$$2\frac{2}{3}\times4\frac{1}{2}=$$
$12$
$$\frac{6+2}{3}\times \frac{4\times 2+1}{2}$$
$$\frac{8}{3}\times \frac{4\times 2+1}{2}$$
$$\frac{8}{3}\times \frac{8+1}{2}$$
$$\frac{8}{3}\times \frac{9}{2}$$
$$\frac{8\times 9}{3\times 2}$$
$$\frac{72}{6}$$
$$12$$
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$2^{2}\times 3$
