Related Experiment Video
Updated: Jun 18, 2026

Using the Race Model Inequality to Quantify Behavioral Multisensory Integration Effects
Published on: May 10, 2019
A generalized fraction: an entity smaller than one on the mental number line
Arava Y Kallai1, Joseph Tzelgov
1Learning Research and Development Center, Department of Psychology, University of Pittsburgh, PA, USA. kallai@pitt.edu
Abstract:
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: (1) 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.
Related Concept Videos
Partial Fractions
Real Number Operations
Indeterminate Products
Orders of Magnitude
The order of magnitude is simply a way of rounding numbers consistently to the nearest power of 10. This makes doing rough mental math...
Rational Expressions
Complex Numbers
