I really like Travertine tile and would like to install it on the bottom floor of my house. However, I have a cracked slab in the living room area. Can I install tile on the side of the house that includes the den, kitchen and bathroom & utility room, and also install hardwood floors in the living room to avoid cracked tiles? Is that good design or a dumb idea?

There is no reason not to. Different floorings can help define room space. Totally normal to have several types of flooring in a house, as long as the colors and styles do not clash with each other.

Thanks, Jaybee. I thought about the travertine in the living room, and researched the anti-fracture membranes to lay down prior to tile installation, but my foundation repair company said that it won't stop a crack from occurring. My house dropped 1" in the corner from the severe drought last year.