To determine the product of \( \frac{21}{14} \) and \(-1.5\), we first simplify \( \frac{21}{14} \).
\[ \frac{21}{14} = \frac{21 \div 7}{14 \div 7} = \frac{3}{2} \]
Now, we calculate the product:
\[ \frac{3}{2} \times (-1.5) \]
We can convert \(-1.5\) to a fraction:
\[ -1.5 = -\frac{3}{2} \]
Now we multiply:
\[ \frac{3}{2} \times -\frac{3}{2} = \frac{3 \times -3}{2 \times 2} = \frac{-9}{4} \]
Now we can convert \(-\frac{9}{4}\) to a decimal:
\[ -\frac{9}{4} = -2.25 \]
Therefore, the product of \( \frac{21}{14} \) and \(-1.5\) is:
\[ \boxed{-2.25} \]