$$3\frac{7}{20}\div1\frac{2}{7}$$
$\frac{469}{180}\approx 2.605555556$
$$\frac{\left(3\times 20+7\right)\times 7}{20\left(1\times 7+2\right)}$$
$$\frac{\left(60+7\right)\times 7}{20\left(1\times 7+2\right)}$$
$$\frac{67\times 7}{20\left(1\times 7+2\right)}$$
$$\frac{469}{20\left(1\times 7+2\right)}$$
$$\frac{469}{20\left(7+2\right)}$$
$$\frac{469}{20\times 9}$$
$$\frac{469}{180}$$
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$\frac{7 \cdot 67}{2 ^ {2} \cdot 3 ^ {2} \cdot 5} = 2\frac{109}{180} = 2.6055555555555556$
