$$2\frac{1}{2}+3\frac{4}{3}$$
$\frac{41}{6}\approx 6.833333333$
$$\frac{4+1}{2}+\frac{3\times 3+4}{3}$$
$$\frac{5}{2}+\frac{3\times 3+4}{3}$$
$$\frac{5}{2}+\frac{9+4}{3}$$
$$\frac{5}{2}+\frac{13}{3}$$
$$\frac{15}{6}+\frac{26}{6}$$
$$\frac{15+26}{6}$$
$$\frac{41}{6}$$
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$\frac{41}{2 \cdot 3} = 6\frac{5}{6} = 6.833333333333333$
