$$17\frac{1}{4}\div\frac{69}{4}=$$
$1$
$$\frac{\left(17\times 4+1\right)\times 4}{4\times 69}$$
$$\frac{1+4\times 17}{69}$$
$$\frac{1+68}{69}$$
$$\frac{69}{69}$$
$$1$$
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