5. Вычислите: \frac{9}{16} \cdot (\frac{1}{4} + \frac{5}{12}) \div \frac{8}{15} - \frac{16}{45}

Ответ: \frac{11}{24}

1. \( \frac{1}{4} + \frac{5}{12} = \frac{3}{12} + \frac{5}{12} = \frac{8}{12} = \frac{2}{3} \)
2. \( \frac{9}{16} \cdot \frac{2}{3} = \frac{9 \cdot 2}{16 \cdot 3} = \frac{18}{48} = \frac{3}{8} \)
3. \( \frac{3}{8} \div \frac{8}{15} = \frac{3}{8} \cdot \frac{15}{8} = \frac{3 \cdot 15}{8 \cdot 8} = \frac{45}{64} \)
4. \( \frac{45}{64} - \frac{16}{45} = \frac{45 \cdot 45}{64 \cdot 45} - \frac{16 \cdot 64}{45 \cdot 64} = \frac{2025}{2880} - \frac{1024}{2880} = \frac{1001}{2880} \approx 0.34757 \)
5. \(\frac{45}{64}-\frac{16}{45}=\frac{45\cdot 45 - 16 \cdot 64}{64\cdot 45} = \frac{2025-1024}{2880} = \frac{1001}{2880}\)
6. \(\frac{45}{64} - \frac{16}{45} = \frac{45 \cdot 45 - 16 \cdot 64}{64 \cdot 45} = \frac{2025 - 1024}{2880} = \frac{1001}{2880}\)
7. \(\frac{3}{8} \div \frac{8}{15} = \frac{3}{8} \cdot \frac{15}{8} = \frac{45}{64}\)
8. \(\frac{45}{64} - \frac{16}{45} = \frac{45 \cdot 45}{64 \cdot 45} - \frac{16 \cdot 64}{45 \cdot 64} = \frac{2025 - 1024}{2880} = \frac{1001}{2880}\)

Ответ: \(\frac{1001}{2880}\)