Calculate the following:

(i) $\dfrac{8}{15} + \dfrac{3}{15}$

(ii) $\dfrac{12}{15} - \dfrac{7}{15}$

(iii) $1 - \dfrac{2}{3}$

(iv) $\dfrac{7}{13} + \dfrac{2}{13} - \dfrac{5}{13}$

(v) $2\dfrac{4}{5} + 3\dfrac{3}{5}$

(vi) $3\dfrac{2}{7} - 1\dfrac{4}{7}$

(i) $\dfrac{8}{15} + \dfrac{3}{15}$

$\Rightarrow \dfrac{8 + 3}{15}\\[1em] \Rightarrow \dfrac{11}{15}$

Hence, $\dfrac{8}{15} + \dfrac{3}{15} = \dfrac{11}{15}$.

(ii) $\dfrac{12}{15} - \dfrac{7}{15}$

$\Rightarrow \dfrac{12 - 7}{15}\\[1em] \Rightarrow \dfrac{5}{15}\\[1em] \Rightarrow \dfrac{1}{3}$

Hence, $\dfrac{12}{15} - \dfrac{7}{15} = \dfrac{1}{3}$.

(iii) $1 - \dfrac{2}{3}$

$\Rightarrow \dfrac{3}{3} - \dfrac{2}{3}\\[1em] \Rightarrow \dfrac{3 - 2}{3}\\[1em] \Rightarrow \dfrac{1}{3}$

Hence, $1 - \dfrac{2}{3} = \dfrac{1}{3}$.

(iv) $\dfrac{7}{13} + \dfrac{2}{13} - \dfrac{5}{13}$

$\Rightarrow \dfrac{7 + 2 - 5}{13}\\[1em] \Rightarrow \dfrac{4}{13}$

Hence, $\dfrac{7}{13} + \dfrac{2}{13} - \dfrac{5}{13} = \dfrac{4}{13}$.

(v) $2\dfrac{4}{5} + 3\dfrac{3}{5}$

$\Rightarrow \dfrac{14}{5} + \dfrac{18}{5}\\[1em] \Rightarrow \dfrac{14 + 18}{5}\\[1em] \Rightarrow \dfrac{32}{5}\\[1em] \Rightarrow 6\dfrac{2}{5}$

Hence, $2\dfrac{4}{5} + 3\dfrac{3}{5} = 6\dfrac{2}{5}$.

(vi) $3\dfrac{2}{7} - 1\dfrac{4}{7}$

$\Rightarrow \dfrac{23}{7} - \dfrac{11}{7}\\[1em] \Rightarrow \dfrac{23 - 11}{7}\\[1em] \Rightarrow \dfrac{12}{7}\\[1em] \Rightarrow 1\dfrac{5}{7}$

Hence, $3\dfrac{2}{7} - 1\dfrac{4}{7} = 1\dfrac{5}{7}$.