

I might agree.

I'm not sure what you meant to write here, but I can guess. It's kind of tricky, as rules seem slightly different for variables, but I would hazard a guess at yes. It's ambiguous either way, although the original question is much less so.

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.

You too are completely missing the point. The coefficient is not "part of the brackets". The coefficient is just multiplication. That's it. It doesn't get priority because it's "attached" to the brackets, it's just more multiplication. The coefficient here is 48/2, because the division is written first.

Also, in BIDMAS, or BEMDAS, or whatever you want to call it, the B does not mean "get rid of the brackets". It does not mean "expand the brackets". It means "solve everything inside the brackets". That's not an opinion, or ambiguous, that's just what it means.

There is nothing in the Axioms of algebra that says anything about Bodmas, pemdas or whatever.

Order of ops is important for kids. Important for computers (And even in programming it seems to be applied patchily with distributivity being applied before and after on the TI-85 and the TI-86 respectively).

Pemdas is not relevent when doing algebra.

I'm not sure most would agree that

A ÷ BD

does not equal

AD ÷ B

There should be brackets after the division symbol but I think the distribution of the 2 into the brackets is implied here.

I lean towards the answer being 2 but I would accept 288.

Why is the distribution implied? It's just multiplication. With symbols or letters it is less clear, but when you have numbers, there is no reason to assume that the multiplication takes preference.

But there is not reason to assume that division takes preference apart from PEMDAS which doesn't appear in any serious Algebreic text.

Edit. And are you saying the laws of one part of mathematics do not apply to others?

I'm not saying it takes preference; they have equal precedence, as they are essentially the same function. Therefore you go from left to right.

I'm not entirely sure of the rules, but Wolfram Alpha, for example, uses implied multiplication with variables but not the question of this thread.

How do variables make it different?

The laws of algebra are the same as the laws of arithmetic.

If:

A = 48,
B = 2,
D = (9 + 3) = 12

Then: A ÷ BD = 2

It is somewhat ambiguous but PEDMAS et al don't exist unless you're teaching a child or a computer what to do.

Look up Laws/Axioms of Algebra/Arithmetic. No statements about order of operations there. And for myself the lack of a symbol between 2 and (9 + 3) implies that the 2 is distributed in first.

I'm not sure on the variables thing. Perhaps I'm wrong about it, but you can put things into Wolfram and it gives different answers depending on whether or not you use variables, and I tend to trust Wolfram on things like this.

The lack of a symbol doesn't mean anything, it just means multiplication. Furthermore, you shouldn't be distributing anyway if you can simplify the inside of the brackets more.

But thats how the distributive law works.

A(3 + 9)= 3A + 9A = A(12) = 12A

See here it doesn't matter whether you process the inside of the brackets first or distribute first.

If you want to do it left to right like some sort of robot just because some computer programs do it fine but there is nothing that stipulates left to right in the Laws of Algebra.

And thus because the format in the question is A(x + y) I would suggest that that implies that it is a single term.

If you wanted it your way it would be written

48(3 + 9) ÷ 2

In that question, no, it does not matter whether you distribute or not. However, in the question of this thread, it does matter, but because the ambiguity is about what the coefficient is. If you distributed 48/2 into the brackets, you would get 288. My point was that being the next to the bracket doesn't by default give it priority as the coefficient.

I see your point about the left-to-right thing. I suppose there is no real answer, and that it is just terribly written - however, I see no real reason to consider 2 more correct than 288, whereas there are reasons to do it the other way around.

Why does writing it as A(x+y) suggest it's a single term? It's just multiplication.

It's not about wanting it 'my way', my point was just that writing it the way you just did doesn't change the meaning of the equation.

 

[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.

I'm not sure what you meant to write here, but I can guess. It's kind of tricky, as rules seem slightly different for variables, but I would hazard a guess at yes. It's ambiguous either way, although the original question is much less so.

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.

