Do yourself a favor, and forget trying to incorporate the old slab into the new garage. The contractor will break up and haul away the old slab, and it will likely be recycled into aggregrate for construction of asphalt roads.
You want your new garage floor to be poured atop a guaranteed properly prepared base, and that just isn't possible with the old cracked slab still there.

Thanks. I know about the properly prepared base, I just didn't know if the broken about slab could be incorporated in the new concrete pour.

I'm happy for any more thoughts, if you have them.

For whatever reason, aggregate from recycled concrete is generally not, I believe, regarded as a suitable type of aggregate for new concrete. It is, as I said, used for making asphalt roads, but concrete and asphalt do not work in the same way to make a suitable road surface. Usually gravel or crushed rock is used for concrete.

Or if you meant just tossing the chunks of old concrete into the new pour, to reduce the amount of new concrete needed, this is not a good idea. New concrete bonds only very weakly, if at all, to already solid, old concrete. No reputable concrete contractor will agree to do this for you, and you would soon be very unhappy with the result if they did.

Look around your property and see if there is anything you could do with the chunks of broken concrete that will result from removing the garage slab. I suppose you could use them like rock and build low "stone" walls, but there will be no disguising the fact that it's just old concrete, and won't really be very attractive.

Thanks for your comments about new concrete not bonding to solid, old concrete. That's what I was wondering about. I don't think broken up concrete is that attractive to look at so it definitely won't be going into our landscaping. In general, I'd rather try and recycle, where possible, than adding to the waste in this country. I appreciate your comments.