$$7 \frac { 1 } { 13 } + 2 \frac { 1 } { 3 } + 3 \frac { 2 } { 5 }$$
$\frac{2498}{195}\approx 12.81025641$
$$\frac{91+1}{13}+\frac{2\times 3+1}{3}+\frac{3\times 5+2}{5}$$
$$\frac{92}{13}+\frac{2\times 3+1}{3}+\frac{3\times 5+2}{5}$$
$$\frac{92}{13}+\frac{6+1}{3}+\frac{3\times 5+2}{5}$$
$$\frac{92}{13}+\frac{7}{3}+\frac{3\times 5+2}{5}$$
$$\frac{276}{39}+\frac{91}{39}+\frac{3\times 5+2}{5}$$
$$\frac{276+91}{39}+\frac{3\times 5+2}{5}$$
$$\frac{367}{39}+\frac{3\times 5+2}{5}$$
$$\frac{367}{39}+\frac{15+2}{5}$$
$$\frac{367}{39}+\frac{17}{5}$$
$$\frac{1835}{195}+\frac{663}{195}$$
$$\frac{1835+663}{195}$$
$$\frac{2498}{195}$$
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$\frac{2 \cdot 1249}{3 \cdot 5 \cdot 13} = 12\frac{158}{195} = 12.810256410256411$
