1. Find two positive irreducible fractions with denominators not exceeding 100, the sum of which is equal to 86/111.
Answer: $2 / 3+4 / 37$

Solution: $111=37 * 3$, i.e., one fraction should have a denominator of 37, and the other should have a denominator of 3. It is clear that the numerator of the second fraction can be 1 or 2. 1/3 does not work, but for $2 / 3$ we get $4 / 37$