$$12 \frac { 1 } { 6 } - 5 \frac { 2 } { 7 } =$$
$\frac{289}{42}\approx 6.880952381$
$$\frac{72+1}{6}-\frac{5\times 7+2}{7}$$
$$\frac{73}{6}-\frac{5\times 7+2}{7}$$
$$\frac{73}{6}-\frac{35+2}{7}$$
$$\frac{73}{6}-\frac{37}{7}$$
$$\frac{511}{42}-\frac{222}{42}$$
$$\frac{511-222}{42}$$
$$\frac{289}{42}$$
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$\frac{17 ^ {2}}{2 \cdot 3 \cdot 7} = 6\frac{37}{42} = 6.880952380952381$