To solve the expression \((−4)×(7/5)×(−3/4)÷(7/15)\), we can break it down step by step using properties of operations and rules for signed numbers.
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Multiply the first two fractions: \[ (−4) \times \left(\frac{7}{5}\right) \times (−3/4) \] First, we note that \((−4)\) can be rewritten as \(-\frac{4}{1}\), so: \[ -\frac{4}{1} \times \frac{7}{5} \times -\frac{3}{4} \]
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Multiply the first two numbers: \[ -\frac{4}{1} \times -\frac{3}{4} = \frac{4 \times 3}{1 \times 4} = \frac{12}{4} = 3 \] