Sometimes there is no symbol "X" in the computer, so "*" is used instead of multiplication sign, so "*" in mathematics means multiplication sign.

"*" is the operation symbol defined in your question. According to you, there may be two situations:

(1)P*Q=(P+Q)/2 means that the operation of "*" is to find the average of two numbers, p and q;

(2)P*Q=(P/2)+Q means that the specified "*" operation is the sum of half of p and q.

Extended data:

It is quite popular to use ""to represent multiplication. At present, schools in continental Europe (Germany, France and other countries) stipulate that ","is a multiplication sign. Other countries use "×" as multiplication sign and "×" as decimal point. Our country stipulates that "×" or "×" can be used as a multiplication sign, and the multiplication sign before letters or brackets can be omitted.

Because this symbol is inconvenient to input, it is generally replaced by the English letter "X" in daily communication. On HTML and XHTML, you can enter an entity reference of ×, × or ×.