Evaluating $6^2\div 2(3)+4$: is the answer $10$ or $58$?

Question

Evaluating $$6^2\div 2(3)+4$$

I understand how people are getting $10$ but I am getting $58$ because I am not distributing the $2$ to the $3$ inside the parentheses. Is that correct?

Answer 1

This can be written as:

$\frac{6^2}{2(3)} + 4$

$6^2 = 36$

$2(3)=6$

So now we have $\frac{36}{6} +4 = 6+4=10$

OR

$\frac{6^2}{2}(3)+4=\frac{36}{2}(3)+4=18(3)+4=54+4=58$

There is ambiguity in the way it is written - that's why it is so important to be crystal clear when writing math.

I can see you are learning basic arithmetic but down the road you will see far less of the '÷' sign and much more of expressing divisions as ratios (fractions) which removes some of the ambiguity.

Answer 2

By the Immutable Laws of Emperor Pemdas, you square the 6 first to get 36. Then you divide by 2 to get 18. Then you multiply by 3 to get 54. Then you add 4 to get 58. You are correct. The sticky part is that the 'divide by 2' and 'multiply by 3' operations are at the same ''level'' in the empire of Pemdas so you compute left to right.