Fractions are crucial, from math and science education to daily activities, but they are hard. A puzzling aspect of fractions is that people over-rely on the numerator when comparing a pair of fractions. Previous work has considered this numerator bias mostly as a reasoning mishap. Still, in a vast amount of pairwise comparisons, across many real-world domains, not just education textbooks, we report a high prior probability that the larger fraction has the larger numerator, and, for a relevant case, we provide formal arguments why. The existence of such a regularity suggests that the numerator bias may reflect a rational adaptation that detects and exploits likely events. In a pair of visual-proportion tasks (discrete and continuous fractions), we confirm that the numerator bias in participants adapts to experimented regularities. Even though weak education and math abilities play a role, adaptation to informative priors outside the classroom poses a challenge to educators, learners, and decision-makers.

从数学和科学教育到日常活动，分数都是至关重要的，但是很难。分数的一个令人困惑的方面是，在比较一对分数时，人们过度依赖分子。先前的工作已将这种分子偏差主要视为推理事故。尽管如此，在许多现实世界中，不仅仅是教育教科书中，在大量成对比较中，我们报告了较大的分数具有较大的分子的较高的先验概率，并且在相关情况下，我们提供了正式理由。这种规律性的存在表明，分子偏差可能反映了一种合理的适应性，可以发现并利用可能的事件。在一对视觉比例任务（离散和连续分数）中，我们确认参与者的分子偏差适应于实验规律性。