$$(\frac{7}{9}+\frac{1}{3})+(\frac{1}{2}+\frac{4}{13})$$
$\frac{449}{234}\approx 1.918803419$
$$\frac{7}{9}+\frac{3}{9}+\frac{1}{2}+\frac{4}{13}$$
$$\frac{7+3}{9}+\frac{1}{2}+\frac{4}{13}$$
$$\frac{10}{9}+\frac{1}{2}+\frac{4}{13}$$
$$\frac{20}{18}+\frac{9}{18}+\frac{4}{13}$$
$$\frac{20+9}{18}+\frac{4}{13}$$
$$\frac{29}{18}+\frac{4}{13}$$
$$\frac{377}{234}+\frac{72}{234}$$
$$\frac{377+72}{234}$$
$$\frac{449}{234}$$
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$\frac{449}{2 \cdot 3 ^ {2} \cdot 13} = 1\frac{215}{234} = 1.9188034188034189$
