To multiply \( 49 \frac{4}{9} \) by \( -3 \frac{3}{1} \), we need to first convert both mixed numbers into improper fractions.
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Convert \( 49 \frac{4}{9} \) to an improper fraction: \[ 49 \frac{4}{9} = 49 + \frac{4}{9} = \frac{49 \times 9 + 4}{9} = \frac{441 + 4}{9} = \frac{445}{9} \]
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Convert \( -3 \frac{3}{1} \) to an improper fraction: \[ -3 \frac{3}{1} = -3 - 3 = -6 \quad \text{(as improper fraction: } -6 = \frac{-6}{1} \text{)} \]
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Now multiply the two fractions: \[ \frac{445}{9} \times \frac{-6}{1} = \frac{445 \times -6}{9 \times 1} = \frac{-2670}{9} \]
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Now convert \( \frac{-2670}{9} \) into a mixed number:
- Divide \( 2670 \) by \( 9 \): \[ 2670 \div 9 = 296 \quad \text{ R } 6 \]
- This means \( \frac{2670}{9} = 296 \frac{6}{9} \).
- Simplify \( \frac{6}{9} \) to \( \frac{2}{3} \): \[ \frac{2670}{9} = 296 \frac{2}{3} \]
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Putting the negative back: \[ \frac{-2670}{9} = -296 \frac{2}{3} \]
Thus, the final answer expressed as a mixed number in simplest form is: \[ \boxed{-296 \frac{2}{3}} \]
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