You too are completely missing the point. The coefficient is not "part of the brackets". The coefficient is just multiplication. That's it. It doesn't get priority because it's "attached" to the brackets, it's just more multiplication. The coefficient here is 48/2, because the division is written first.

Also, in BIDMAS, or BEMDAS, or whatever you want to call it, the B does not mean "get rid of the brackets". It does not mean "expand the brackets". It means "solve everything inside the brackets". That's not an opinion, or ambiguous, that's just what it means.

There is nothing in the Axioms of algebra that says anything about Bodmas, pemdas or whatever.

Order of ops is important for kids. Important for computers (And even in programming it seems to be applied patchily with distributivity being applied before and after on the TI-85 and the TI-86 respectively).

Pemdas is not relevent when doing algebra.

I'm not sure most would agree that

A ÷ BD

does not equal

AD ÷ B

There should be brackets after the division symbol but I think the distribution of the 2 into the brackets is implied here.

I lean towards the answer being 2 but I would accept 288.

Why is the distribution implied? It's just multiplication. With symbols or letters it is less clear, but when you have numbers, there is no reason to assume that the multiplication takes preference.

But there is not reason to assume that division takes preference apart from PEMDAS which doesn't appear in any serious Algebreic text.

Edit. And are you saying the laws of one part of mathematics do not apply to others?

I'm not saying it takes preference; they have equal precedence, as they are essentially the same function. Therefore you go from left to right.

I'm not entirely sure of the rules, but Wolfram Alpha, for example, uses implied multiplication with variables but not the question of this thread.

How do variables make it different?

The laws of algebra are the same as the laws of arithmetic.

If:

A = 48,
B = 2,
D = (9 + 3) = 12

Then: A ÷ BD = 2

It is somewhat ambiguous but PEDMAS et al don't exist unless you're teaching a child or a computer what to do.

Look up Laws/Axioms of Algebra/Arithmetic. No statements about order of operations there. And for myself the lack of a symbol between 2 and (9 + 3) implies that the 2 is distributed in first.

I'm not sure on the variables thing. Perhaps I'm wrong about it, but you can put things into Wolfram and it gives different answers depending on whether or not you use variables, and I tend to trust Wolfram on things like this.

The lack of a symbol doesn't mean anything, it just means multiplication. Furthermore, you shouldn't be distributing anyway if you can simplify the inside of the brackets more.

But thats how the distributive law works.

A(3 + 9)= 3A + 9A = A(12) = 12A

See here it doesn't matter whether you process the inside of the brackets first or distribute first.

If you want to do it left to right like some sort of robot just because some computer programs do it fine but there is nothing that stipulates left to right in the Laws of Algebra.

And thus because the format in the question is A(x + y) I would suggest that that implies that it is a single term.

If you wanted it your way it would be written

48(3 + 9) ÷ 2

In that question, no, it does not matter whether you distribute or not. However, in the question of this thread, it does matter, but because the ambiguity is about what the coefficient is. If you distributed 48/2 into the brackets, you would get 288. My point was that being the next to the bracket doesn't by default give it priority as the coefficient.

I see your point about the left-to-right thing. I suppose there is no real answer, and that it is just terribly written - however, I see no real reason to consider 2 more correct than 288, whereas there are reasons to do it the other way around.

Why does writing it as A(x+y) suggest it's a single term? It's just multiplication.

It's not about wanting it 'my way', my point was just that writing it the way you just did doesn't change the meaning of the equation.

There is no real reason. I'm mostly playing devils advocate

But it's not written 48/2(9+3). It's written 48 ÷ 2(9 + 3) and since past primary school the only place for a division symbol is the inversion of fractions. So to me this is the division of two fractions; 48/1 and 2(9 + 3)/1.

 

[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.

So you're trying to tell me that


.........AC
A ÷ BC = --
.........B

No.

If it were

A ÷ B * C

I might agree.

