$$15\frac{1}{3}-[\frac{2}{3}\div\{(\frac{5}{2}-\frac{1}{3})\times\frac{3}{13}\}]$$
$14$
$$\frac{45+1}{3}-\frac{\frac{2}{3}}{\left(\frac{5}{2}-\frac{1}{3}\right)\times \frac{3}{13}}$$
$$\frac{46}{3}-\frac{\frac{2}{3}}{\left(\frac{5}{2}-\frac{1}{3}\right)\times \frac{3}{13}}$$
$$\frac{46}{3}-\frac{\frac{2}{3}}{\left(\frac{15}{6}-\frac{2}{6}\right)\times \frac{3}{13}}$$
$$\frac{46}{3}-\frac{\frac{2}{3}}{\frac{15-2}{6}\times \frac{3}{13}}$$
$$\frac{46}{3}-\frac{\frac{2}{3}}{\frac{13}{6}\times \frac{3}{13}}$$
$$\frac{46}{3}-\frac{\frac{2}{3}}{\frac{13\times 3}{6\times 13}}$$
$$\frac{46}{3}-\frac{\frac{2}{3}}{\frac{3}{6}}$$
$$\frac{46}{3}-\frac{\frac{2}{3}}{\frac{1}{2}}$$
$$\frac{46}{3}-\frac{2}{3}\times 2$$
$$\frac{46}{3}-\frac{2\times 2}{3}$$
$$\frac{46}{3}-\frac{4}{3}$$
$$\frac{46-4}{3}$$
$$\frac{42}{3}$$
$$14$$
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$2\times 7$