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 and use the properties of multiplication and division.
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Start with the multiplication and division from left to right.
The expression can be rewritten as: \[ ((8/9) \times (-3/4)) \div (1/9) \times (-4/5) \div (3/5) \]
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Calculate \((8/9) \times (-3/4)\): \[ = \frac{8 \times -3}{9 \times 4} = \frac{-24}{36} = \frac{-2}{3} \]
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Now substitute this result back into the expression: \[ \frac{-2}{3} \div (1/9) \]
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Dividing by a fraction is the same as multiplying by its reciprocal, so: \[ \frac{-2}{3} \times 9 \] \[ = \frac{-2 \times 9}{3} = \frac{-18}{3} = -6 \]
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Now we have: \[ -6 \times (-4/5) \div (3/5) \]
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Calculate \(-6 \times (-4/5)\): \[ = \frac{-6 \times -4}{5} = \frac{24}{5} \]
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Next, we need to divide by \((3/5)\): \[ \frac{24}{5} \div (3/5) \] Again, divide by a fraction: \[ = \frac{24}{5} \times \frac{5}{3} \] \[ = \frac{24 \times 5}{5 \times 3} = \frac{24}{3} = 8 \]
Thus, the final result is: \[ \boxed{8} \]