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It can because rate law is experimentally determined so if the experiment yields a result that allows for a negative reaction order then that is possible. Typically I don't think we will be dealing much with negative reaction order because it is not as common but it is good to know that it can exist.
Yes, negative orders are possible and just means that whatever the substance is, it decreases and cases the reaction rate to increase. I had the same confusion, but a TA told me to get familiar with negative orders and fractions.
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