To multiply \( \frac{4}{9} \) by \(-3\), we can first express \(-3\) as a fraction:
\[ -3 = \frac{-3}{1} \]
Now we can multiply the two fractions:
\[ \frac{4}{9} \times \frac{-3}{1} = \frac{4 \times -3}{9 \times 1} = \frac{-12}{9} \]
Next, we simplify \(\frac{-12}{9}\). Both the numerator and the denominator can be divided by their greatest common divisor (GCD), which is 3:
\[ \frac{-12 \div 3}{9 \div 3} = \frac{-4}{3} \]
Since \(-4\) is the numerator, we can convert \(\frac{-4}{3}\) into a mixed number.
- The integer part is \(-1\), and the remainder is \(1\) (because \(4 - 3 = 1\)).
- Therefore, \(-4/3\) can be written as:
\[ -1 \frac{1}{3} \]
So, the final answer is:
\[ -1 \frac{1}{3} \]