Math Question

what is 6^2/2(3)+4

Power calculation before point calculation before line calculation,
then from left to right.

\(\frac{6^2}{2\times 3}+4=\frac{36}{6}+4=6+4\color{blue}=10\)

Whoever wants can also shorten de Bruch by 6.    (\(\frac{36}{6}=\frac{6}{1}\) )

  !

This is a rare example in mathematics where, I believe, parentheses is necessary in order to evaluate the expression without ambiguity. I will demonstrate why.

Strictly speaking, asinus's interpretation is incorrect. If you were to evaluate this with a calculator inputted like as is, the calculator would evaluate it as \(\frac{6^2}{2}*3+4\). This is because the 2(3) is really multiplication, so division takes precedence since it is comes first in the expression. First it does 6^2, then it divides 6^2 by 2 because division is first from left to right, and then it multiplies that quantity by 3. Here is another example with a variable 

8/2y

Using the same logic as above, this equation, in fraction form is strictly \(\frac{8}{2}y\)--not \(\frac{8}{2y}\). Some would argue, however, that 2y is a term, so it shouldn't be separated.  

How do we eliminate this ambiguity if there is no fraction button to speak of? Use parentheses! 

Asinus's interpretation of \(\frac{6^2}{2*3}+4\) will be unambiguous once you add 1 set of parentheses with \(6^2/(2(3))+4\). Now, the only correct interpretation is \(\frac{6^2}{2*3}+4\) because the parentheses indicate that we are dividing by the quantity of the product of 2 and 3.

The strict interpretation is \(\frac{6^2}{2}*3+4\) should be written like \((6^2/2)(3)+4\). In this case, the quantity of six squared divided by two is all multiplied by three. No more ambiguity.

Okay, after all of this ranting, now I will evaluate what I believe to be, under the current rules of the order of operations, the way to evaluate the expression 6^2/2(3)+4 as \(\frac{6^2}{2}*3+4\):