When is the quotient of two numbers negative?

The quotient of two numbers is negative when one number is negative and the other is positive. This is based on the rules of division involving signed numbers. When you divide a negative number by a positive number, the result is negative because the positive number represents a quantity that is being subtracted from zero, while the negative number indicates a quantity that is opposite to the positive direction on the number line. As a result, the quotient reflects this opposition, yielding a negative outcome.

In contrast, dividing two negative numbers would produce a positive result because the two negatives cancel each other out. Similarly, if both numbers are positive, the quotient is also positive, as the division of two positive quantities maintains their positive value. Lastly, if one number is zero, the quotient remains undefined or zero based on specific scenarios, but does not contribute to a negative result. Thus, the scenario of one number being negative and the other positive exclusively leads to a negative quotient.