On Common Ground: Evidence for an Association Between Fractions and the Ratios They Represent

This study tested two hypotheses central to the theory that understanding fractions as symbolic representations of magnitude (e.g. ½) may rely on cognitive systems of ratio processing that are common to the perception of ratios (e.g. the length of one line relative to another). Specifically, we tested: 1) whether nonsymbolic ratio stimuli support more efficient magnitude processing than symbolic fractions and 2) whether comparisons between nonsymbolic and symbolic stimuli require significant translation costs relative to within format comparisons. Participants were asked to indicate the larger of two fractions in three different conditions: paired symbolic fractions, paired nonsymbolic line ratios, and mixed symbolic/nonsymbolic cross-notation pairs. We found that adults were consistently faster when comparing nonsymbolic ratios relative to symbolic fractions. Furthermore, adults were neither slower nor less accurate when making cross-notation comparisons than when making symbolic fraction comparisons within format, suggesting a common magnitude code can be accessed without substantial translation costs. Both results contrast with conclusions from previous studies examining whole-number processing and suggest that extracting symbolic fraction magnitudes and perceiving nonsymbolic ratio magnitudes may rely on shared mechanisms of magnitude processing.