6.58 Найдите сумму:

Решение:

1. \( \frac{8}{13} + \frac{3}{13} = \frac{8+3}{13} = \frac{11}{13} \)
2. \( \frac{31}{60} + \frac{29}{60} = \frac{31+29}{60} = \frac{60}{60} = 1 \)
3. \( 18 + \frac{4}{19} = \frac{18 \cdot 19}{19} + \frac{4}{19} = \frac{342+4}{19} = \frac{346}{19} \)
4. \( 23 + \frac{9}{10} = \frac{23 \cdot 10}{10} + \frac{9}{10} = \frac{230+9}{10} = \frac{239}{10} \)
5. \( 2 \frac{7}{9} + \frac{8}{9} = \frac{2 \cdot 9 + 7}{9} + \frac{8}{9} = \frac{18+7}{9} + \frac{8}{9} = \frac{25}{9} + \frac{8}{9} = \frac{25+8}{9} = \frac{33}{9} = \frac{11}{3} \)
6. \( 15 \frac{8}{11} + 4 \frac{3}{11} = (15+4) + (\frac{8}{11} + \frac{3}{11}) = 19 + \frac{11}{11} = 19 + 1 = 20 \)
7. \( 4 \frac{1}{2} + 3 \frac{1}{4} = \frac{4 \cdot 2 + 1}{2} + \frac{3 \cdot 4 + 1}{4} = \frac{9}{2} + \frac{13}{4} = \frac{9 \cdot 2}{4} + \frac{13}{4} = \frac{18}{4} + \frac{13}{4} = \frac{18+13}{4} = \frac{31}{4} \)
8. \( 5 \frac{1}{7} + 3 \frac{20}{21} = \frac{5 \cdot 7 + 1}{7} + \frac{3 \cdot 21 + 20}{21} = \frac{36}{7} + \frac{63+20}{21} = \frac{36 \cdot 3}{21} + \frac{83}{21} = \frac{108}{21} + \frac{83}{21} = \frac{108+83}{21} = \frac{191}{21} \)

Ответ: 1) \( \frac{11}{13} \); 2) \( 1 \); 3) \( \frac{346}{19} \); 4) \( \frac{239}{10} \); 5) \( \frac{11}{3} \); 6) \( 20 \); 7) \( \frac{31}{4} \); 8) \( \frac{191}{21} \).