$$\frac{5}{7}+\frac{1}{3}+\frac{8}{9}+\frac{1}{14}$$
$\frac{253}{126}\approx 2.007936508$
$$\frac{15}{21}+\frac{7}{21}+\frac{8}{9}+\frac{1}{14}$$
$$\frac{15+7}{21}+\frac{8}{9}+\frac{1}{14}$$
$$\frac{22}{21}+\frac{8}{9}+\frac{1}{14}$$
$$\frac{66}{63}+\frac{56}{63}+\frac{1}{14}$$
$$\frac{66+56}{63}+\frac{1}{14}$$
$$\frac{122}{63}+\frac{1}{14}$$
$$\frac{244}{126}+\frac{9}{126}$$
$$\frac{244+9}{126}$$
$$\frac{253}{126}$$
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$\frac{11 \cdot 23}{2 \cdot 3 ^ {2} \cdot 7} = 2\frac{1}{126} = 2.007936507936508$
