Chapter 3.3, Problem 6P

To solve $512-146,$ a student writes the following:

   $\begin{array}{l}512\text{ 400 }\\ \frac{-146}{-4}\frac{\text{-30}}{370}\text{ 512-146=366}\\ \frac{-30}{400}\frac{-4}{366}\end{array}$

Describe the student’s solution strategy and discuss why the strategy makes sense. Expanded forms may be helpful to your discussion.