2.245. Найдите сумму: а) 38 1/8 + 4 5/24; б) 4 19/75 + 6 17/45; в) 47 3/14 + 1 8/21; г) 54 3/4 + 18 5/6; д) 28 5/9 + 13 3/4; е) 4/7 + 2 3/5; ж) 9 + 2 2/9; з) 3 11/24 + 1/6.

Приведём дробные части к общему знаменателю и сложим целые и дробные части.

1. \(38\frac{1}{8}+4\frac{5}{24}=42+\left(\frac{3}{24}+\frac{5}{24}\right)=42\frac{8}{24}=42\frac{1}{3}\).
2. \(4\frac{19}{75}+6\frac{17}{45}=10+\left(\frac{57}{225}+\frac{85}{225}\right)=10\frac{142}{225}\).
3. \(47\frac{3}{14}+1\frac{8}{21}=48+\left(\frac{9}{42}+\frac{16}{42}\right)=48\frac{25}{42}\).
4. \(54\frac{3}{4}+18\frac{5}{6}=72+\left(\frac{9}{12}+\frac{10}{12}\right)=72\frac{19}{12}=73\frac{7}{12}\).
5. \(28\frac{5}{9}+13\frac{3}{4}=41+\left(\frac{20}{36}+\frac{27}{36}\right)=41\frac{47}{36}=42\frac{11}{36}\).
6. \(\frac{4}{7}+2\frac{3}{5}=2+\left(\frac{20}{35}+\frac{21}{35}\right)=2\frac{41}{35}=3\frac{6}{35}\).
7. \(9+2\frac{2}{9}=11\frac{2}{9}\).
8. \(3\frac{11}{24}+\frac{1}{6}=3+\left(\frac{11}{24}+\frac{4}{24}\right)=3\frac{15}{24}=3\frac{5}{8}\).

Ответ: а) \(42\frac{1}{3}\); б) \(10\frac{142}{225}\); в) \(48\frac{25}{42}\); г) \(73\frac{7}{12}\); д) \(42\frac{11}{36}\); е) \(3\frac{6}{35}\); ж) \(11\frac{2}{9}\); з) \(3\frac{5}{8}\).