$$6\frac{1}{2}\div1\frac{3}{8}=$$
$\frac{52}{11}\approx 4.727272727$
$$\frac{\left(6\times 2+1\right)\times 8}{2\left(1\times 8+3\right)}$$
$$\frac{4\left(1+2\times 6\right)}{3+8}$$
$$\frac{4\left(1+12\right)}{3+8}$$
$$\frac{4\times 13}{3+8}$$
$$\frac{52}{3+8}$$
$$\frac{52}{11}$$
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$\frac{2 ^ {2} \cdot 13}{11} = 4\frac{8}{11} = 4.7272727272727275$