[…] Odani's truism is a mathematical result that says that if you want to compare the fractions a/b and c/d, it often is sufficient to compare the sums (a+d) and (b+c) rather than the products a*d and b*c. (All of the integers a, b, c, and d are positive.) If you compare the products, you will know the correct answer 100% of the time because a/b < c/d if and only if a*d < b*c. However, K. Odani proved (1998) that the expression (a+d) < (b+c) is true 91% of the time when the integers a, b, c, and d are chosen uniformly at random in the interval [1,N], where N is a very large integer. A previous article shows a Monte Carlo simulation that demonstrates Odani's truism. …