Can you leave a bowl of salt or even a bulb of garlic somewhere to cleanse the area without saying a chant or prayer to state the intention for it to work? Or do you have to say something?
Yes you can. I will do this from time to time and I choose to say something like "May the negativity in the house be drawn here and leave the people alone." After a day or two, I throw it out with the trash.
Saying things while doing workings often feels awkward to me, but I reckon if you call up the intention of what you're asking the garlic or salt to do it will give everything a push, that's what I do most of the time :)