\( \displaystyle 8\frac{5}{6} + 5\frac{2}{3} - 17\frac{7}{15} \\=8+\dfrac{5}{6} + 5+\dfrac{2}{3} - \color{red}{\{ 17+\dfrac{7}{15}\} }=\{ 8+5-17 \} +\{ \dfrac{5}{6} + \dfrac{2}{3} \color{red}{-} \dfrac{7}{15}\} \\
=-4 + \{ \dfrac{25}{30} + \dfrac{20}{30} - \dfrac{14}{30}\}~~~\because~the~ Lowest~ Common ~Multiple~is~~30\\=-4 + \dfrac{31}{30}=-5+1 \dfrac{1}{30} =-4+1+\dfrac{1}{30}=-3+\dfrac{1}{30}\\=\color{red}{-2+\{-1+\dfrac{1}{30} \} }=-2\dfrac{29}{30}~~\\Note~how ~we~ borrowed~-1~from~~- 3~~to~add~\dfrac{29}{30}~~\)

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