You would write it this way so the second method executed after the fadeOut completed. However in this case the hide() is not necessary since the fadeOut() sets the element's display to none when the animation is complete.
Its not actually working as you are intending. Since you have the anchor link, if you click on it, a post back is occuring. Based on what I'm seeing in your code, you simply want to use the anchor element for triggering the div hiding effect, correct? So, then you dont want the normal behavior of you anchor element to occur. To prevent it you need to include the preventDefault() method.