Example of Relational vs. Instrumental Approach in Math

The division of fractions is a good example how both relational and instrumental approach are useful.   A relational pictorial representation of the problems helps us understand the problem, and it's wording.   However in order to solve similar problems of a larger scale, having formula or fractions to manipulate makes the problem manageable and achievable.   When an answer is derived, one can return back to a relational mindset to ask oneself,  "does this answer make sense".   Hence, both methods complement one another.