$$5 \frac { 1 } { 6 } \div 4 \frac { 1 } { 2 }$$
$\frac{31}{27}\approx 1.148148148$
$$\frac{\left(5\times 6+1\right)\times 2}{6\left(4\times 2+1\right)}$$
$$\frac{1+5\times 6}{3\left(1+2\times 4\right)}$$
$$\frac{1+30}{3\left(1+2\times 4\right)}$$
$$\frac{31}{3\left(1+2\times 4\right)}$$
$$\frac{31}{3\left(1+8\right)}$$
$$\frac{31}{3\times 9}$$
$$\frac{31}{27}$$
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$\frac{31}{3 ^ {3}} = 1\frac{4}{27} = 1.1481481481481481$
