$$1\frac{2}{3}+\frac{3}{4}+2\frac{5}{12}+3\frac{7}{16}$$
$\frac{397}{48}\approx 8.270833333$
$$\frac{3+2}{3}+\frac{3}{4}+\frac{2\times 12+5}{12}+\frac{3\times 16+7}{16}$$
$$\frac{5}{3}+\frac{3}{4}+\frac{2\times 12+5}{12}+\frac{3\times 16+7}{16}$$
$$\frac{20}{12}+\frac{9}{12}+\frac{2\times 12+5}{12}+\frac{3\times 16+7}{16}$$
$$\frac{20+9}{12}+\frac{2\times 12+5}{12}+\frac{3\times 16+7}{16}$$
$$\frac{29}{12}+\frac{2\times 12+5}{12}+\frac{3\times 16+7}{16}$$
$$\frac{29}{12}+\frac{24+5}{12}+\frac{3\times 16+7}{16}$$
$$\frac{29}{12}+\frac{29}{12}+\frac{3\times 16+7}{16}$$
$$\frac{29+29}{12}+\frac{3\times 16+7}{16}$$
$$\frac{58}{12}+\frac{3\times 16+7}{16}$$
$$\frac{29}{6}+\frac{3\times 16+7}{16}$$
$$\frac{29}{6}+\frac{48+7}{16}$$
$$\frac{29}{6}+\frac{55}{16}$$
$$\frac{232}{48}+\frac{165}{48}$$
$$\frac{232+165}{48}$$
$$\frac{397}{48}$$
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$\frac{397}{2 ^ {4} \cdot 3} = 8\frac{13}{48} = 8.270833333333334$
