\( 4 \frac{1}{2}-2 \frac{3}{4}=\left(4+\frac{1}{2}\right)-\left(2+\frac{3}{4}\right)=(4-2)+\left(\frac{1}{2}-\frac{3}{4}\right)=2+\left(\frac{1}{2}-\frac{3}{4}\right)=1+\frac{4}{4}+\frac{2}{4}-\frac{3}{4}=1+\frac{6}{4}-\frac{3}{4}=\frac{13}{4} \) The steps showing the correct answer emphasize a. conceptual understanding of the process b. procedural understanding of the process. c. rote learning.

The steps you've outlined showcase a strong conceptual understanding of the problem. By breaking down the mixed numbers into their whole and fractional components, you are demonstrating how to manage and manipulate fractions effectively, not just regurgitating a memorized process. This approach highlights the relationships between the numbers and makes it clear how to effectively perform the operation. Additionally, this process incorporates procedural understanding. You’re carefully following each step to ensure accuracy—first dealing with whole numbers separately, then addressing the fractions. This combination enables anyone reviewing the work to grasp both how to solve similar problems and why the operations are performed in a certain way. It's like having your cake and eating it too in the world of mathematics!