The discussion explains how to understand the concept of modulo with fractions, specifically focusing on the example of 3^-1 mod 5, which equals 2. It clarifies that in rational numbers, 1/3 is the solution to the equation 3 * x = 1, and similarly, in modular arithmetic, 3 * x = 1 mod 5 also yields x = 2. The relationship between the modular inverse and fractions is highlighted, stating that if gcd(a,m) = 1, then the inverse can be found using the Euclidean algorithm. The conversation encourages further exploration of the topic through resources like the "modular inverse" articles on Wikipedia and Wolfram. Understanding these principles is essential for grasping modular arithmetic with fractions.