I'm not sure what you meant to write here, but I can guess. It's kind of tricky, as rules seem slightly different for variables, but I would hazard a guess at yes. It's ambiguous either way, although the original question is much less so.

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.

You too are completely missing the point. The coefficient is not "part of the brackets". The coefficient is just multiplication. That's it. It doesn't get priority because it's "attached" to the brackets, it's just more multiplication. The coefficient here is 48/2, because the division is written first.

Also, in BIDMAS, or BEMDAS, or whatever you want to call it, the B does not mean "get rid of the brackets". It does not mean "expand the brackets". It means "solve everything inside the brackets". That's not an opinion, or ambiguous, that's just what it means.

There is nothing in the Axioms of algebra that says anything about Bodmas, pemdas or whatever.

Order of ops is important for kids. Important for computers (And even in programming it seems to be applied patchily with distributivity being applied before and after on the TI-85 and the TI-86 respectively).

Pemdas is not relevent when doing algebra.

I'm not sure most would agree that

A ÷ BD

does not equal

AD ÷ B

There should be brackets after the division symbol but I think the distribution of the 2 into the brackets is implied here.

I lean towards the answer being 2 but I would accept 288.

Why is the distribution implied? It's just multiplication. With symbols or letters it is less clear, but when you have numbers, there is no reason to assume that the multiplication takes preference.

But there is not reason to assume that division takes preference apart from PEMDAS which doesn't appear in any serious Algebreic text.

Edit. And are you saying the laws of one part of mathematics do not apply to others?

I'm not saying it takes preference; they have equal precedence, as they are essentially the same function. Therefore you go from left to right.

I'm not entirely sure of the rules, but Wolfram Alpha, for example, uses implied multiplication with variables but not the question of this thread.

How do variables make it different?

The laws of algebra are the same as the laws of arithmetic.

If:

A = 48,
B = 2,
D = (9 + 3) = 12

Then: A ÷ BD = 2

It is somewhat ambiguous but PEDMAS et al don't exist unless you're teaching a child or a computer what to do.

Look up Laws/Axioms of Algebra/Arithmetic. No statements about order of operations there. And for myself the lack of a symbol between 2 and (9 + 3) implies that the 2 is distributed in first.

I'm not sure on the variables thing. Perhaps I'm wrong about it, but you can put things into Wolfram and it gives different answers depending on whether or not you use variables, and I tend to trust Wolfram on things like this.

The lack of a symbol doesn't mean anything, it just means multiplication. Furthermore, you shouldn't be distributing anyway if you can simplify the inside of the brackets more.

But thats how the distributive law works.

A(3 + 9)= 3A + 9A = A(12) = 12A

See here it doesn't matter whether you process the inside of the brackets first or distribute first.

If you want to do it left to right like some sort of robot just because some computer programs do it fine but there is nothing that stipulates left to right in the Laws of Algebra.

And thus because the format in the question is A(x + y) I would suggest that that implies that it is a single term.

If you wanted it your way it would be written

48(3 + 9) ÷ 2

In that question, no, it does not matter whether you distribute or not. However, in the question of this thread, it does matter, but because the ambiguity is about what the coefficient is. If you distributed 48/2 into the brackets, you would get 288. My point was that being the next to the bracket doesn't by default give it priority as the coefficient.

I see your point about the left-to-right thing. I suppose there is no real answer, and that it is just terribly written - however, I see no real reason to consider 2 more correct than 288, whereas there are reasons to do it the other way around.

Why does writing it as A(x+y) suggest it's a single term? It's just multiplication.

It's not about wanting it 'my way', my point was just that writing it the way you just did doesn't change the meaning of the equation.

There is no real reason. I'm mostly playing devils advocate

But it's not written 48/2(9+3). It's written 48 ÷ 2(9 + 3) and since past primary school the only place for a division symbol is the inversion of fractions. So to me this is the division of two fractions; 48/1 and 2(9 + 3)/1.

