Numerically

$$ $$\(\begin{align*} \dfrac{1}{2} \text{ of } 3 \ & \class{timed in4}{= \dfrac{1}{2} \times 3} \\ \ & \class{timed in5}{= \dfrac{1\times 3}{2}} \\ \ & \class{timed in6}{= \dfrac{3}{2} \text{ or } 1\dfrac{1}{2} } \end{align*}\)

Using a  Diagram

\(\dfrac{1}{4} \times \dfrac{8}{9} \quad\quad\) means \(\quad\quad \dfrac{1}{4} \text{ of } \dfrac{8}{9}\)

The answer (or the product) is the fraction of the area of the total rectangle that is shaded and striped.

Therefore,

\(\dfrac{1}{4} \times \dfrac{8}{9} \class{timed in10}{= \dfrac{8}{36}} \class{timed in11}{ = \dfrac{2}{9}}\)

Is it clear from the diagram why the denominator is \(36\)?

Is it also clear why the numerator is \(8\)?

Using a Diagram