:
is not universally used for division. In contemporary Hungarian, it is indeed standard. I was taught
$a:b$ before
$a/b$ in primary school. But in English, it is not. At the elementary level, ÷
, and not :
is used for division. Yes, math notation is specific to languages too. Think of it as decimal comma vs. decimal point.
:
is often used for the concept of "ratios". This is how W|A is interpreting it here, and this is why the operator precedence is different.
To sum up: If you mean the arithmetic operation, use /
. Use :
only if you want to operate with ratios that are explicitly kept in ratio form. There is no numerical result for :
, but you can have more than one term in the ratio, e.g. try 2 : 6 : 4
. It will simplify to 1 : 3 : 2
.
A marginally related note: The influence of computer languages seems to be slowly changing the standard math notation. I see
$*$ used for multiplication more and more often, written in LaTeX. I often see people writing things like
$a*\frac{b}{c}$ online. This use really makes me cringe, but maybe I am just old-fashioned. I am used to
$*$ meaning convolution or some other uncommon (or even unspecified) mathematical operation in textbooks. I wonder when we will see the first textbook using
$*$ for multiplication ...