Ted, your concrete slab sits on top of foundation walls, so in effect your concrete is an open box turned upside down. The foundation walls will normally be 8" thick, and extend about 24" below ground, and the floor inside will be 4" thick. Assuming the crack you speak of is running basically vertically, then you have had some pretty fair motion in your foundation. Also noting that you are having a problem with ants, I'd say one part of the problem is way too much moisture around the outside of the home. Proper drainage is a must, yet many homes do not have it.
I would look carefully at the home, inside and out, especially along the wall which is cracked and see if you have any signs of motion that is causing problems, i.e. doors that no longer fit correctly, cracks in drywall. If you don't find any damage, you may need to watch for it in the future.
If there's no damage or structural repair needed, the crack can be addressed 2 ways; epoxy injection, a very permanent closure but harder to accomplish on a crack this large, or, seal the crack with a polyurethane caulking or other flexible caulking such as BigStretch. Now, for either of these to be truly effective, you'll need to expose the crack preferrably all the way down, so there will be some digging involved, but the dig need only be large enough to reach into and work with a wire brush and caulking gun. If you choose to epoxy inject, you'll need to call a professional foundation repair co. for that work.
To caulk the crack once you've exposed it all, clean the wall with a wire brush. Be sure and scrape any soil or loose matter out of the crack itself, too, the if you have compressed air blow it out with that. If you don't have air, at least clean it by blowing it out with a turkey baster or tube you can get into the crack with. From your hardware store or lumberyard, buy what's called backer rod, which is a foam strip, and be sure you get a size large enough it will wedge in the crack. Using a paint paddle or small putty knife wedge the backer rod into the crack, preferrably about 2" back, but at least 1/2" if thats all you can get. Note: as the crack gets smaller, this is not needed, so only use the rod where the crack is bigger; it's only there to create a backing for your caulk.
Next, have some duct tape ready, and begin caulking the crack from the bottom. Force the crack full as you work upwards, and once you've got 6" or so filled, start a strip of duct tape up the face of the crack. This will hold the caulking in place while it cures. Continue this process to the top. As this is a big crack, plan on having 3 or 4 tubes of caulking on hand, as it will take a lot.
Once you've sealed the crack, I'd look closely at the drainage around the house. Do everything you can to ensure good drainage away from the house; this is your first defense against further problems. Good Luck