Đặt \(\overrightarrow {PA} = x\overrightarrow {SA} ,\,\,\overrightarrow {BQ} = y\overrightarrow {BN} \).

Khi đó, \(\overrightarrow {PQ} = \overrightarrow {PA} + \overrightarrow {AB} + \overrightarrow {BQ} = x\overrightarrow {SA} + \left( {\overrightarrow {SB} - \overrightarrow {SA} } \right) + y\left( {\overrightarrow {SN} - \overrightarrow {SB} } \right)\)

                   \( = \left( {x - 1} \right)\overrightarrow {SA} + \left( {1 - y} \right)\overrightarrow {SB} + y\overrightarrow {SN} \)\( = \left( {x - 1} \right)\overrightarrow {SA} + \left( {1 - y} \right)\overrightarrow {SB} + \frac{y}{2}\overrightarrow {SC} \)

                   \( = \left( {x - 1} \right)\overrightarrow a + \left( {1 - y} \right)\overrightarrow b + \frac{y}{2}\overrightarrow c \).

Lại có \(\overrightarrow {CM} = \overrightarrow {SM} - \overrightarrow {SC} = \frac{1}{2}\left( {\overrightarrow {SA} + \overrightarrow {SB} } \right) - \overrightarrow {SC} = \frac{1}{2}\overrightarrow a + \frac{1}{2}\overrightarrow b - \overrightarrow c \).

Vì \(PQ\,{\rm{//}}\,CM\) nên tồn tại số thực \(k \ne 0\) sao cho \(\overrightarrow {PQ} = k\overrightarrow {CM} \).

Suy ra \(\frac{{\frac{1}{2}}} = \frac{{\frac{1}{2}}} = \frac{{\frac{y}{2}}}{{ - 1}}\)\( \Leftrightarrow \left\{ \begin{array}{l}x = \frac{2}{3}\\y = \frac{4}{3}\end{array} \right.\).

Khi đó, \(\overrightarrow {PQ} = - \frac{1}{3}\overrightarrow a - \frac{1}{3}\overrightarrow b + \frac{2}{3}\overrightarrow c \). Vậy \(\frac{m}{n} + \frac{p}{q} + \frac{r}{z} = \frac{1}{3} + \frac{1}{3} + \frac{2}{3} = \frac{4}{3} \approx 1,3\).

Đáp số: \(1,3\).