Edward I.

asked • 12/14/16

what does 8/4(2) =?

does parentheses override simple left to right? In other words:
does 8/4(2) = 8/4x2?

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Danny T. answered • 12/14/16

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Order of operation:
P.E.M.D.A.S.
Parentheses
Exponent
Multiplication
Division
Addition
Subtraction
 
You perform the operation inside the parentheses first.  In your case, the parentheses only have a number in there; no calculation is needed.  It is the same as you putting the "x" like you did.  
8/4(2) = 8 / 4 x 2 = 2 x 2 = 4
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Gregg K. answered • 12/14/16

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when division and mutiplication is in the same problem you perform them left to right
 
You should divide first
 
8/4 =2
2(2) = 4
 
The answer is not 1
 
 
 
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Gregg K.

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PEMDAS
 
I always say there are 4 steps
 
1. P
2. E
3. MD (left to right)
4. AS (left to right)
 
PEMDAS is a little misleading since it has M before D and A before S
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12/14/16

Kenneth S.

Not misleading if you remember that Left to Right prevails, ALL PRIORITIES BEING EQUAL, which they are in the case of MD & AS.
 
It's a matter of scanning L to R, seeking the next operation to perform; as soon as there are two operands known, and an operation between them, that should be performed, PROVIDED THAT NEXT OPERATION DOES NOT HAVE A HIGHER PRIORITY THAN THE ONE PENDING.
 
View it like this: I see 8; then I see division (/), next I see 4; IS the 4 available for the binary operation (/)? Peeking ahead, I see the next operation is multiplication, WHICH IS IMPLIED due to adjacency. Therefore I divide and have 8/4, so I have 2...what's to be done with it?  Multiply, by (2), which gives final answer 4.
 
In this case, the parentheses were employed to segregate the 2 (denominator) from the other two SO THAT MULTIPLICATION is the next operation. Those parentheses can be replaced by writing the desired expression as (8/4)*2, using an explicit symbol for multiplication (*, from programming languages or • from the repertoire of operator symbols, or even the x symbol (a.k.a. 'times') but the latter is a terrible choice due to the popularity of letter x as the name of a variable).
 
I almost dread telling you that in the U.K. (a.k.a. Great Britain) their mnemonic for order-of-operations is different and they interpret some problems of this type differently. They don't even call parentheses by our word--their term is brackets.
 
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12/14/16

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