This study investigated processing/strategy complexity to activate magnitude representation for common fractions (1/4, 1/3, 1/2, 2/3, and 3/4), and the precision of their magnitude representations on the mental number line. We compared the magnitude comparison performance for pairs involving any one of common fractions and pairs of two uncommon fractions. We hypothesized the mean reaction time to be shorter for pairs involving a common fraction with a simple processing/strategy to activate the magnitude representation, and the magnitude distance effect to be smaller for pairs involving common fractions with precise magnitude representation. Bayesian mixed-effect regression analysis found a shorter mean reaction time for pairs involving common fractions except 1/4. Comparisons involving common fractions did not show a smaller magnitude distance effect. Thus, processing to activate magnitude representation is simpler for common (except 1/4) than for uncommon fractions, although common fractions do not have more precise magnitude representation than uncommon fractions.

Familiar fractions (e.g., 1/2, 2/3, and 3/4) play a key role in fraction representations. Recent studies showed that, evenin mathematically matured adults, fraction processing was facilitated for familiar fractions (Liu, 2017; Taniguchi, et al.,2017). The working hypothesis was that fractions with small denominators are represented through retrieval and underpinthe representation of larger denominator fractions (Liu, 2017). However, the list of the distinctive basic denominators hasnot been systematically investigated. Thirty university students performed number line estimation of fractions with 2-19in the denominators. The results showed that the fraction 1/2 showed shorter RT and error distance than fractions withother denominators. Additionally, fractions with three in the denominator showed shorter RT than other fractions, but wereequivalent in accuracy. This suggests that fractions with two and three in the denominator are distinctive, and those withlarger denominators would need additional processes at least for number line estimation.

Our previous studies (presented at the London meeting of EPS in 2017 and submitted for ICPS 2017) suggested thatimmediate serial recall tasks access magnitude representation of fraction. A subsequent research task is to explore the inter-correlations among four tasks stimulating representations of fraction magnitude: an immediate serial recall task with fractionstimuli and three typical tasks, number line estimation, comparison, and calculation of fractions. The purpose of this study is toexamine whether our new measure, the size of the magnitude similarity effect on immediate serial recall of fractions, relates toother typical measures for adults. The results from 36 university students showed a significant correlation between the size ofthe magnitude similarity effect and the RT of fraction calculation tasks but no correlations among any other tasks. This resultsuggests that it is necessary to reexamine what tasks could access the magnitudinal representation of fraction in adults.