What does 6^2/2(3)+4 evaluate to?

Question

My instincts tells me this evaluates to 10, but a counter evaluation has it evaluate to 58. In variable notation i see it as a^2 / b(c) + d. one argument has it that you ignore the parenthesis and treat it like B*C reading left to right to get 58. the other argument is treating the b(c) as a single separate number which gives the ten answer.

 

honestly i am uncertain but what is the actual regarding such occurrences?

Answer 1

As written, it is ambiguous.  Is it

 

6²

--- * 3 + 4 = 58

 2

 

or

 

 6²

---- + 4 = 10

2*3

 

The ambiguity involves where the 3 is - is it in the numerator or denominator?  I believe that PEMDAS was invented to provide guidance when an equation is written ambiguously, and PEMDAS tells you to do the multiplication before the division, so the answer would be 10.  Many people will tell you that you just do the multiplications and divisions left to right, which would give an answer of 58.  If you plug the equation as written into your calculator, it will come out as 58.  But I contend that doing the multiplications and divisions left to right is valid only when the equation is written unambiguously.  So the real lesson here is to not write ambiguous equations.  The equation should be written as either:

 

6²/(2*3) + 4    which equals 10

 

or

 

(6²/2)*3 + 4    which equals 58

 

depending on what you mean.  Then you don't have to worry about it.