Most commercial grade granite has a fairly uniform, fine grain. Traditionally, it was cut similar to the way glass is cut - by scribing and breaking along the scribe line. In the case of granite, the scribe line was made with a flat chisel and hammer. This works for thick sections, but may also work with your 1" thick slabs. Try using a 1/2" chisel and see if you can make a line about 1/16" deep. If you can do this without breaking the stone, then support the larger side on a flat, straight edge and give the overhanging side a good wallop and see what you get. Breaking the stone this way will give you a different, hand made look that you may prefer over the machine cut appearance you get with a saw. Depends on what effect you're trying to achieve.