Решение:

a) $$6 + 8\frac{7}{13} = 6 + \frac{8 \cdot 13 + 7}{13} = 6 + \frac{104 + 7}{13} = 6 + \frac{111}{13} = \frac{6 \cdot 13}{13} + \frac{111}{13} = \frac{78}{13} + \frac{111}{13} = \frac{78 + 111}{13} = \frac{189}{13}$$

б) $$12 + 19\frac{5}{24} = 12 + \frac{19 \cdot 24 + 5}{24} = 12 + \frac{456 + 5}{24} = 12 + \frac{461}{24} = \frac{12 \cdot 24}{24} + \frac{461}{24} = \frac{288}{24} + \frac{461}{24} = \frac{288 + 461}{24} = \frac{749}{24}$$

в) $$5\frac{7}{15} + 8\frac{4}{15} = \frac{5 \cdot 15 + 7}{15} + \frac{8 \cdot 15 + 4}{15} = \frac{75 + 7}{15} + \frac{120 + 4}{15} = \frac{82}{15} + \frac{124}{15} = \frac{82 + 124}{15} = \frac{206}{15}$$

г) $$13\frac{5}{101} + 7\frac{25}{101} = \frac{13 \cdot 101 + 5}{101} + \frac{7 \cdot 101 + 25}{101} = \frac{1313 + 5}{101} + \frac{707 + 25}{101} = \frac{1318}{101} + \frac{732}{101} = \frac{1318 + 732}{101} = \frac{2050}{101}$$