1) \( \frac{1}{6} + \frac{15}{19} - \frac{13}{19} = \frac{1}{6} + \frac{2}{19} = \frac{19 + 12}{114} = \frac{31}{114} \)
2) \( 6 \frac{5}{27} + 4 \frac{12}{27} = 10 \frac{17}{27} \)
3) \( 1 - \frac{9}{17} = \frac{17}{17} - \frac{9}{17} = \frac{8}{17} \)
4) \( 9 \frac{3}{12} - 5 \frac{1}{2} = 9 \frac{1}{4} - 5 \frac{1}{2} = 9 \frac{1}{4} - 5 \frac{2}{4} = 8 \frac{5}{4} - 5 \frac{2}{4} = 3 \frac{3}{4} \)