To divide the mixed number \(2 \frac{1}{3}\) by the fraction \(\frac{1}{2}\), follow these steps:
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Convert the mixed number \(2 \frac{1}{3}\) to an improper fraction: \[ 2 \frac{1}{3} = 2 \times 3 + 1 = 6 + 1 = 7 \quad \text{so} \quad 2 \frac{1}{3} = \frac{7}{3} \]
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To divide by a fraction, you multiply by its reciprocal. The reciprocal of \(\frac{1}{2}\) is \(2\). So, we rewrite the expression: \[ \frac{7}{3} \div \frac{1}{2} = \frac{7}{3} \times 2 \]
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Perform the multiplication: \[ \frac{7 \times 2}{3 \times 1} = \frac{14}{3} \]
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Convert \(\frac{14}{3}\) back to a mixed number if needed: \[ 14 \div 3 = 4 \quad \text{remainder} , 2 \quad \text{so} \quad \frac{14}{3} = 4 \frac{2}{3} \]
Therefore, the answer is: \[ 2 \frac{1}{3} \div \frac{1}{2} = \frac{14}{3} , \text{or} , 4 \frac{2}{3} \]