Applying language models (LMs) to tables is challenging due to the inherent structural differences between two-dimensional tables and one-dimensional text for which the LMs were originally designed. Furthermore, when applying linearized tables to LMs, the maximum token lengths often imposed in self-attention calculations make it difficult to comprehensively understand the context spread across large tables. To address these challenges, we present PieTa (Piece of Table), a new framework for subtable-based question answering (QA). PieTa operates through an iterative process of dividing tables into smaller windows, using LMs to select relevant cells within each window, and merging these cells into a subtable. This multi-resolution approach captures dependencies across multiple rows and columns while avoiding the limitations caused by long context inputs. Instantiated as a simple iterative subtable union algorithm, PieTa demonstrates improved performance over previous subtable-based QA approaches.