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Introduction: The double-representation of fractions theory states that fractions are doubly represented in the brain, as (1) analog quantities and (2) calculated true numerical values. This double-representation of fractions model should be reflected in the pattern of responses to different kinds of mathematical problems. Objectives: To either falsify or give confirmatory evidence to this theory, this study explored how different cognitions commonly associated with mathematical abilities (mental rotation, complex calculations, etc.) relate to one another and in particular to fraction estimation in the performance of a large sample of individuals (n= 22,221). Methodology: We distributed through social media a set of 23 questions extracted from tests used to identify difficulties in mathematical performance. We combined cluster analysis (to identify groups of similar items) and regression analyses (over the groups identified by the cluster analysis) to further evaluate the similarities and differences among distinct groups of cognitions. Results: When running polynomial regressions controlled by age and gender, the coefficients for educational attainment are very similar for fraction estimation and complex calculations, indicating that highly educated participants might solve fraction estimation problems as complex calculations, using true numerical values. On the other hand, mental rotation and fraction estimation merge when using different methods of hierarchical clustering. Also, they both show very similar aging patterns and gender dependency when running polynomial regressions controlled by educational attainment. Discussion: These results suggest that when it seems unfavorable or impossible to use calculated true numerical values to solve fraction estimation problems, they can be addressed using analog estimated quantities, relying on perceptual cognitive mechanisms that may be common to mental rotation tasks. Therefore, our findings give supporting evidence to the double-representation of fractions theory, implying that fraction estimation can be processed as calculated true numerical values or as analog quantities.

fractions; mental representation of fractions; rational numbers; massive online experiments