519. Найдите значение выражения: a) $\frac{1}{4} \cdot 4 \cdot \frac{3}{4} \cdot \frac{16}{57} + (4\frac{3}{4} + 1\frac{2}{3}) \cdot \frac{16}{21} + \frac{2}{27} \cdot 4\frac{1}{2}$; б) $(\frac{4}{5} + \frac{1}{6}) \cdot (23\frac{2}{3} - 15\frac{1}{5}) - \frac{45}{58} - \frac{1}{2}$

a) $\frac{1}{4} \cdot 4 \cdot \frac{3}{4} \cdot \frac{16}{57} + (4\frac{3}{4} + 1\frac{2}{3}) \cdot \frac{16}{21} + \frac{2}{27} \cdot 4\frac{1}{2} = \frac{1 \cdot 4 \cdot 3 \cdot 16}{4 \cdot 4 \cdot 57} + (\frac{19}{4} + \frac{5}{3}) \cdot \frac{16}{21} + \frac{2}{27} \cdot \frac{9}{2} = \frac{48}{228} + (\frac{57}{12} + \frac{20}{12}) \cdot \frac{16}{21} + \frac{18}{54} = \frac{4}{19} + (\frac{77}{12}) \cdot \frac{16}{21} + \frac{1}{3} = \frac{4}{19} + \frac{77 \cdot 16}{12 \cdot 21} + \frac{1}{3} = \frac{4}{19} + \frac{1232}{252} + \frac{1}{3} = \frac{4}{19} + \frac{44}{9} + \frac{1}{3} = \frac{4}{19} + \frac{44}{9} + \frac{1}{3} = \frac{108 + 3344 + 57}{513} = \frac{3509}{513} $ б) $(\frac{4}{5} + \frac{1}{6}) \cdot (23\frac{2}{3} - 15\frac{1}{5}) - \frac{45}{58} - \frac{1}{2} = (\frac{24}{30} + \frac{5}{30}) \cdot (\frac{71}{3} - \frac{76}{5}) - \frac{45}{58} - \frac{1}{2} = \frac{29}{30} \cdot (\frac{355}{15} - \frac{228}{15}) - \frac{45}{58} - \frac{1}{2} = \frac{29}{30} \cdot \frac{127}{15} - \frac{45}{58} - \frac{1}{2} = \frac{3683}{450} - \frac{45}{58} - \frac{1}{2} = \frac{3683 \cdot 58 - 45 \cdot 450 - 1 \cdot 225 \cdot 58}{26100} = \frac{213614 - 20250 - 13050}{26100} = \frac{180314}{26100} = \frac{90157}{13050}$