Add fractions together first: (15+6+16)/24=37/24+M+N=3; M+N=3-37/24=(72-37)/24=35/24. The values of M and N are varied as 24ths. If we list them as pairs we have (1,34), (2,33), (3,32), (4,31), (5,30), (6,29), (7,28), (8,27), (9,26), (10,25), (11,24), (12,23), (13,22), (14,21), (15,20), (16,19), (17,18). The first 10 include improper fractions; the 11th has M or N equal to 1; the last 6 qualify as "ordinary" fractions. The "best" fractions are produced using (15,20): M=15/24=5/8 and M=20/24=5/6. The next "best" are produced using (14,21): M=14/24=7/12 and M=21/24=7/8. The remaining fractions include 24ths. The best answers are M=5/8 and N=5/6 or M=7/12 and N=7/8.