To multiply the mixed number \(1 \frac{8}{9}\) by the fraction \(\frac{4}{5}\), follow these steps:
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Convert the mixed number to an improper fraction: \[ 1 \frac{8}{9} = \frac{9 \times 1 + 8}{9} = \frac{9 + 8}{9} = \frac{17}{9} \]
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Now multiply the two fractions: \[ \frac{17}{9} \times \frac{4}{5} = \frac{17 \times 4}{9 \times 5} = \frac{68}{45} \]
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The fraction \(\frac{68}{45}\) is an improper fraction, so we can convert it back to a mixed number: \[ 68 \div 45 = 1 \quad \text{(remainder: 23)} \] Hence, \[ \frac{68}{45} = 1 \frac{23}{45} \]
Therefore, the product of \(1 \frac{8}{9}\) and \(\frac{4}{5}\) is: \[ \frac{68}{45} \text{ or } 1 \frac{23}{45}. \]