$$1 \frac { 1 } { 2 } \div 1 \frac { 1 } { 3 }$$
$\frac{9}{8}=1.125$
$$\frac{\left(1\times 2+1\right)\times 3}{2\left(1\times 3+1\right)}$$
$$\frac{\left(2+1\right)\times 3}{2\left(1\times 3+1\right)}$$
$$\frac{3\times 3}{2\left(1\times 3+1\right)}$$
$$\frac{9}{2\left(1\times 3+1\right)}$$
$$\frac{9}{2\left(3+1\right)}$$
$$\frac{9}{2\times 4}$$
$$\frac{9}{8}$$
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$\frac{3 ^ {2}}{2 ^ {3}} = 1\frac{1}{8} = 1.125$
