Explore the fundamental theory of fractions in this 24-minute mathematics video. Learn how to rigorously set up a theory of fractions, objects of the form a/b where a and b are natural numbers. Delve into the challenges of arithmetic with fractions, understand the concept of fractions, and examine primary operations. Investigate the comparison of products, prove the rule of addition, and study the laws of arithmetic including the distributive law. Gain insights into why fractions are essential in mathematics and how they form a crucial foundation for more advanced mathematical concepts. Suitable for students and enthusiasts seeking a deeper understanding of this fundamental aspect of arithmetic.