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

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

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

---

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

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

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

---

$\text{c)}\frac{7}{10}+\frac{4}{5}+\frac{1}{2}=\frac{7}{10}+\frac{8}{10}+\frac{5}{10}=\frac{15}{10}+\frac{5}{10}=\frac{20}{10}=2$

$\frac{3}{4}+\frac{5}{7}+1\frac{1}{2}=\frac{21}{28}+\frac{20}{28}+1\frac{14}{28}=\frac{41}{28}+1\frac{14}{28}=1\frac{55}{28}=2\frac{27}{28}$

$\frac{7}{8}+\frac{1}{2}+\frac{2}{4}=\frac{7}{8}+\frac{4}{8}+\frac{4}{8}=\frac{11}{8}+\frac{4}{8}=\frac{15}{8}=1\frac{7}{8}$  

---

$\text{d)}2\frac{1}{6}+\frac{7}{10}+1\frac{2}{5}=2\frac{5}{30}+\frac{21}{30}+1\frac{12}{30}=2\frac{26}{30}+1\frac{12}{30}=3\frac{38}{30}=4\frac{8}{30}=4\frac{4}{15}$  

$1\frac{7}{8}+\frac{1}{3}+2\frac{5}{6}=1\frac{21}{24}+\frac{8}{24}+2\frac{20}{24}=1\frac{29}{24}+2\frac{20}{24}=3\frac{49}{24}=5\frac{1}{24}$    

$2\frac{7}{12}+1\frac{1}{15}+\frac{1}{2}=2\frac{35}{60}+1\frac{4}{60}+\frac{30}{60}=3\frac{39}{60}+\frac{30}{60}=3\frac{69}{60}=4\frac{9}{60}=4\frac{3}{20}$