Understanding fractions as operators remains a persistent challenge in the upper grades of primary education, particularly when students are required to transfer this knowledge across different contexts and representations. This study examined how Grade 4, 5, and 6 students solve fraction-as-operator tasks involving both whole and fractional base quantities. Each task was presented in two formats—contextualised word problems and decontextualised bare-number exercises—and required either an arithmetic or a graphic solution. Using a cross-sectional, comparative ex post facto design with matched task pairs, we analysed success rates together with process-related variables to capture grade-level patterns of performance. A profile-based approach provided a fine-grained description of outcomes across tasks. The results reveal three consistent patterns. First, procedural consolidation was more visible in tasks with whole-number bases, though less stable when representational variation was required. Second, tasks with fractional bases produced high omission rates and recurrent error patterns, especially in graphic formats. Third, contextualised word problems supported performance only when linguistic and visual demands were relatively low; otherwise, outcomes tended to decline. These findings align with theoretical accounts that emphasise the verbal articulation of multiplicative relationships and representational flexibility in developing a robust understanding of the operator. The study extends this literature by documenting, at scale, the specific task conditions under which difficulties become most visible, thereby offering diagnostic value for instructional design and assessment practices.
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