To prove that the product of the two rational numbers \( \frac{4}{3} \) and \( \frac{9}{2} \) is a rational number, we calculate the product:
\[ \frac{4}{3} \times \frac{9}{2} = \frac{4 \times 9}{3 \times 2} = \frac{36}{6} = 6. \]
Since 6 can be expressed as \( \frac{6}{1} \), which is in the form \( \frac{a}{b} \) with integers \( a = 6 \) and \( b = 1 \) (and \( b \neq 0 \)), the product is a rational number. My reasoning is that the product of two rational numbers is always rational, as it can be expressed as a fraction of integers.