$$\frac{2}{3}+\frac{3}{4}+\frac{2}{9}+\frac{7}{7}$$
$\frac{95}{36}\approx 2.638888889$
$$\frac{2}{3}+\frac{3}{4}+\frac{2}{9}+1$$
$$\frac{8}{12}+\frac{9}{12}+\frac{2}{9}+1$$
$$\frac{8+9}{12}+\frac{2}{9}+1$$
$$\frac{17}{12}+\frac{2}{9}+1$$
$$\frac{51}{36}+\frac{8}{36}+1$$
$$\frac{51+8}{36}+1$$
$$\frac{59}{36}+1$$
$$\frac{59}{36}+\frac{36}{36}$$
$$\frac{59+36}{36}$$
$$\frac{95}{36}$$
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$\frac{5 \cdot 19}{2 ^ {2} \cdot 3 ^ {2}} = 2\frac{23}{36} = 2.638888888888889$
