To solve the problem of dividing two-thirds by \(\frac{4}{5}\), we can follow these steps:
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Write the expression: \[ \frac{2}{3} \div \frac{4}{5} \]
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Change division to multiplication: When dividing by a fraction, you can multiply by its reciprocal. The reciprocal of \(\frac{4}{5}\) is \(\frac{5}{4}\). Thus, we have: \[ \frac{2}{3} \div \frac{4}{5} = \frac{2}{3} \times \frac{5}{4} \]
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Multiply the fractions: To multiply fractions, multiply the numerators and the denominators: \[ \frac{2 \times 5}{3 \times 4} = \frac{10}{12} \]
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Simplify if necessary: We can simplify \(\frac{10}{12}\) by dividing both the numerator and the denominator by 2: \[ \frac{10 \div 2}{12 \div 2} = \frac{5}{6} \]
Therefore, the result of \(\frac{2}{3} \div \frac{4}{5}\) is \(\frac{5}{6}\).
The correct answer is: \(\frac{5}{6}\).