Will the opposite of a positive number always, sometimes, or never be a positive number? explain your reasoning.

Depends on what you mean by opposite, opposite according multiplication or addition?. If opposite multiplication you have to take "-1" power of a number like 5^-1. If opposite of addition you must multiply a number by - 1 so like : 5 * - 1 = - 5. And a positive number's opposite addition would never be positive. (Sorry for bad english, not familiar with english math terms)