If we multiply a number by $\frac{5}{2}$ and add $\frac{2}{3}$ to the product, we get $\frac{-7}{12}$. Find the number.

Let the number be $x$.

Then $\left(\frac{5}{2}\right)x + \frac{2}{3} = -\frac{7}{12}$ $$\left(\frac{5}{2}\right)x = -\frac{7}{12} - \frac{2}{3} = -\frac{7}{12} - \frac{8}{12} = -\frac{15}{12} = -\frac{5}{4}$$ $$x = \left(-\frac{5}{4}\right) \times \left(\frac{2}{5}\right) = -\frac{1}{2}$$
 Hence, the number is $-\frac{1}{2}$.

Hence, the number is $\frac{-1}{2}$.