$$(12\frac{1}{6}+4\frac{5}{8}-3\frac{1}{2}):13\frac{7}{24}+1$$
$2$
$$\frac{\frac{72+1}{6}+\frac{4\times 8+5}{8}-\frac{3\times 2+1}{2}}{\frac{13\times 24+7}{24}}+1$$
$$\frac{\frac{73}{6}+\frac{4\times 8+5}{8}-\frac{3\times 2+1}{2}}{\frac{13\times 24+7}{24}}+1$$
$$\frac{\frac{73}{6}+\frac{32+5}{8}-\frac{3\times 2+1}{2}}{\frac{13\times 24+7}{24}}+1$$
$$\frac{\frac{73}{6}+\frac{37}{8}-\frac{3\times 2+1}{2}}{\frac{13\times 24+7}{24}}+1$$
$$\frac{\frac{292}{24}+\frac{111}{24}-\frac{3\times 2+1}{2}}{\frac{13\times 24+7}{24}}+1$$
$$\frac{\frac{292+111}{24}-\frac{3\times 2+1}{2}}{\frac{13\times 24+7}{24}}+1$$
$$\frac{\frac{403}{24}-\frac{3\times 2+1}{2}}{\frac{13\times 24+7}{24}}+1$$
$$\frac{\frac{403}{24}-\frac{6+1}{2}}{\frac{13\times 24+7}{24}}+1$$
$$\frac{\frac{403}{24}-\frac{7}{2}}{\frac{13\times 24+7}{24}}+1$$
$$\frac{\frac{403}{24}-\frac{84}{24}}{\frac{13\times 24+7}{24}}+1$$
$$\frac{\frac{403-84}{24}}{\frac{13\times 24+7}{24}}+1$$
$$\frac{\frac{319}{24}}{\frac{13\times 24+7}{24}}+1$$
$$\frac{\frac{319}{24}}{\frac{312+7}{24}}+1$$
$$\frac{\frac{319}{24}}{\frac{319}{24}}+1$$
$$1+1$$
$$2$$
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