$$1\frac{2}{3}\div2\frac{1}{2}\times\frac{3}{7}$$
$\frac{2}{7}\approx 0.285714286$
$$\frac{\left(1\times 3+2\right)\times 2}{3\left(2\times 2+1\right)}\times \frac{3}{7}$$
$$\frac{\left(3+2\right)\times 2}{3\left(2\times 2+1\right)}\times \frac{3}{7}$$
$$\frac{5\times 2}{3\left(2\times 2+1\right)}\times \frac{3}{7}$$
$$\frac{10}{3\left(2\times 2+1\right)}\times \frac{3}{7}$$
$$\frac{10}{3\left(4+1\right)}\times \frac{3}{7}$$
$$\frac{10}{3\times 5}\times \frac{3}{7}$$
$$\frac{10}{15}\times \frac{3}{7}$$
$$\frac{2}{3}\times \frac{3}{7}$$
$$\frac{2\times 3}{3\times 7}$$
$$\frac{2}{7}$$
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$\frac{2}{7} = 0.2857142857142857$
