$\begin{array}{l} \text{Gegeben: } D=\left|\begin{array}{ccc} a1\ & b1 & c1\\ a2&b2 & c2\\ a3& b3 & c3 \end{array}\right| \\ \\ \\ \text{Gesucht: } \\\text{ Wert der Determinante D } \\ \\ \textbf{Gegeben:} \\ D=\left|\begin{array}{ccc} 1\frac{4}{5}\ & \frac{9}{13} & 3\frac{3}{4}\\ \frac{2}{5}&1\frac{5}{14} & 5\\ \frac{5}{8}& \frac{1}{2} & 1 \end{array}\right| \\ \\ \textbf{Rechnung:} \\ D=\left|\begin{array}{ccc} 1\frac{4}{5}\ & \frac{9}{13} & 3\frac{3}{4}\\ \frac{2}{5}&1\frac{5}{14} & 5\\ \frac{5}{8}& \frac{1}{2} & 1 \\ \end{array}\right| \begin{array}{cc} 1\frac{4}{5}\ & \frac{9}{13} \\ \frac{2}{5}&1\frac{5}{14} \\ \frac{5}{8}& \frac{1}{2} \end{array} \\ D=1\frac{4}{5} \cdot 1\frac{5}{14} \cdot 1+ \frac{9}{13} \cdot 5 \cdot \frac{5}{8} + 3\frac{3}{4} \cdot \frac{2}{5} \cdot \frac{1}{2} \\ - 3\frac{3}{4} \cdot 1\frac{5}{14} \cdot \frac{5}{8} - 1\frac{4}{5} \cdot 5 \cdot \frac{1}{2} - \frac{9}{13} \cdot \frac{2}{5} \cdot 1=-2,6 \end{array}$