$$1\frac{4}{5}+3\frac{2}{5}+2\frac{2}{3}$$
$\frac{118}{15}\approx 7.866666667$
$$\frac{5+4}{5}+\frac{3\times 5+2}{5}+\frac{2\times 3+2}{3}$$
$$\frac{9}{5}+\frac{3\times 5+2}{5}+\frac{2\times 3+2}{3}$$
$$\frac{9}{5}+\frac{15+2}{5}+\frac{2\times 3+2}{3}$$
$$\frac{9}{5}+\frac{17}{5}+\frac{2\times 3+2}{3}$$
$$\frac{9+17}{5}+\frac{2\times 3+2}{3}$$
$$\frac{26}{5}+\frac{2\times 3+2}{3}$$
$$\frac{26}{5}+\frac{6+2}{3}$$
$$\frac{26}{5}+\frac{8}{3}$$
$$\frac{78}{15}+\frac{40}{15}$$
$$\frac{78+40}{15}$$
$$\frac{118}{15}$$
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$\frac{2 \cdot 59}{3 \cdot 5} = 7\frac{13}{15} = 7.866666666666666$
