That's exactly the thing, though. When the / is used, it CAN implicate a fraction bar. Not that it necessarily does, but it CAN. That is what ÷ can't mean. ÷ is a straight forward division between exactly two numbers, and cannot implicate that a fraction is going on.
EDIT: To be honest, I would almost like to call it mathematically illegal to put up the equation as it has been, exactly because it is not possible to determine whether there is talk of a fraction or a simple division. There's just no way to know for sure, in which case of course you can only argue that you should go from left to right, and that brackets are needed to make it an official fraction, so yes, I suppose you guys are right. But still, to make this a proper, straight forward calculation, ÷ should have been used, and not /.
EDIT: To be honest, I would almost like to call it mathematically illegal to put up the equation as it has been, exactly because it is not possible to determine whether there is talk of a fraction or a simple division. There's just no way to know for sure, in which case of course you can only argue that you should go from left to right, and that brackets are needed to make it an official fraction, so yes, I suppose you guys are right. But still, to make this a proper, straight forward calculation, ÷ should have been used, and not /.
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Perhaps I wasn't clear.
THIS IS A FRACTION:
6/(2*(1+2))
It's the same as 6 over (2*(1+2)) which is the same as 6 over (2*3) which is the same as 6 over 3.
THIS IS ALSO A FRACTION:
(6/2)*(1+2)
It's the same as 6 over 2 times 3 (over one, if you wish).
The first example is one big fraction, while the second has a fraction multiplied by 3 over 1.
If there are no parentheses after the / sign, this indicates that the fraction ENDS after the first term (I'm stretching the definition of the word "term" to include numbers separated by any operation, not just addition or subtraction).
6/2*(1+2) means that the fraction ENDS after the two. The rest of the equation is not a part of the fraction. If it were, you'd have to add parentheses to indicate that there is more than one term in the denominator.
Fractions ARE division statements. They may look different, but they mean the exact same thing.
6/2*3 is the exact same as 6÷2*3. They both equal 9.
6/(2*3) is the exact same as 6÷(2*3). They both equal 1.
EDIT: Lol Wayne....
THIS IS A FRACTION:
6/(2*(1+2))
It's the same as 6 over (2*(1+2)) which is the same as 6 over (2*3) which is the same as 6 over 3.
THIS IS ALSO A FRACTION:
(6/2)*(1+2)
It's the same as 6 over 2 times 3 (over one, if you wish).
The first example is one big fraction, while the second has a fraction multiplied by 3 over 1.
If there are no parentheses after the / sign, this indicates that the fraction ENDS after the first term (I'm stretching the definition of the word "term" to include numbers separated by any operation, not just addition or subtraction).
6/2*(1+2) means that the fraction ENDS after the two. The rest of the equation is not a part of the fraction. If it were, you'd have to add parentheses to indicate that there is more than one term in the denominator.
Fractions ARE division statements. They may look different, but they mean the exact same thing.
6/2*3 is the exact same as 6÷2*3. They both equal 9.
6/(2*3) is the exact same as 6÷(2*3). They both equal 1.
EDIT: Lol Wayne....
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PsiGuard wrote:
Fractions are division statements, but they can be notated differently.
6/(2*(1+2)) = 1, which is the same as 6 over (2*3)
(6/2)*(1+2) = 9, which is the same as 6 over 2 times 3 (over one).
It all depends on where you put the parentheses. Since the OP doesn't have any clear differentiation, Nighthawk's method is correct. Do the operations in order from right to left.
6/2*(1+2) = 6/2*3 = 3*3 = 9
If you want the answer of 1, you have to add some parentheses or write it as a fraction. Using the / sign does not indicate that the rest of the equation is the denominator of a fraction unless the following operations are grouped with parentheses or brackets.
yea that
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6/(2*(1+2)) = 1, which is the same as 6 over (2*3)
(6/2)*(1+2) = 9, which is the same as 6 over 2 times 3 (over one).
It all depends on where you put the parentheses. Since the OP doesn't have any clear differentiation, Nighthawk's method is correct. Do the operations in order from right to left.
6/2*(1+2) = 6/2*3 = 3*3 = 9
If you want the answer of 1, you have to add some parentheses or write it as a fraction. Using the / sign does not indicate that the rest of the equation is the denominator of a fraction unless the following operations are grouped with parentheses or brackets.