To divide \( 2 \frac{1}{3} \) by \( \frac{2}{5} \), we first convert \( 2 \frac{1}{3} \) into an improper fraction.
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Convert \( 2 \frac{1}{3} \) to an improper fraction: \[ 2 \frac{1}{3} = \frac{2 \times 3 + 1}{3} = \frac{6 + 1}{3} = \frac{7}{3} \]
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Now divide \( \frac{7}{3} \) by \( \frac{2}{5} \). To divide by a fraction, we multiply by its reciprocal: \[ \frac{7}{3} \div \frac{2}{5} = \frac{7}{3} \times \frac{5}{2} \]
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Multiply the fractions: \[ \frac{7 \times 5}{3 \times 2} = \frac{35}{6} \]
So, the final result of the division is \( \frac{35}{6} \).
Since this fraction does not match any of the provided responses, it seems that we have a misalignment. However, since \( \frac{35}{6} \) does not fit the list, here's the summary of what we computed and the correct answer:
- The division results in \( \frac{35}{6} \) (which could also be expressed as \( 5 \frac{5}{6} \)).
Therefore, the closest correct response from your options should be \( 5 \frac{5}{6} \).