$$\frac{ 2 }{ 3 } \times \frac{ 4 }{ 5 } + \frac{ 9 }{ 3 } \times \frac{ 5 }{ 6 } + \frac{ 1 }{ 7 }$$
$\frac{667}{210}\approx 3.176190476$
$$\frac{2\times 4}{3\times 5}+\frac{9}{3}\times \frac{5}{6}+\frac{1}{7}$$
$$\frac{8}{15}+\frac{9}{3}\times \frac{5}{6}+\frac{1}{7}$$
$$\frac{8}{15}+3\times \frac{5}{6}+\frac{1}{7}$$
$$\frac{8}{15}+\frac{3\times 5}{6}+\frac{1}{7}$$
$$\frac{8}{15}+\frac{15}{6}+\frac{1}{7}$$
$$\frac{8}{15}+\frac{5}{2}+\frac{1}{7}$$
$$\frac{16}{30}+\frac{75}{30}+\frac{1}{7}$$
$$\frac{16+75}{30}+\frac{1}{7}$$
$$\frac{91}{30}+\frac{1}{7}$$
$$\frac{637}{210}+\frac{30}{210}$$
$$\frac{637+30}{210}$$
$$\frac{667}{210}$$
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$\frac{23 \cdot 29}{2 \cdot 3 \cdot 5 \cdot 7} = 3\frac{37}{210} = 3.176190476190476$
