$$249\frac{3}{4}\div27\frac{3}{4}$$
$9$
$$\frac{\left(249\times 4+3\right)\times 4}{4\left(27\times 4+3\right)}$$
$$\frac{3+4\times 249}{3+4\times 27}$$
$$\frac{3+996}{3+4\times 27}$$
$$\frac{999}{3+4\times 27}$$
$$\frac{999}{3+108}$$
$$\frac{999}{111}$$
$$9$$
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$3^{2}$