It is a well-documented fact that many students struggle with fractions. Problems in understanding and applying fractions persist into adulthood, with moderate to severe consequences for everyday and occupational decision making. Why is it that fractions present such a difficult topic conceptually and procedurally? Is it because of deficiencies in teachers’ pedagogical content knowledge? Or is the nature of common, nondecimal fractions quite hard to grasp and internalize? And then, what is the nature of fractions anyway? In this presentation, we will look at the history of fractions and fraction operations in the ancient Egyptian and classic Chinese mathematical traditions as well as modern Japanese teaching approaches. These exercises will help us define some effective ways to understand, teach, and learn fractions.