Вычислите: \(\left(\frac{15}{28} - \frac{11}{36}\right) \cdot \frac{21}{29} - 6 \frac{6}{7} : \left(-\frac{16}{21}\right) : \frac{33}{2}\)

Решение: 1. Найдем общий знаменатель для 28 и 36. 28 = 2 \(\cdot\) 2 \(\cdot\) 7, 36 = 2 \(\cdot\) 2 \(\cdot\) 3 \(\cdot\) 3. Общий знаменатель = 2 \(\cdot\) 2 \(\cdot\) 3 \(\cdot\) 3 \(\cdot\) 7 = 252. \(\frac{15}{28} - \frac{11}{36} = \frac{15 \cdot 9}{28 \cdot 9} - \frac{11 \cdot 7}{36 \cdot 7} = \frac{135}{252} - \frac{77}{252} = \frac{135-77}{252} = \frac{58}{252} = \frac{29}{126}\) 2. \(\frac{29}{126} \cdot \frac{21}{29} = \frac{29 \cdot 21}{126 \cdot 29} = \frac{21}{126} = \frac{1}{6}\) 3. \(6 \frac{6}{7} = \frac{6 \cdot 7 + 6}{7} = \frac{42+6}{7} = \frac{48}{7}\) 4. \(\frac{48}{7} : \left(-\frac{16}{21}\right) = \frac{48}{7} \cdot \left(-\frac{21}{16}\right) = -\frac{48 \cdot 21}{7 \cdot 16} = -\frac{3 \cdot 3}{1 \cdot 1} = -9\) 5. \(-9 : \frac{33}{2} = -9 \cdot \frac{2}{33} = -\frac{9 \cdot 2}{33} = -\frac{3 \cdot 2}{11} = -\frac{6}{11}\) 6. \(\frac{1}{6} - \left(-\frac{6}{11}\right) = \frac{1}{6} + \frac{6}{11} = \frac{11}{66} + \frac{36}{66} = \frac{11+36}{66} = \frac{47}{66}\) Ответ: \(\frac{47}{66}\)