1 15/24 : 1 4/6 =

Convert mixed numbers to improper fractions: 1 15/24 = 39/24, 1 4/6 = 10/6. Divide the fractions: (39/24) / (10/6) = (39/24) * (6/10) = (39 * 6) / (24 * 10) = 234 / 240. Simplify the fraction: 234/240 = 39/40. The answer is 39/40.