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

Arava Y. Kallai, Joseph Tzelgov

Research output: Contribution to journalArticlepeer-review

88 Scopus citations

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.

Original languageEnglish
Pages (from-to)1845-1864
Number of pages20
JournalJournal of Experimental Psychology: Human Perception and Performance
Volume35
Issue number6
DOIs
StatePublished - 1 Dec 2009

Keywords

  • automatic processing
  • fractions
  • mental representations
  • numerical cognition

ASJC Scopus subject areas

  • Experimental and Cognitive Psychology
  • Arts and Humanities (miscellaneous)
  • Behavioral Neuroscience

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