What is the order of operations in a given formula? My question is probably very basic. It's related to the order of operations in the following simple formula:
$$\frac{A}{B\times C}.$$
My question arises when I want to write this formula in a single line. For instance: $150/1.5\times 0.33$.
Should I write $150/1.5\times 0.33$ or $150/(1.5\times 0.33)$. Is the answer equal to $300$ or $33.3$? I mean, it's obviously $300$ according to the original formula. But I am a bit confused with the single line formula.
I remember that the multiplication has a preference over the division. So, the parenthesis is not needed... But then the answer might be $33.3$, which is not correct. I get stuck with this quite simple thing. 
 A: The other answers here address the mathematics of "order of operations" - operator precendence in programming languages. They pretty much tell you to use the parentheses.
I want to address this point explicitly:

My question arises when I want to write this formula in a single line.

You are asking here about communication. The important issue is to make your meaning unambiguously clear. So when writing inline you should use the parentheses in the denominator, even if they are unnecessary because your reader or your compiler "knows what you mean". 
A: *

*Grouping (fractions, parantheses, $a\choose{b}$, etc)

*Exponents ($x^3$ and $\sqrt[a]{x}$)

*Multiplication (and division)

*Addition (and subtraction)


In $\frac{A}{BC}$ We can split it into $A \div (BC)$, first we do the grouping, the parentheses around $(BC)$, so we multiply $B$ by $C$. Then, we divide $A$ by $BC$.
This applies to all equations, across all mathematics.
A: Multiplication does not have precedence over division; they have the same precedence. And we perform operations with the same precedence from left to right. Same for addition and subtraction.
$
\def\lfrac#1#2{{\large\frac{#1}{#2}}}
$
Hence $A / B \times C = ( A \div B ) \times C$ which is different from $A / ( B \times C ) = \lfrac{A}{B \times C}$.
Curiously $\lfrac{AB}{C} = ( A \times B ) \div C = A \times B \div C = A \times ( B \div C ) = A \lfrac{B}{C}$.
But $\lfrac{A}{BC} = ( A \div B ) \div C = A \div B \div C \ne A \div ( B \div C ) = A \lfrac{C}{B}$.
Got it?
A: To understand this we must first explain what division means.
Division is multiplication by an inverse element. In a group or a field there is ensured to exist an inverse element such that if you multiply it it becomes 1 : $\frac{a}{a} = a^{-1}a= aa^{-1} = 1$. What is important is to specify which element should be inverted before multiplication. In many programming languages there is a convention that division has higher precedence. That is just to make sure one knows which number we should find the multiplicative inverse for before performing multiplication with it.
$$\frac{a}{bc} = a(bc)^{-1}, \frac{ab}{c} = ab(c)^{-1}$$
Where $(bc)^{-1}$ is the multiplicative inverse to $bc$ and $(c)^{-1}$ is the multiplicative inverse for $c$.
The horizontal division sign ____ only helps us explaining this for commutative algebras as we otherwise need to also decide from which side the division occurs. Or in other words from which side we should multiply with the multiplicative inverse.
