Would you use the term in the prompt even if textbooks or exams do not?
Does decimal division work in a similar way?
In regards to fraction division, do you justify the equivalent calculation of multiplying by a reciprocal in this way? Do you think it’s important to justify? If so, when would the justification happen? Would you assess a justification in a unit test?
How do you explain why we would bother to rationalise the denominator? Is it an opportunity to discuss the history of mathematics, or is it a technique that is isolated with no obvious application or reason?