$$6\frac{8}{9}\div\frac{11}{9}=$$
$\frac{62}{11}\approx 5.636363636$
$$\frac{\left(6\times 9+8\right)\times 9}{9\times 11}$$
$$\frac{8+6\times 9}{11}$$
$$\frac{8+54}{11}$$
$$\frac{62}{11}$$
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$\frac{2 \cdot 31}{11} = 5\frac{7}{11} = 5.636363636363637$
