[tex](( \frac{4}{5} + \frac{5}{6} \times \frac{3}{25} ) \div \frac{9}{2} - \frac{1}{15} ) \times 3 \frac{3}{4} + \frac{1}{2} = \\ (( \frac{4}{5} + \frac{1}{10} ) \div \frac{9}{2} - \frac{1}{15} ) \times \frac{15}{4} + \frac{1}{2} = \\ (( \frac{8}{10} + \frac{1}{10} ) \div \frac{9}{2} - \frac{1}{15} ) \times \frac{15}{4} + \frac{1}{2} = \\ ( \frac{9}{10} \times \frac{2}{9 } - \frac{1}{15} ) \times \frac{15}{4} + \frac{1}{2} = \\ ( \frac{1}{5} - \frac{1}{15} ) \times \frac{15}{4} + \frac{1}{2} = \\ ( \frac{3 }{15} - \frac{1}{15} ) \times \frac{15}{4} + \frac{1}{2} = \\ \frac{2}{15} \times \frac{15}{4} + \frac{1}{2} = \\ \frac{1}{2} + \frac{1}{2} = \frac{2}{2} = 1[/tex]
