To solve the expression \((\frac{4}{5} \times \frac{2}{6}) \div \frac{1}{5} \times \frac{1}{1}\), we will follow the order of operations:
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Calculate \(\frac{4}{5} \times \frac{2}{6}\): \[ \frac{4 \times 2}{5 \times 6} = \frac{8}{30} \] This can be simplified by dividing both the numerator and the denominator by 2: \[ \frac{8 \div 2}{30 \div 2} = \frac{4}{15} \]
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Now, we need to divide this result by \(\frac{1}{5}\): \[ \frac{4}{15} \div \frac{1}{5} = \frac{4}{15} \times \frac{5}{1} \] We can multiply: \[ = \frac{4 \times 5}{15 \times 1} = \frac{20}{15} \] This can be simplified by dividing both the numerator and the denominator by 5: \[ \frac{20 \div 5}{15 \div 5} = \frac{4}{3} \]
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Finally, we multiply by \(\frac{1}{1}\): \[ \frac{4}{3} \times \frac{1}{1} = \frac{4}{3} \]
So, the final result is \(\frac{4}{3}\).