To multiply \(2 \frac{3}{10}\) by \(\frac{2}{3}\), follow these steps:
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Convert the mixed number \(2 \frac{3}{10}\) to an improper fraction. \[ 2 \frac{3}{10} = \frac{(2 \times 10) + 3}{10} = \frac{20 + 3}{10} = \frac{23}{10} \]
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Now, multiply the improper fraction by \(\frac{2}{3}\): \[ \frac{23}{10} \times \frac{2}{3} = \frac{23 \times 2}{10 \times 3} = \frac{46}{30} \]
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Simplify the fraction \(\frac{46}{30}\) by finding the greatest common divisor (GCD) of 46 and 30, which is 2: \[ \frac{46 \div 2}{30 \div 2} = \frac{23}{15} \]
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Convert \(\frac{23}{15}\) back to a mixed number: \[ 23 \div 15 = 1 \quad \text{(with a remainder of 8)} \] So, \[ 1 \frac{8}{15} \]
Thus, \(2 \frac{3}{10} \times \frac{2}{3} = \frac{23}{15}\) or \(1 \frac{8}{15}\).