Решение примеров:

Пример 3 (сложение):

$$9 \frac{8}{21} + 4 \frac{11}{14} = (9 + 4) + (\frac{8}{21} + \frac{11}{14})$$

$$= 13 + (\frac{8 \cdot 2}{21 \cdot 2} + \frac{11 \cdot 3}{14 \cdot 3}) = 13 + (\frac{16}{42} + \frac{33}{42})$$

$$= 13 + \frac{16 + 33}{42} = 13 + \frac{49}{42} = 13 + \frac{7}{6} = 13 + 1 \frac{1}{6} = 14 \frac{1}{6}$$

Ответ: $$14 \frac{1}{6}$$

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Пример 4 (сложение):

$$8 \frac{5}{9} + 7 \frac{3}{4} + 12 \frac{7}{12} = (8 + 7 + 12) + (\frac{5}{9} + \frac{3}{4} + \frac{7}{12})$$

$$= 27 + (\frac{5 \cdot 4}{9 \cdot 4} + \frac{3 \cdot 9}{4 \cdot 9} + \frac{7 \cdot 3}{12 \cdot 3}) = 27 + (\frac{20}{36} + \frac{27}{36} + \frac{21}{36})$$

$$= 27 + \frac{20 + 27 + 21}{36} = 27 + \frac{68}{36} = 27 + \frac{17}{9} = 27 + 1 \frac{8}{9} = 28 \frac{8}{9}$$

Ответ: $$28 \frac{8}{9}$$

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Пример 3 (вычитание):

$$11 \frac{11}{12} - 5 \frac{7}{9} = (11 - 5) + (\frac{11}{12} - \frac{7}{9})$$

$$= 6 + (\frac{11 \cdot 3}{12 \cdot 3} - \frac{7 \cdot 4}{9 \cdot 4}) = 6 + (\frac{33}{36} - \frac{28}{36})$$

$$= 6 + \frac{33 - 28}{36} = 6 + \frac{5}{36} = 6 \frac{5}{36}$$

Ответ: $$6 \frac{5}{36}$$

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Пример 4 (вычитание):

$$9 \frac{17}{24} - 8 \frac{11}{36} = (9 - 8) + (\frac{17}{24} - \frac{11}{36})$$

$$= 1 + (\frac{17 \cdot 3}{24 \cdot 3} - \frac{11 \cdot 2}{36 \cdot 2}) = 1 + (\frac{51}{72} - \frac{22}{72})$$

$$= 1 + \frac{51 - 22}{72} = 1 + \frac{29}{72} = 1 \frac{29}{72}$$

Ответ: $$1 \frac{29}{72}$$