A Generalized Fraction: An Entity Smaller Than One on the Mental Number Line

The representation of fractions in long-term memory (LTM) was investigated by examining the automatic processing of such numbers in a physical comparison task, and their intentional processing in a numerical comparison task. The size congruity effect (SiCE) served as a marker of automatic processing and consequently as an indicator of the access to the primitives of numerical representation in LTM. Mixed pairs composed of a natural number and a fraction showed both a SiCE and a distance effect. The SiCE for mixed pairs was stable across relative sizes of natural numbers compared to the fraction digits (Experiment 4). However, comparing pairs of fractions revealed a strong influence of fractional components: An inverse SiCE was found for pairs of unit fractions (Experiment 1), while no SiCE was found for pairs of non-unit fractions (Experiments 2-3). This leads to the conclusions that: (I) there are no unique representations of distinct fraction values in LTM, and (2) there is a representation of a "generalized fraction" as an "entity smaller than one" that emerges from the notational structure common to all fractions.