$$10 \frac{ 6 \frac{ 8 }{ 10 } }{ 10 \frac { 10 } { 12 } } =$$
$\frac{408}{65}\approx 6.276923077$
$$10\times \frac{\left(6\times 10+8\right)\times 12}{10\left(10\times 12+10\right)}$$
$$10\times \frac{6\left(8+6\times 10\right)}{5\left(10+10\times 12\right)}$$
$$10\times \frac{6\left(8+60\right)}{5\left(10+10\times 12\right)}$$
$$10\times \frac{6\times 68}{5\left(10+10\times 12\right)}$$
$$10\times \frac{408}{5\left(10+10\times 12\right)}$$
$$10\times \frac{408}{5\left(10+120\right)}$$
$$10\times \frac{408}{5\times 130}$$
$$10\times \frac{408}{650}$$
$$10\times \frac{204}{325}$$
$$\frac{10\times 204}{325}$$
$$\frac{2040}{325}$$
$$\frac{408}{65}$$
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$\frac{2 ^ {3} \cdot 3 \cdot 17}{5 \cdot 13} = 6\frac{18}{65} = 6.276923076923077$
