$$3 \frac{ 1 }{ 2 } \div 1 \frac{ 1 }{ 6 }$$
$3$
$$\frac{\left(3\times 2+1\right)\times 6}{2\left(1\times 6+1\right)}$$
$$\frac{3\left(1+2\times 3\right)}{1+6}$$
$$\frac{3\left(1+6\right)}{1+6}$$
$$\frac{3\times 7}{1+6}$$
$$\frac{21}{1+6}$$
$$\frac{21}{7}$$
$$3$$
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