Which of the following operations is not typically performed with rational numbers?

Rational numbers are defined as numbers that can be expressed as the quotient of two integers, where the denominator is not zero. This means that operations involving rational numbers—such as addition, subtraction, and multiplication—are defined and can be performed without issue.

When it comes to division by zero, however, this operation is undefined in mathematics. Dividing by zero does not yield a rational number or any number, as it does not make sense to divide something into zero parts. Therefore, division by zero cannot be performed with rational numbers, making it the operation that is not typically associated with rational numbers.

In summary, since rational numbers allow for addition, subtraction, and multiplication, but not division by zero, the correct choice is the operation that involves division by zero.