$$3\frac{4}{5}+2\frac{3}{10}+1\frac{1}{15}$$
$\frac{43}{6}\approx 7.166666667$
$$\frac{15+4}{5}+\frac{2\times 10+3}{10}+\frac{1\times 15+1}{15}$$
$$\frac{19}{5}+\frac{2\times 10+3}{10}+\frac{1\times 15+1}{15}$$
$$\frac{19}{5}+\frac{20+3}{10}+\frac{1\times 15+1}{15}$$
$$\frac{19}{5}+\frac{23}{10}+\frac{1\times 15+1}{15}$$
$$\frac{38}{10}+\frac{23}{10}+\frac{1\times 15+1}{15}$$
$$\frac{38+23}{10}+\frac{1\times 15+1}{15}$$
$$\frac{61}{10}+\frac{1\times 15+1}{15}$$
$$\frac{61}{10}+\frac{15+1}{15}$$
$$\frac{61}{10}+\frac{16}{15}$$
$$\frac{183}{30}+\frac{32}{30}$$
$$\frac{183+32}{30}$$
$$\frac{215}{30}$$
$$\frac{43}{6}$$
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$\frac{43}{2 \cdot 3} = 7\frac{1}{6} = 7.166666666666667$
