Prove why the product of two negative real numbers is a positive real number.
Let and be two positive real numbers. Subsequently, and are the respective additive inverses.
We then add to both sides of the equation:
which simplifies to
To prove why the quotient of two negative real numbers is a positive real number, just treat either or as the multiplicative inverse (division is the multiplication of reciprocals).
Check out my other notes at Proof, Disproof, and Derivation