To solve the expression \((−3/5) \times (5/16) \times (7/12) \div (−3/16) \times (−5/7)\), we will follow the order of operations and simplify step by step.
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Identifying the terms: \[ A = \left(-\frac{3}{5}\right), \quad B = \left(\frac{5}{16}\right), \quad C = \left(\frac{7}{12}\right), \quad D = \left(-\frac{3}{16}\right), \quad E = \left(-\frac{5}{7}\right) \]
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Reorganizing the expression to make it easier to simplify: \[ A \times B \times C \div D \times E = A \times B \times C \times \frac{1}{D} \times E \]
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Calculating numerator: \[ (-3) \times 5 \times 7 = -105 \] And for the denominator: \[ 5 \times 16 \times 12 = 960 \]
So, we have: \[ \frac{-105}{960} \]
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Now calculating \(\div (-3/16)\): Dividing by a fraction is the same as multiplying by its reciprocal: \[ \frac{-105}{960} \times \frac{-16}{3} \]
The negatives cancel out: \[ \frac{105 \times 16}{960 \times 3} \]
Now calculating the numerator and denominator: \[ 105 \times 16 = 1680 \] \[ 960 \times 3 = 2880 \]
So now we have: \[ \frac{1680}{2880} \]
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Simplifying \(\frac{1680}{2880}\): We can divide both the numerator and the denominator by 240: \[ \frac{1680 \div 240}{2880 \div 240} = \frac{7}{12} \]
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Now multiply by \(-5/7\): \[ \frac{7}{12} \times \left(-\frac{5}{7}\right) \]
The \(7\)s cancel out: \[ = \frac{-5}{12} \]
Therefore, the final answer is: \[ \boxed{-\frac{5}{12}} \]