1. **Problem a:** Berechne $$-2 \frac{1}{4} \cdot \frac{2}{3} - \left[\left(-5 \frac{1}{2}\right) - \left(-1 \frac{1}{2}\right) : \frac{4}{5}\right]$$ 2. **Umwandlung in unechte Brüche:** $$-2 \frac{1}{4} = -\frac{9}{4}, \quad -5 \frac{1}{2} = -\frac{11}{2}, \quad -1 \frac{1}{2} = -\frac{3}{2}$$ 3. **Berechnung des ersten Terms:** $$-\frac{9}{4} \cdot \frac{2}{3} = -\frac{18}{12} = -\frac{3}{2}$$ 4. **Berechnung des Ausdrucks in der Klammer:** $$\left(-\frac{11}{2}\right) - \left(-\frac{3}{2}\right) : \frac{4}{5} = -\frac{11}{2} - \left(-\frac{3}{2} \cdot \frac{5}{4}\right)$$ 5. **Multiplikation im zweiten Term:** $$-\frac{3}{2} \cdot \frac{5}{4} = -\frac{15}{8}$$ 6. **Subtraktion in der Klammer:** $$-\frac{11}{2} - \left(-\frac{15}{8}\right) = -\frac{11}{2} + \frac{15}{8} = -\frac{44}{8} + \frac{15}{8} = -\frac{29}{8}$$ 7. **Endergebnis a:** $$-\frac{3}{2} - \left(-\frac{29}{8}\right) = -\frac{3}{2} + \frac{29}{8} = -\frac{12}{8} + \frac{29}{8} = \frac{17}{8} = 2 \frac{1}{8}$$ --- 1. **Problem b:** Berechne $$3 \frac{1}{4} : \frac{1}{2} - \left(-\frac{1}{2}\right) \cdot \left[\frac{1}{3} - \left(-2 \frac{1}{2}\right) \cdot 2\right]$$ 2. **Umwandlung in unechte Brüche:** $$3 \frac{1}{4} = \frac{13}{4}, \quad -2 \frac{1}{2} = -\frac{5}{2}$$ 3. **Division:** $$\frac{13}{4} : \frac{1}{2} = \frac{13}{4} \cdot 2 = \frac{26}{4} = \frac{13}{2}$$ 4. **Berechnung des Ausdrucks in der Klammer:** $$\frac{1}{3} - \left(-\frac{5}{2}\right) \cdot 2 = \frac{1}{3} + \frac{5}{2} \cdot 2 = \frac{1}{3} + 5 = \frac{1}{3} + \frac{15}{3} = \frac{16}{3}$$ 5. **Multiplikation mit $-\frac{1}{2}$:** $$-\left(-\frac{1}{2}\right) \cdot \frac{16}{3} = \frac{1}{2} \cdot \frac{16}{3} = \frac{16}{6} = \frac{8}{3}$$ 6. **Endergebnis b:** $$\frac{13}{2} + \frac{8}{3} = \frac{39}{6} + \frac{16}{6} = \frac{55}{6} = 9 \frac{1}{6}$$ --- 1. **Problem c:** Berechne $$\left(-\frac{3}{4}\right) \cdot \left(-\frac{4}{5}\right) + \frac{5}{8} \cdot \left(-\frac{4}{5}\right)$$ 2. **Multiplikationen:** $$\left(-\frac{3}{4}\right) \cdot \left(-\frac{4}{5}\right) = \frac{12}{20} = \frac{3}{5}$$ $$\frac{5}{8} \cdot \left(-\frac{4}{5}\right) = -\frac{20}{40} = -\frac{1}{2}$$ 3. **Addition:** $$\frac{3}{5} - \frac{1}{2} = \frac{6}{10} - \frac{5}{10} = \frac{1}{10}$$ --- 1. **Problem d:** Berechne $$1 \frac{2}{5} : \frac{6}{25} - \left(-3 \frac{1}{15}\right) : \frac{6}{25}$$ 2. **Umwandlung in unechte Brüche:** $$1 \frac{2}{5} = \frac{7}{5}, \quad -3 \frac{1}{15} = -\frac{46}{15}$$ 3. **Divisionen:** $$\frac{7}{5} : \frac{6}{25} = \frac{7}{5} \cdot \frac{25}{6} = \frac{175}{30} = \frac{35}{6}$$ $$-\frac{46}{15} : \frac{6}{25} = -\frac{46}{15} \cdot \frac{25}{6} = -\frac{1150}{90} = -\frac{115}{9}$$ 4. **Endergebnis d:** $$\frac{35}{6} - \left(-\frac{115}{9}\right) = \frac{35}{6} + \frac{115}{9} = \frac{105}{18} + \frac{230}{18} = \frac{335}{18} = 18 \frac{11}{18}$$