$$2\frac{3}{5}+4\frac{3}{7}$$
$\frac{246}{35}\approx 7.028571429$
$$\frac{10+3}{5}+\frac{4\times 7+3}{7}$$
$$\frac{13}{5}+\frac{4\times 7+3}{7}$$
$$\frac{13}{5}+\frac{28+3}{7}$$
$$\frac{13}{5}+\frac{31}{7}$$
$$\frac{91}{35}+\frac{155}{35}$$
$$\frac{91+155}{35}$$
$$\frac{246}{35}$$
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$\frac{2 \cdot 3 \cdot 41}{5 \cdot 7} = 7\frac{1}{35} = 7.0285714285714285$
