$$(\frac{1}{4}+\frac{1}{3})+(1\frac{8}{9}+4\frac{2}{7})$$
$\frac{1703}{252}\approx 6.757936508$
$$\frac{3}{12}+\frac{4}{12}+\frac{1\times 9+8}{9}+\frac{4\times 7+2}{7}$$
$$\frac{3+4}{12}+\frac{1\times 9+8}{9}+\frac{4\times 7+2}{7}$$
$$\frac{7}{12}+\frac{1\times 9+8}{9}+\frac{4\times 7+2}{7}$$
$$\frac{7}{12}+\frac{9+8}{9}+\frac{4\times 7+2}{7}$$
$$\frac{7}{12}+\frac{17}{9}+\frac{4\times 7+2}{7}$$
$$\frac{21}{36}+\frac{68}{36}+\frac{4\times 7+2}{7}$$
$$\frac{21+68}{36}+\frac{4\times 7+2}{7}$$
$$\frac{89}{36}+\frac{4\times 7+2}{7}$$
$$\frac{89}{36}+\frac{28+2}{7}$$
$$\frac{89}{36}+\frac{30}{7}$$
$$\frac{623}{252}+\frac{1080}{252}$$
$$\frac{623+1080}{252}$$
$$\frac{1703}{252}$$
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$\frac{13 \cdot 131}{2 ^ {2} \cdot 3 ^ {2} \cdot 7} = 6\frac{191}{252} = 6.757936507936508$
