I don't know why, but Wolfram|Alpha gives the two symbols / and : for division two different precedences: / has high precedence, : ha low precedence. 
Also, if I type a b/c d when the MathInput button is inactive, it is interpreted as a(b/c)d. If I type the very same characters a b/c d with the MathInput button active, it is interpreted as a(b/(c d)).
Caveat user.