$$1\frac{2}{3}+2\frac{1}{2}\times\frac{3}{7}$$
$\frac{115}{42}\approx 2.738095238$
$$\frac{3+2}{3}+\frac{2\times 2+1}{2}\times \frac{3}{7}$$
$$\frac{5}{3}+\frac{2\times 2+1}{2}\times \frac{3}{7}$$
$$\frac{5}{3}+\frac{4+1}{2}\times \frac{3}{7}$$
$$\frac{5}{3}+\frac{5}{2}\times \frac{3}{7}$$
$$\frac{5}{3}+\frac{5\times 3}{2\times 7}$$
$$\frac{5}{3}+\frac{15}{14}$$
$$\frac{70}{42}+\frac{45}{42}$$
$$\frac{70+45}{42}$$
$$\frac{115}{42}$$
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$\frac{5 \cdot 23}{2 \cdot 3 \cdot 7} = 2\frac{31}{42} = 2.738095238095238$