$$\frac{5}{3}+\frac{5}{119}$$
$\frac{610}{357}\approx 1.708683473$
$$\frac{595}{357}+\frac{15}{357}$$
$$\frac{595+15}{357}$$
$$\frac{610}{357}$$
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$\frac{2 \cdot 5 \cdot 61}{3 \cdot 7 \cdot 17} = 1\frac{253}{357} = 1.7086834733893557$