275. Найдите сумму:

Решение:

1. \( 4\frac{5}{9} + 7\frac{1}{6} = \frac{4 · 9 + 5}{9} + \frac{7 · 6 + 1}{6} = \frac{36+5}{9} + \frac{42+1}{6} = \frac{41}{9} + \frac{43}{6} = \frac{41 · 2}{9 · 2} + \frac{43 · 3}{6 · 3} = \frac{82}{18} + \frac{129}{18} = \frac{211}{18} = 11\frac{13}{18} \)
2. \( 6\frac{11}{12} + 8\frac{13}{18} = \frac{6 · 12 + 11}{12} + \frac{8 · 18 + 13}{18} = \frac{72+11}{12} + \frac{144+13}{18} = \frac{83}{12} + \frac{157}{18} = \frac{83 · 3}{12 · 3} + \frac{157 · 2}{18 · 2} = \frac{249}{36} + \frac{314}{36} = \frac{563}{36} = 15\frac{23}{36} \)
3. \( 2\frac{3}{16} + 1\frac{7}{24} + 3\frac{1}{12} = \frac{2 · 16 + 3}{16} + \frac{1 · 24 + 7}{24} + \frac{3 · 12 + 1}{12} = \frac{32+3}{16} + \frac{24+7}{24} + \frac{36+1}{12} = \frac{35}{16} + \frac{31}{24} + \frac{37}{12} = \frac{35 · 3}{16 · 3} + \frac{31 · 2}{24 · 2} + \frac{37 · 4}{12 · 4} = \frac{105}{48} + \frac{62}{48} + \frac{148}{48} = \frac{315}{48} = \frac{105}{16} = 6\frac{9}{16} \)

Ответ: 1) \( 11\frac{13}{18} \); 2) \( 15\frac{23}{36} \); 3) \( 6\frac{9}{16} \).