Unpacking a student example of dividing by a fraction

Today in class students were choosing different practice activities for review for our test tomorrow. One pair of students was working on a worksheet that involved dividing an integer by a fraction. This is a topic we have not reviewed yet but that students have learned in past years. As I looked at his work I knew that I wanted him to explain his process to me. As I listened I knew this was something that I wanted to share. While some of his explanation is now based on procedures I really get the feeling that he has a deeper understanding than a student that is just taught to 'flip and multiply'.

In preparation for looking at it in a future lesson I tried to look at what is happening with the mathematics behind his explanation and what to do when a problem addressed is a little messier.

Comments, suggestions and additional strategies are welcome!

Here is the student's work from when he showed the class:

This is my take on what is happening as the student is moving forward with his procedure:

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