To solve the expression \((−4) \times (7/5) \times (−3/4) ÷ (7/15)\), we will follow the order of operations and the rules for multiplying and dividing signed numbers.
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Compute the product in the numerator: \[ (−4) \times (7/5) \times (−3/4) \]
Start by multiplying the first two terms: \[ (−4) \times (7/5) = \frac{−4 \times 7}{5} = \frac{−28}{5} \]
Now, multiply this result by the third term: \[ \frac{−28}{5} \times (−3/4) = \frac{−28 \times -3}{5 \times 4} = \frac{84}{20} \]
Simplifying \(\frac{84}{20}\): \[ \frac{84 \div 4}{20 \div 4} = \frac{21}{5} \]
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Now divide by the last term \((7/15)\): \[ \frac{21/5}{7/15} = \frac{21}{5} \times \frac{15}{7} \]
By multiplying fractions, we get: \[ = \frac{21 \times 15}{5 \times 7} \]
Now calculate the numerator and denominator: \[ 21 \times 15 = 315 \] \[ 5 \times 7 = 35 \]
Thus, we have: \[ \frac{315}{35} \]
Simplifying \(\frac{315}{35}\): \[ 315 \div 35 = 9 \]
So, the final result of the expression \((−4) \times (7/5) \times (−3/4) ÷ (7/15)\) is \(\boxed{9}\).
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