The Common Representation Of Fractions And Decimals In Different Tasks

Numbers play an important role in our daily life. Many studies found the distance effect in the representation of integers. Although several studies have compared the representation of fractions and decimals, no study has investigated whether fractions and decimals, as two types of rational numbers, share a common representation of magnitude.Researchers put forward two representation models for fractions:(1) Holistic representation:According to this model. the representation of fractions relies on the holistic magnitude of fractions. (2) Componential representation:This kind of representation relies on the constituent numerator or denominator. Most researchers put forward that the componential representation has an advantage over the holistic representation. Fractions are coarsely treated as entities " smaller than one " when compared with integers. In contrast to abundant studies of fractions, only a few studies have investigated the mental representation of decimals. These researchers demonstrate that the processing of decimals is determined by the numerical distance and the position of the digit. Only a few studies compared the processing of decimals and fractions and found an advantage for decimals. The numerical comparison and matching tasks are the most popular paradigms in this area. It is said that the matching and comparison tasks, although similar. each provide an unique piece of information. It is not clear whether fractions and decimals share a common representation of magnitude, whether this representation depends on the tasks.The present study includes two different number pairs which were presented sequentially:fraction- decimal mixed pairs and decimal - fraction mixed pairs in three studies. The first study includes two experiments. Both of them are comparison tasks. The small distance of the first experiment is 0.1 and the large distance is 0.3 in the experiment 1. and the small distance is 0.3 and the large distance is 1.3 in experiment 2. Both two experiments showed a distance effect.The second study is the numerical matching task and includes two experiments too. The small distance of the first experiment is 0.1 and the large distance is 0.3 in the experiment 1, and the small distance is 0.3 and the large distance is 1.3 in experiment 2. The distance effect only appears in the experiment 2.The last study repeats the first two studies, but takes children as participants. The results is same as the fist two studies. When the mixed pairs were very close numerically with the distance 0.1 or 0.3. there was a significant distance effect in the comparison task but not in the matching task. However, when the mixed pairs were further apart numerically with the distance 0.3 or 1.3, the distance effect appears in both tasks. In addition, all the experiments showed a main effect of the order.To sum up the results, fractions and decimals share a common representation of magnitude and this representation is dependent on task paradigms. Fractions and decimals could be translated into a common representation of magnitude in the numerical comparison task. However, in the numerical matching task the representation of fractions and decimals was less accurate and they could be translated into a common representation of magnitude only when the distance between fraction and decimal pairs was larger. There is an advantage for the representation of decimal. The representation model of fractions and decimals is same in adults and children.