1. **Problem:** Izračunaj in okrajšaj kolikor je to mogoče izraz: $$\frac{5}{8} - \frac{5}{12} + \frac{3}{4} - \frac{2}{3} + \frac{1}{6} + \frac{1}{24}$$ 2. **Formula and rules:** Za seštevanje in odštevanje ulomkov moramo najprej poenotiti imenovalce. Najmanjši skupni imenovalec (NSI) za 8, 12, 4, 3, 6, 24 je 24. 3. **Intermediate work:** $$\frac{5}{8} = \frac{5 \times 3}{8 \times 3} = \frac{15}{24}$$ $$\frac{5}{12} = \frac{5 \times 2}{12 \times 2} = \frac{10}{24}$$ $$\frac{3}{4} = \frac{3 \times 6}{4 \times 6} = \frac{18}{24}$$ $$\frac{2}{3} = \frac{2 \times 8}{3 \times 8} = \frac{16}{24}$$ $$\frac{1}{6} = \frac{1 \times 4}{6 \times 4} = \frac{4}{24}$$ $$\frac{1}{24} = \frac{1}{24}$$ 4. **Sum and simplify:** $$\frac{15}{24} - \frac{10}{24} + \frac{18}{24} - \frac{16}{24} + \frac{4}{24} + \frac{1}{24} = \frac{15 - 10 + 18 - 16 + 4 + 1}{24} = \frac{12}{24}$$ 5. **Cancel common factors:** $$\frac{\cancel{12}}{\cancel{24}} = \frac{1}{2}$$ **Final answer:** $$\boxed{\frac{1}{2}}$$