Question 247184: I have a question about order of operations...
The problem is
a = 3
18 ÷ 2a
My question is....can the variable be separated from the number, thereby treating it like 18 ÷ 2 * 3, resulting in the answer 27,
or does the variable stay attached to the number 18 ÷ 2(3), resulting in the answer 3
Thanks,
Schel
Found 3 solutions by richwmiller, Theo, edjones:
Answer by richwmiller(17219)   (Show Source):
You can put this solution on YOUR website! Yes, the a is "stuck" to the 2 to get 3
To clarify, that you could write 18/(2a) or (18/2)*(1/a) to show that you want to factor it or even (1/2)*(18/a)
To get 27 you would need to write something like (18/2)*a. Compare this with
(18/2)*(1/a) from above.
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! a = 3
18 ÷ 2a
Technically speaking you would be correct if you interpreted it as (18/2) * a because the order of arithmetic says multiplication and division are done together from left to right if parentheses don't change the natural order.
The natural order without parentheses is:
exponents and roots first.
then multiplication and division.
then addition and subtraction.
within each level, you process left to right.
this means if you have a multiplication followed by a division, you do the multiplication first, and if you have a division followed by a multiplication, you do the division first.
Select the following link to see one of the tutorials on the web concerning this.
http://www.math.com/school/subject2/lessons/S2U1L2GL.html
I tend to think, the way it was written with the other division sign, and the way the 2 and the a were stuck together, that they meant 18 / (2*a), but that would not be technically correct if you follow the rules exactly.
It's a matter of interpretation.
You would not be wrong if you assumed (18/2) * a based on a strict interpretation of the rules.
If the book shows you the answer, you can determine from that.
If not, you can answer with an (if it is this way, then the answer is ...) and (if it is that way, then the answer is ...)
My gut says 18 / (2*a) but the strict interpretation of the rules says (18/2) * a.
I can see why you're confused.
Answer by edjones(8007)  (Show Source):
You can put this solution on YOUR website! Good question!
A lot of questions on this site don't get answered because they are ambiguous.
Let's take a tougher one. x+1/x-2. Is this x + (1/x) -2 or (x+1)/(x-2) Parentheses clarify the issue.
18/(2a) is a clear way to write the problem.
Another way is  .
18 / 2a written this way I would give an answer of 3.
.
Ed
|
|
|
