a) $1\frac{1}{2}+1\frac{1}{3}=\frac{3}{2}+\frac{4}{3}=\frac{9}{6}+\frac{8}{6}=\frac{17}{6}$
b) $2\frac{2}{3}-1\frac{4}{7}=\frac{8}{3}-\frac{11}{7}=\frac{56}{21}-\frac{33}{21}=\frac{23}{21}$
c) $2\frac{2}{3}\times 5\frac{1}{4}=\frac{8}{3}\times \frac{21}{4}=\frac{168}{12}=14$
d) $3\frac{1}{2}\div 2\frac{1}{4}=\frac{7}{2}\div \frac{9}{4}=\frac{28}{18}=\frac{14}{9}$