21. \( \frac{1}{6}+\frac{2}{3}-\frac{5}{12} \) 22. \( \frac{3}{10}-\frac{1}{5}+\frac{7}{20} \) 23. \( \frac{5}{12}+\frac{1}{4}-\frac{3}{8} \) 24. \( \frac{7}{15}-\frac{1}{5}+\frac{3}{10} \) 25. \( \frac{2}{9}+\frac{5}{6}-\frac{7}{18} \) 26. \( \frac{3}{7}-\frac{1}{14}+\frac{5}{28} \) 27. \( \frac{4}{5}+\frac{7}{10}-\frac{9}{20} \) 28. \( \frac{5}{6}-\frac{1}{3}+\frac{7}{12} \) 29. \( \frac{8}{15}+\frac{2}{5}-\frac{3}{10} \) 30. \( \frac{9}{20}-\frac{1}{4}+\frac{3}{10} \)

To find the result of \( \frac{1}{6}+\frac{2}{3}-\frac{5}{12} \), first, we convert all the fractions to have a common denominator, which is 12. This gives us \( \frac{2}{12} + \frac{8}{12} - \frac{5}{12} = \frac{5}{12} \). For \( \frac{3}{10}-\frac{1}{5}+\frac{7}{20} \), we also need a common denominator, which is 20. This converts to \( \frac{6}{20} - \frac{4}{20} + \frac{7}{20} = \frac{9}{20} \). Now, when solving \( \frac{5}{12}+\frac{1}{4}-\frac{3}{8} \), we convert everything to a denominator of 24. This becomes \( \frac{10}{24} + \frac{6}{24} - \frac{9}{24} = \frac{7}{24} \). Continuing, for \( \frac{7}{15}-\frac{1}{5}+\frac{3}{10} \), we find a common denominator of 30: \( \frac{14}{30} - \frac{6}{30} + \frac{9}{30} = \frac{17}{30} \). For \( \frac{2}{9}+\frac{5}{6}-\frac{7}{18} \), using a common denominator of 18, we get \( \frac{4}{18} + \frac{15}{18} - \frac{7}{18} = \frac{12}{18} \) or \( \frac{2}{3} \). Next, \( \frac{3}{7}-\frac{1}{14}+\frac{5}{28} \) can be simplified with a common denominator of 28: \( \frac{12}{28} - \frac{2}{28} + \frac{5}{28} = \frac{15}{28} \). For \( \frac{4}{5}+\frac{7}{10}-\frac{9}{20} \), we convert to a denominator of 20, yielding \( \frac{16}{20} + \frac{14}{20} - \frac{9}{20} = \frac{21}{20} \). Next, \( \frac{5}{6}-\frac{1}{3}+\frac{7}{12} \) combined gives us a denominator of 12: \( \frac{10}{12} - \frac{4}{12} + \frac{7}{12} = \frac{13}{12} \). For \( \frac{8}{15}+\frac{2}{5}-\frac{3}{10} \), using common denominators of 30 leads to \( \frac{16}{30} + \frac{12}{30} - \frac{9}{30} = \frac{19}{30} \). Finally, \( \frac{9}{20}-\frac{1}{4}+\frac{3}{10} \) transforms into a common denominator of 20, resulting in \( \frac{9}{20} - \frac{5}{20} + \frac{6}{20} = \frac{10}{20} \) or \( \frac{1}{2} \). Math is all about practice, and simplifying fractions can often lead to mistakes! One quick tip is to carefully redo any calculations when adding or subtracting fractions. Many mistakes come from failing to find that common denominator, so always double-check your work and keep your fractions organized! If you're fascinated by mathematical concepts, diving deeper into rational numbers and fractions offers rich territory! Consider exploring books on number theory or algebra for greater insights and fun problems to solve. You'll not only sharpen your skills, but you may also discover new techniques to wow your friends!