To rewrite the division problem \( \frac{4}{9} ÷ \frac{1}{2} \) as multiplication, you can multiply by the reciprocal of the second fraction. The reciprocal of \( \frac{1}{2} \) is \( \frac{2}{1} \).
So, the problem becomes:
\[ \frac{4}{9} × \frac{2}{1} \]
Now, we multiply the numerators and the denominators:
Numerators: \( 4 × 2 = 8 \)
Denominators: \( 9 × 1 = 9 \)
Putting it all together, the answer is:
\[ \frac{8}{9} \]