This study explored the relationship between the efficiency of alerting, orienting and executive control networks (attentional executive function) and accessing numerical magnitudes in adults, during a fraction comparison task, presenting pairs of fractions either with (CC) or without (WCC) common components. The results indicate that CC fractions are processed in a componential style, are affected by a whole number bias (WNB) and that performance in this block does not depend on the efficiency of attentional networks. By contrast, pairs of WCC fractions are processed in a holistic way, the WNB interacts with the numerical distance between fractions and performance in this block correlates with the efficiency of attentional orienting and executive control systems. Taken together, our findings show that the efficient selection of information and inhibitory control of intervening variables play an important role in processing fractions, particularly when the task requires the use of more holistic strategies to access the numerical magnitude of the fraction.