$$1\frac{1}{6}+1\frac{1}{2}+1\frac{1}{6}$$
$\frac{23}{6}\approx 3.833333333$
$$\frac{6+1}{6}+\frac{1\times 2+1}{2}+\frac{1\times 6+1}{6}$$
$$\frac{7}{6}+\frac{1\times 2+1}{2}+\frac{1\times 6+1}{6}$$
$$\frac{7}{6}+\frac{2+1}{2}+\frac{1\times 6+1}{6}$$
$$\frac{7}{6}+\frac{3}{2}+\frac{1\times 6+1}{6}$$
$$\frac{7}{6}+\frac{9}{6}+\frac{1\times 6+1}{6}$$
$$\frac{7+9}{6}+\frac{1\times 6+1}{6}$$
$$\frac{16}{6}+\frac{1\times 6+1}{6}$$
$$\frac{8}{3}+\frac{1\times 6+1}{6}$$
$$\frac{8}{3}+\frac{6+1}{6}$$
$$\frac{8}{3}+\frac{7}{6}$$
$$\frac{16}{6}+\frac{7}{6}$$
$$\frac{16+7}{6}$$
$$\frac{23}{6}$$
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$\frac{23}{2 \cdot 3} = 3\frac{5}{6} = 3.8333333333333335$
