Xavier and Abby are trying to find a rule for dividing any two numbers, p and q. All they know is that neither p nor q is 0.

Abby: “I think that any number p/(-q) is the same as (-p)/q, and I think they will both be at the same spot on the number line.”

Xavier: “I don’t think so. p/(-q) has to be in a different place than (-p)/q because the negative signs are in different places.