6.

Решение:

\( 36 \frac{2}{3} : 15 + 8 \frac{2}{3} \cdot 7 - 2 \frac{3}{8} + \frac{3}{4} + 24 \frac{7}{9} \)

Первая часть:

\( 36 \frac{2}{3} : 15 = \frac{110}{3} : 15 = \frac{110}{3 \cdot 15} = \frac{110}{45} = \frac{22}{9} \)

\( 8 \frac{2}{3} \cdot 7 = \frac{26}{3} \cdot 7 = \frac{182}{3} \)

\( \frac{22}{9} + \frac{182}{3} = \frac{22 + 182 \cdot 3}{9} = \frac{22 + 546}{9} = \frac{568}{9} \)

Вторая часть:

\( 2 \frac{3}{8} + \frac{3}{4} = \frac{19}{8} + \frac{6}{8} = \frac{25}{8} \)

\( 24 \frac{7}{9} = \frac{216 + 7}{9} = \frac{223}{9} \)

\( \frac{568}{9} - \frac{25}{8} + \frac{223}{9} \)

\( \frac{568 + 223}{9} - \frac{25}{8} = \frac{791}{9} - \frac{25}{8} = \frac{791 \cdot 8 - 25 \cdot 9}{72} = \frac{6328 - 225}{72} = \frac{6103}{72} \)

Нижняя строка:

\( 12 \frac{3}{7} - 7 \frac{2}{3} \)

\( 157 \frac{4}{5} : 24 \)

\( 12 \frac{3}{7} = \frac{87}{7} \)

\( 7 \frac{2}{3} = \frac{23}{3} \)

\( \frac{87}{7} - \frac{23}{3} = \frac{87 \cdot 3 - 23 \cdot 7}{21} = \frac{261 - 161}{21} = \frac{100}{21} \)

\( 157 \frac{4}{5} : 24 = \frac{789}{5} : 24 = \frac{789}{5 \cdot 24} = \frac{789}{120} = \frac{263}{40} \)

Решаем верхний пример:

\( \frac{6103}{72} \approx 84.76 \)

Решаем нижний пример:

\( \frac{100}{21} - \frac{263}{40} = \frac{100 \cdot 40 - 263 \cdot 21}{840} = \frac{4000 - 5523}{840} = \frac{-1523}{840} \)

Ответ: Верхний пример \( \frac{6103}{72} \), Нижний пример \( \frac{-1523}{840} \).