$(\frac{3}{15} - 2\frac{7}{25}) : 1\frac{2}{25} + 1\frac{4}{13} = (\frac{15}{75} - 2\frac{21}{75}) : \frac{27}{25} + 1\frac{4}{13} = -2\frac{6}{75} * \frac{25}{27} + 1\frac{4}{13} = -2\frac{2}{25} * \frac{25}{27} + 1\frac{4}{13} = -\frac{52}{25} * \frac{25}{27} + 1\frac{4}{13} = -\frac{52}{1} * \frac{1}{27} + 1\frac{4}{13} = -1\frac{25}{27} + 1\frac{4}{13} = -1\frac{325}{351} + 1\frac{108}{351} = -\frac{217}{351}$