To solve the expression \((8/9) \times (-3/4) \times (-4/5) \div (3/5)\), we can break it down step by step.
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First, let's multiply the fractions together: \[ (8/9) \times (-3/4) \times (-4/5) \]
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Multiply the first two fractions: \[ \frac{8}{9} \times \frac{-3}{4} = \frac{8 \times -3}{9 \times 4} = \frac{-24}{36} \] This can be simplified: \[ \frac{-24}{36} = \frac{-2}{3} \]
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Now multiply this result by \(-4/5\): \[ \frac{-2}{3} \times \frac{-4}{5} = \frac{-2 \times -4}{3 \times 5} = \frac{8}{15} \]
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Now, we need to divide by \((3/5)\): \[ \frac{8}{15} \div \frac{3}{5} = \frac{8}{15} \times \frac{5}{3} \]
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Multiply the fractions: \[ \frac{8 \times 5}{15 \times 3} = \frac{40}{45} \] This can be simplified: \[ \frac{40}{45} = \frac{8}{9} \]
So, the final answer is: \[ \frac{8}{9} \]