# Correct precedence of division operators

Say i have the followingv operation - $6/3/6$, i get different answers depending on which division i perform first.

$6/3/6 = 2/6 = .33333...$

$6/3/6 = 6/.5 = 12$

So which answer is correct?

-
Ask whoever gave you the formula without specifying what he meant by it. – Henning Makholm Apr 17 '12 at 12:24
The notation 6/3/6 is highly ambiguous and best avoided in practice. Usually, I would assume that the first case is what is meant. – Johannes Kloos Apr 17 '12 at 12:26
Many programming languages use the convention that operations with equal precedence are evaluated from left to right (except for exponentiation which evaluates from right to left) and these would interpret $6/3/6$ as $(6/3)/6 = .333\ldots$ or as $(6/3)/6 = 2/6 = 0$. With human beings, who knows? Henning Makholm's advice is most applicable in this case. – Dilip Sarwate Apr 17 '12 at 12:30

## 1 Answer

By convention it's done from left to right, but by virtually universal preference it's not done at all; one uses parentheses.

However, I see students writing fractions like this: $$\begin{array}{c} a \\ \hline \\ b \\ \hline \\ c \end{array}$$ Similarly they write $\sqrt{b^2 - 4a} c$ or $\sqrt{b^2 - 4}ac$ or even $\sqrt{b^2 -{}}4ac$ when they actually need $\sqrt{b^2 - 4ac}$, etc.

-
I have always told my students to write the normal density as $$f(x) = \frac{1}{\sigma\sqrt{2\pi}}\exp\left(-\frac{x^2}{2\sigma^2}\right)$$ rather than as $$f(x) = \frac{1}{\sqrt{2\pi}\sigma}\exp\left(-\frac{x^2}{2\sigma^2}\right)$$ because the latter degenerates into $$f(x) = \frac{1}{\sqrt{2\pi\sigma}}\exp\left(-\frac{x^2}{2\sigma^2}\right)$$ by the end of the semester. Creeping radicalism is eschewed by all right-thinking people. – Dilip Sarwate Apr 17 '12 at 12:59
Doubtless no puns were intended in the comment above, except by the person who posted it. – Michael Hardy Apr 17 '12 at 13:51