a)

$1\frac{2}{5}+\frac{1}{3}=1\frac{6}{15}+\frac{5}{15}=1\frac{11}{15}$  

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b)

$2\frac{3}{8}-\frac{5}{7}=2\frac{21}{56}-\frac{40}{56}=1\frac{77}{56}-\frac{40}{56}=1\frac{37}{56}$  

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c)

$1\frac{3}{5}\cdot \frac{5}{8}=\frac{{}^1\sout{8}}{{}_1\cancel{5}}\cdot \frac{{\cancel{5}}^1}{{\sout{8}}_1}=1$   

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d)

$2\frac{1}{3}:1\frac{5}{6}=\frac{7}{3}:\frac{11}{6}=\frac{7}{{}_1\cancel{3}}\cdot \frac{{\cancel{6}}^2}{11}=\frac{7}{1}\cdot \frac{2}{11}=\frac{14}{11}=1\frac{3}{11}$