/ and ÷ mean the same thing when writing maths in this way. Again, my problem with the second part is that you are assuming the 2 to be part of the brackets, which I am not. It looks like that's the only thing we're disagreeing on.

 

[TiefBlau]

i'm starting to think you're deliberately being an idiot here. what the professor said was that the equation gives off an ambiguity because of the ÷ symbol, which he states is also why it isn't used anymore. setting up the equation with the dash-division sign is a much easier way of showing unambiguous statements.

Step 1) Show the "professor's" quote to your friend.
Step 2) Ask him if the professor is saying it's ambiguous.
Step 3) Slap yourself in the face for being so stupid.

Ask 5 people. Ask 50 people. No one will agree with you. Nowhere in that quote does he say anything about the symbol being ambiguous. That's utterly retarded.

the standard convention, if applied precisely and rigorously, does give an unambiguous procedure to follow

Just how the hell do you draw "the symbol is ambiguous" from that?

as far as i am concerned this topic was over right then and there. i'm not sure why you keep persisting as if there was something personal at stake, and if there is, it's none of my business. now please, go back to your highschool class.

I can practically smell your frustration from here. What, didn't expect me to call you out on your obvious lie? Care to draw attention away from it now?

I'd have no problem at all if you just admitted you were wrong, and that it was your own mistake. But you just can't do that, can you? That's so fucking pathetic. Grow up.

 

[TheKwertyeweyoppe]

BODMAS
brackets of divide multiply add subtract.
that's maths for a ten year old
(answer's 2 obviously)

I'm kinda sick of the people who come into this thread thinking it's simple maths and boasting about dumb we are while completely missing the point of the thread because I can only assume they didn't bother to read it.

1) It really IS simple maths.
2) missing the point of the thread am I? "is it 2 or 288?" I really don't see how...
3) I believe you meant to say 'about HOW dumb we are'. Believe that shows it didn't need saying...

1) You may have missed the many good explanations on how it is 288, in fact by your own logic (BODMAS) it is 288.

48 / 2 *(9+3)

Brackets
48 / 2 *(12),_____(9 + 3 = 12)

'of'(what?)

Divide,multiply (In order of appearance from left to right)
24 * (12),_____(48 / 2 = 24)
288,_____(24 * 12 = 288)

Addition, Subtraction (In order of appearance from left to right)
288,_____(Not applicable)

2) Fair point, I think the point of the thread was trolling so that was actually a dumb thing for me to say.

3) Oops, should have proofread that better.

 

[luke10123]

BODMAS
brackets of divide multiply add subtract.
that's maths for a ten year old
(answer's 2 obviously)

I'm kinda sick of the people who come into this thread thinking it's simple maths and boasting about dumb we are while completely missing the point of the thread because I can only assume they didn't bother to read it.

1) It really IS simple maths.
2) missing the point of the thread am I? "is it 2 or 288?" I really don't see how...
3) I believe you meant to say 'about HOW dumb we are'. Believe that shows it didn't need saying...

1) You may have missed the many good explanations on how it is 288, in fact by your own logic (BODMAS) it is 288.

48 / 2 *(9+3)

Brackets
48 / 2 *(12),_____(9 + 3 = 12)

'of'(what?)

Divide,multiply (In order of appearance from left to right)
24 * (12),_____(48 / 2 = 24)
288,_____(24 * 12 = 288)

Addition, Subtraction (In order of appearance from left to right)
288,_____(Not applicable)

2) Fair point, I think the point of the thread was trolling so that was actually a dumb thing for me to say.

3) Oops, should have proofread that better.

Okay here we go:

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

OR

48÷2(12)
48÷24
=2

with BODMAS it doesn't matter if you multiply or divide first. Some folk use BOMDAS instead. Think about it like: 48÷(2(9+3))

2/3) no worries mate, happens to the best of us!