Answer :
Answer:
Let's denote the other rational number as \(x\). We know that the product of two rational numbers is \(-\frac{9}{4}\) and one of the numbers is \(-\frac{12}{7}\). We want to find \(x\).
We have the equation:
\[ \left(-\frac{12}{7}\right) \times x = -\frac{9}{4} \]
To solve for \(x\), multiply both sides by \(-\frac{7}{12}\) (the reciprocal of \(-\frac{12}{7}\)):
\[ x = \left(-\frac{9}{4}\right) \times \left(-\frac{7}{12}\right) \]
Now, perform the multiplication:
\[ x = \frac{-9 \times -7}{4 \times 12} \]
\[ x = \frac{63}{48} \]
To simplify \(x\), find the greatest common divisor (GCD) of \(63\) and \(48\), which is \(3\):
\[ x = \frac{63 \div 3}{48 \div 3} \]
\[ x = \frac{21}{16} \]
Therefore, the other rational number \(x\) is \( \boxed{\frac{21}{16}} \).