To solve the expression \((−3/5)×(5/16)×(7/12)÷(−3/16)×(−5/7)\) step by step, we will convert the division into multiplication by taking the reciprocal and then simplify.
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Rewrite the expression: \[ (-3/5) \times (5/16) \times (7/12) \div (-3/16) \times (-5/7) \] becomes \[ (-3/5) \times (5/16) \times (7/12) \times \left(-\frac{16}{3}\right) \times \left(-\frac{7}{5}\right) \]
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Multiplying the negative signs:
- \(-3/5\) times \(-16/3\) results in a positive product.
- \(-5/7\) will not affect the product since it will be multiplied by another negative.
Now we can group and multiply: \[ = \left((-3/5) \times (-16/3)\right) \times \left((5/16) \times (7/12) \times (-5/7)\right) \]
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Calculate the first group: \[ (-3/5) \times (-16/3) = \frac{3 \times 16}{5 \times 3} = \frac{16}{5} \]
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Now calculate the second group: \[ (5/16) \times (7/12) \times (-5/7) \] First, cancel out the \(5\) and \(7\): \[ = (5/16) \times (-5/7) \to -\frac{5 \times 5}{16 \times 7} = -\frac{25}{112} \] and since \(7/12\) remains in this grouping, we calculate: \[ = (-25/112) \times (7/12) = -\frac{25 \times 7}{112 \times 12} \]
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Now let's compute this: \[ -\frac{175}{1344} \]
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Now we multiply these two results: \[ = \frac{16}{5} \times \left(-\frac{175}{1344}\right) = -\frac{16 \times 175}{5 \times 1344} \]
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Simplify: \[ = -\frac{2800}{6720} \] Dividing top and bottom by 280: \[ = -\frac{10}{24}= -\frac{5}{12} \]
So the final result of the expression \((−3/5)×(5/16)×(7/12)÷(−3/16)×(−5/7)\) is:
\[ =\boxed{-\frac{5}{12}} \]
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