To multiply \( \frac{4}{9} \) by \( -3 \), we can first express \( -3 \) as a fraction:
\[ -3 = \frac{-3}{1} \]
Now, multiplying the fractions gives:
\[ \frac{4}{9} \times \frac{-3}{1} = \frac{4 \times -3}{9 \times 1} = \frac{-12}{9} \]
Next, we simplify \( \frac{-12}{9} \). We can find the greatest common divisor (GCD) of 12 and 9, which is 3. Dividing both the numerator and the denominator by 3:
\[ \frac{-12 \div 3}{9 \div 3} = \frac{-4}{3} \]
Next, we convert \( \frac{-4}{3} \) to a mixed number. Since \(-4\) can be written as \(-1 \frac{1}{3}\):
The final answer in mixed number form is:
\[ -1 \frac{1}{3} \]
Thus, the answer is:
\[ \boxed{-1 \frac{1}{3}} \]