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I think it is pointless to argue about what is the definition of a symbol. If you write your own book, you can make it whatever you want it to be. For as long as you are clear about it, it is still a good book.

W|A is clear about its interpretation.

So what is the problem then?

Also, how would you represent ratios if : is taken for division only?

This is a bit like arguing that either Fortran, C or Mathematica is "wrong" when they denote exponentiation by **, pow and ^ respectively. Yet all three work just fine, and all three can compute powers.

Thanks all for your answers. I now looked after the meaning of : symbol to clear it up and the situation is still interesting. Here's the definition on Wikipedia, and focus on the example on the right side:

So it is right the same as / symbol's:

10:2=5 ??? 10/2=5

WHICH MEANS:

48:2(9+3) ? 48/2(9+3)

WHICH MEANS that they must lead to the same result. So the question is now stronger than before: Why WolframAlpha handles them different?

It is interesting to see how mathematical notation changes over time. Today, in English, we use decimal points (on the baseline), and we use a comma for digit groups. In Hungarian (and in many other European continental countries), we use a decimal comma, and a thin space for digit groups.

However, if I look at a Hungarian language encyclopaedia published in the 1920s, I see a centred decimal point, a comma for the thousands group and a baseline point for the million group.

The same encyclopaedia uses $\frac{a}{b}$ or $a:b$ for divison, but not $a/b$.

: 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 ...