$a)$

$\frac{1}{2}+\frac{3}{4}=\frac{2}{4}+\frac{3}{4}=\frac{2+3}{4}=\frac{5}{4}=1\frac{1}{4}$

$\frac{1}{3}+\frac{7}{9}=\frac{3}{9}+\frac{7}{9}=\frac{3+7}{9}=\frac{10}{9}=1\frac{1}{9}$

$\frac{5}{6}+1\frac{1}{4}=\frac{10}{12}+1\frac{3}{12}=1+\frac{13}{12}=1+1\frac{1}{12}=2\frac{1}{12}$

$b)$  

$1\frac{3}{5}+2\frac{4}{15}=1\frac{9}{15}+2\frac{4}{15}=1+2+\frac{9+4}{15}=3+\frac{13}{15}=3\frac{13}{15}$

$2\frac{1}{4}+1\frac{2}{3}=2\frac{3}{12}+1\frac{8}{12}=2+1+\frac{3+8}{12}=3+\frac{11}{12}=3\frac{11}{12}$

$1\frac{5}{6}+\frac{7}{9}=1\frac{15}{18}+\frac{14}{18}=1+\frac{15+14}{18}=1+\frac{29}{18}=1+1\frac{11}{18}=2\frac{11}{18}$

$c)$

$\frac{7}{10}+\frac{4}{5}+\frac{1}{2}=\frac{7}{10}+\frac{8}{10}+\frac{5}{10}=\frac{7+8+5}{10}=\frac{20}{10}=2$

$\frac{3}{4}+\frac{5}{7}+1\frac{1}{2}=\frac{21}{28}+\frac{20}{28}+1\frac{14}{28}$ $=1+\frac{21+20+14}{28}=1+\frac{55}{28}=1+1\frac{27}{28}=2\frac{27}{28}$

$\frac{7}{8}+\frac{1}{2}+\frac{2}{4}=\frac{7}{8}+\frac{4}{8}+\frac{4}{8}=\frac{7+4+4}{8}=\frac{15}{8}=1\frac{7}{8}$

$d)$

$2\frac{1}{6}+\frac{7}{10}+1\frac{2}{5}=2\frac{5}{30}+\frac{21}{30}+1\frac{12}{30}$ $=2+1+\frac{5+21+12}{30}=3+\frac{38}{30}=3+\frac{19}{15}=3+1\frac{4}{15}=4\frac{4}{15}$

$1\frac{7}{8}+\frac{1}{3}+2\frac{5}{6}=1\frac{21}{24}+\frac{8}{24}+2\frac{20}{24}$ $=1+2+\frac{21+8+20}{24}=3+\frac{49}{24}=3+2\frac{1}{24}=5\frac{1}{24}$

$2\frac{7}{12}+1\frac{1}{15}+\frac{1}{2}=2\frac{35}{60}+1\frac{4}{60}+\frac{30}{60}=2+1+\frac{35+4+30}{60}$ $=3+\frac{69}{60}=3+\frac{23}{20}=3+1\frac{3}{20}=4\frac{3}{20}$