To solve the expression \((8/9) \times (-3/4) \div (1/9) \times (-4/5) \div (3/5)\), we will follow the order of operations: handle multiplication and division from left to right.
Let's break it down step by step:
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Calculate the first multiplication: \[ (8/9) \times (-3/4) = \frac{8 \times -3}{9 \times 4} = \frac{-24}{36} = \frac{-2}{3} \]
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Next, divide by \((1/9)\): \[ \frac{-2}{3} \div \frac{1}{9} = \frac{-2}{3} \times \frac{9}{1} = \frac{-2 \times 9}{3 \times 1} = \frac{-18}{3} = -6 \]
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Now multiply by \((-4/5)\): \[ -6 \times \left(-\frac{4}{5}\right) = \frac{24}{5} \]
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Finally, divide by \((3/5)\): \[ \frac{24}{5} \div \frac{3}{5} = \frac{24}{5} \times \frac{5}{3} = \frac{24 \times 5}{5 \times 3} = \frac{24}{3} = 8 \]
Therefore, the final result is:
\[ \boxed{8} \]
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