It is bad maths to write such a non-algebraic sum without an operator between the number and the bracket, therefore the result is ambiguous. Please refine the question before answering.
I give up. Can't be bothered to explain this to people who can't listen and be taught anything.Believe whatever the hell you want. I, and a lot of others know the answer is 2.
The very fact that there is no sign between the 2 and the brackets means that the 2 belongs to the brackets.
People need to realise that BODMAS/BIDMAS is not the only mathematical theory going on here. There is also algebra to think of.
EDIT (less confusing explanation)
There is no multiplication sign to be put between the 2 and the brackets. 2(9+3) does not mean 2 x (9+3). It means (2x9)+(2x3). Anyone who has successfully studied algebra will know this.
Sorry, that's just not true: 2(9+3) really does mean 2 x (9+3). And taken as an expression on its own it also means (2 x 9) + (2 x 3):
a(b + c) = a x (b + c) = (a x b) + (a x c)
We can hopefully all agree on that. The problem is that some of you are taking the above and forgetting the wider context of the original question, and you are assuming that because the 2 is next to the brackets it somehow 'belongs' to the expression inside the brackets. That assumption is simply not correct.
48 ÷ 2(9+3) is simple short-hand for 48 ÷ 2 x (9+3). And, using BODMAS and left-to-right precedence (recall that multiplication and division have equal precedence), the answer is 288.
Again, for the avoidance of doubt: omitting the multiplication sign between the 2 and the brackets does emphatically not imply that the 2 is in any sense linked to the brackets in a way which trumps the rules of precedence.
(Qualification: maths degree; not that it matters because this is not grad-level maths. For those inclined to doubt my assertions, and indeed the rules of precedence themselves, I suggest that you post this question on a maths forum)
The very fact that there is no sign between the 2 and the brackets means that the 2 belongs to the brackets.
No, that's wrong. BODMAS doesn't say that, nor is there anything else in maths which says that. All the brackets say is to calculate what is inside them first.
Out of interest, what is "z" in the following equation?
z = 4y ÷ 2y
Is it
a) 2
or
b) 2y^2
If you think the answer to the OP is 288, then I presume you would also go for b) here.
Why? Because, replacing the immediate multipliers with a multiply sign (and I'll use "*" instead of "x"), you have:
z = 4 * y ÷ 2 * y
Breaking it down with left-to-right precedence for multiplication and division:
4 * y ÷ 2 = 2y
2y * y = 2y^2
But if you consider "2y" to be an immediate multiplier (and "2(12)" to be the same), then suddenly your answer is different.
Out of interest, what is "z" in the following equation?
z = 4y ÷ 2y
The spaces are potentially confusing and could be wrongly taken to imply brackets around the 2y, so let's write it as
4y÷2*y
which is two times y squared.
Out of interest, what is "z" in the following equation?
z = 4y ÷ 2y
Is it
a) 2
or
b) 2y^2
If you think the answer to the OP is 288, then I presume you would also go for b) here.
Why? Because, replacing the immediate multipliers with a multiply sign (and I'll use "*" instead of "x"), you have:
z = 4 * y ÷ 2 * y
Breaking it down with left-to-right precedence for multiplication and division:
4 * y ÷ 2 = 2y
2y * y = 2y^2
But if you consider "2y" to be an immediate multiplier (and "2(12)" to be the same), then suddenly your answer is different.
It is bad maths to write such a non-algebraic sum without an operator between the number and the bracket, therefore the result is ambiguous. Please refine the question before answering.
Best answer so far. The question was posed in very sloppy notation. In "grown up" maths the "÷" sign is rarely used anyway.
The spaces are potentially confusing and could be wrongly taken to imply brackets around the 2y, so let's write it as
4y÷2*y
which is two times y squared.
Spaces imply absolutely nothing in algebraic equations (as long as there is an operator on at least one side of a space).
Comments
In algebra you should treat 2(9+3) as (2x(9+3)) not 2x(9+3)
therefore expanding the original question 48÷2(9+3) you get
48÷(2x(9+3))
If you want 288 then it should be written
(48÷2)x(9+3)
Exactly this. This is why I was on about algebra to start with! Glad someone else is thinking like me lol
2x(9+3) does not give 18+ 6 ever
it gives 2x (12)
2 lots of (9+3)
mean exactly the same as:
2x(9+3)
?
a(b+c) means exactly the same thing as ax(b+c) (x being a multplication sign of course)
and
2(9+3)
means exactly the same as
2x(9+3)
which is
2x12
Sorry, that's just not true: 2(9+3) really does mean 2 x (9+3). And taken as an expression on its own it also means (2 x 9) + (2 x 3):
a(b + c) = a x (b + c) = (a x b) + (a x c)
We can hopefully all agree on that. The problem is that some of you are taking the above and forgetting the wider context of the original question, and you are assuming that because the 2 is next to the brackets it somehow 'belongs' to the expression inside the brackets. That assumption is simply not correct.
48 ÷ 2(9+3) is simple short-hand for 48 ÷ 2 x (9+3). And, using BODMAS and left-to-right precedence (recall that multiplication and division have equal precedence), the answer is 288.
Again, for the avoidance of doubt: omitting the multiplication sign between the 2 and the brackets does emphatically not imply that the 2 is in any sense linked to the brackets in a way which trumps the rules of precedence.
(Qualification: maths degree; not that it matters because this is not grad-level maths. For those inclined to doubt my assertions, and indeed the rules of precedence themselves, I suggest that you post this question on a maths forum)
? = 48 ÷ 2(9+3)
? = 48 ÷ 2(12)
? x 2(12) = 48
? x 24 = 48
? = 48 ÷ 24
? = 2
But my calculator makes it 2
Me too, just seeing how much confusion there can be.
This is simple arithmetic, god help us if someone comes up with a maths puzzler.
2.
BODMAS
Brackets Over Division Multiplication Addition Subtraction.
z = 4y ÷ 2y
Is it
a) 2
or
b) 2y^2
If you think the answer to the OP is 288, then I presume you would also go for b) here.
Why? Because, replacing the immediate multipliers with a multiply sign (and I'll use "*" instead of "x"), you have:
z = 4 * y ÷ 2 * y
Breaking it down with left-to-right precedence for multiplication and division:
4 * y ÷ 2 = 2y
2y * y = 2y^2
But if you consider "2y" to be an immediate multiplier (and "2(12)" to be the same), then suddenly your answer is different.
2ab + 2ac = 2a(b+c)
So you cant say:
2a(b+c) = 2ab + c. It's just wrong.
I hate maths with a passion and I'm so glad I have never had the misfortune to work with it since I left school!
For what it's worth, I think the answer is 2... But then again, I was crap at maths.
4y÷2*y
which is two times y squared.
Same answer... 2
z = 4y ÷ 2y
z = 2y ÷ y
z = 2
In this case we are debating maths notation rather than maths itself
Best answer so far. The question was posed in very sloppy notation. In "grown up" maths the "÷" sign is rarely used anyway.
Spaces imply absolutely nothing in algebraic equations (as long as there is an operator on at least one side of a space).