$("div").click(function(e){
var pWidth = $(this).innerWidth(); //use .outerWidth() if you want borders
var pOffset = $(this).offset();
var x = e.pageX - pOffset.left;
if(pWidth/2 > x)
$(this).text('left');
else
$(this).text('right');
});
DEMO:
http://jsfiddle.net/dirtyd77/QRKn7/1/
Hope this helps! Let me know if you have any questions!