Representations of Fractions: Evidence for Accessing the Whole Magnitude in Adults

Abstract

Proficiency with fractions serves as a foundation for later mathematics and is critical for learning algebra, which plays a role in college success and lifetime earnings. Yet children often struggle to learn fractions. Educators have argued that a conceptual understanding of fractions involves learning that a fraction represents a magnitude different from its whole number components. However, it is not well understood whether adults represent a fraction's magnitude similarly to whole numbers. This study investigated the distance effect during a comparison task using fraction pairs that discouraged comparing a fraction's components. Accuracy improved and reaction times decreased with greater distance between fraction pairs, showing a distance effect similar to that seen with whole numbers. This study suggests that a representation of a fraction's magnitude is present in the fully developed number system.