$$\frac{3}{2}\div\frac{8}{12}=\frac{3}{2}\times\frac{12}{8}=$$
$\text{true}$
$$\frac{3\times 12}{2\times 8}=\frac{3}{2}\times \frac{12}{8}$$
$$\frac{3\times 3}{4}=\frac{3}{2}\times \frac{12}{8}$$
$$\frac{9}{4}=\frac{3}{2}\times \frac{12}{8}$$
$$\frac{9}{4}=\frac{3}{2}\times \frac{3}{2}$$
$$\frac{9}{4}=\frac{3\times 3}{2\times 2}$$
$$\frac{9}{4}=\frac{9}{4}$$
$$\text{true}$$
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