To multiply \(\frac{4}{9}\) by \(-3\), we can first express \(-3\) as a fraction:
\[ -3 = \frac{-3}{1} \]
Now, we can multiply the 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, which is 3:
\[ \frac{-12 \div 3}{9 \div 3} = \frac{-4}{3} \]
Now, we can express \(\frac{-4}{3}\) as a mixed number. To do this, we divide the numerator by the denominator:
- The whole number part is \(-1\) (since \(-4\) divided by \(3\) gives \(-1\) with a remainder).
- The remainder is \(1\) (because \(-4 = -3 - 1\)).
- Thus, we write the improper fraction as \(-1 \frac{1}{3}\).
Therefore, the answer in simplest form as a mixed number is:
\[ \boxed{-1 \frac{1}{3}} \]
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