Spot the doggy integer

How many of the following 10 numbers are integers?

\[ \begin{array} {rrrrr} 0, &1, &-1, &\frac{1}{2} , &\frac{2}{1}, \\ \frac{3}{2}, &\frac{2}{3} , &2 \times 3, &2 \times \frac{1}{2}, &3 \times \frac{1}{2}. \end{array} \]

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