$$2\frac{3}{4}\div\frac{7}{8}\times(\frac{1}{3}+\frac{1}{4})+\frac{5}{7}+\frac{3}{4}\times\frac{3}{7}$$
$\frac{241}{84}\approx 2.869047619$
$$\frac{\left(2\times 4+3\right)\times 8}{4\times 7}\left(\frac{1}{3}+\frac{1}{4}\right)+\frac{5}{7}+\frac{3}{4}\times \frac{3}{7}$$
$$\frac{2\left(3+2\times 4\right)}{7}\left(\frac{1}{3}+\frac{1}{4}\right)+\frac{5}{7}+\frac{3}{4}\times \frac{3}{7}$$
$$\frac{2\left(3+8\right)}{7}\left(\frac{1}{3}+\frac{1}{4}\right)+\frac{5}{7}+\frac{3}{4}\times \frac{3}{7}$$
$$\frac{2\times 11}{7}\left(\frac{1}{3}+\frac{1}{4}\right)+\frac{5}{7}+\frac{3}{4}\times \frac{3}{7}$$
$$\frac{22}{7}\left(\frac{1}{3}+\frac{1}{4}\right)+\frac{5}{7}+\frac{3}{4}\times \frac{3}{7}$$
$$\frac{22}{7}\left(\frac{4}{12}+\frac{3}{12}\right)+\frac{5}{7}+\frac{3}{4}\times \frac{3}{7}$$
$$\frac{22}{7}\times \frac{4+3}{12}+\frac{5}{7}+\frac{3}{4}\times \frac{3}{7}$$
$$\frac{22}{7}\times \frac{7}{12}+\frac{5}{7}+\frac{3}{4}\times \frac{3}{7}$$
$$\frac{22\times 7}{7\times 12}+\frac{5}{7}+\frac{3}{4}\times \frac{3}{7}$$
$$\frac{22}{12}+\frac{5}{7}+\frac{3}{4}\times \frac{3}{7}$$
$$\frac{11}{6}+\frac{5}{7}+\frac{3}{4}\times \frac{3}{7}$$
$$\frac{77}{42}+\frac{30}{42}+\frac{3}{4}\times \frac{3}{7}$$
$$\frac{77+30}{42}+\frac{3}{4}\times \frac{3}{7}$$
$$\frac{107}{42}+\frac{3}{4}\times \frac{3}{7}$$
$$\frac{107}{42}+\frac{3\times 3}{4\times 7}$$
$$\frac{107}{42}+\frac{9}{28}$$
$$\frac{214}{84}+\frac{27}{84}$$
$$\frac{214+27}{84}$$
$$\frac{241}{84}$$
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$\frac{241}{2 ^ {2} \cdot 3 \cdot 7} = 2\frac{73}{84} = 2.869047619047619$
