Facebook Friends

Is it rude to ignore friend requests from coworkers? I don't want to be facebook friends with coworkers that I'm not really friends with. I know if you don't want people to know your business, don't put it on the internet. But I am only friends with people I know and who probably already know my business or don't really care. So if you ignore someone who works with you, does that make you a bad coworker? Especially if you are suppose to be a "family" at work? I am fb friends with some people at work, but I consider them friends, not just coworkers. So am I being rude?? Hmmm...good question.