Without further ado is the correct phrase, which means without much fuss or without further delay. Doing something without further ado means you do it at once right away. Without further adieu is an incorrect term meaning without further goodbye, or I'm out of here!
What is an example of without further ado?
I am convinced that a great deal can and must be done without further ado. Provided that they matched and the certificate was satisfactory, the animal would enter the country without further ado. We should vote for the revival motion without further ado.
What is ADO slang?
Ado implies a confused bustle of activity, a considerable emotional upset, and a great deal of talking: Much Ado About Nothing. To-do, now more commonly used, may mean merely excitement and noise and may be pleasant or unpleasant: a great to-do over a movie star.