Product of two rational numbers = \(\frac{-16}{9}\)
One rational number = \(\frac{-4}{3}\)
Let the other rational number = x
Now,
According to the question,
\(\frac{-4}{3}\times \text{x} = \frac{-16}{9}\) \(\)
\(\Rightarrow\) \(\text{x} =\frac{-16}{9}\div\frac{-4}{3}\)
\(\Rightarrow\) \(\text{x}=\frac{-16}{9}\times\frac{3}{-4}\)
\(\Rightarrow\) \(\text{x}=\frac{-16\times3}{9\times-4}\)
\(\Rightarrow \) \(\text{x}=\frac{-48\times-1}{-36\times-1}=\frac{48}{36}\)
\(\Rightarrow \) \(\text{x}=\frac{48}{36}=\frac{48\div12}{36\div12}=\frac{4}{3}\)
Hence, the other rational number is \(\frac{4}{3}\)
