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I'm looking for the FrontEnd`Foo[...]-like command that's triggered when pressing Ctrl + /.

Are there any discoverability features in Mathematica that would have helped in this case?

E.g., in Emacs I could have just pressed Ctrl + h k Ctrl + / ("Find function for key Ctrl + /").

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I don't know of any discoverability features, but there are docs and in particular – Michael E2 Apr 6 '13 at 12:23
@ens Please make sure that when you get enough rep you post it as a real answer instead of a comment! Nice and lucky first question, welcome to the site! – István Zachar Apr 6 '13 at 13:08

With Michael's help (thanks) I figured out this snippet to do the job:

    FrontEndToken[FrontEnd`InputNotebook[], "Fraction"]
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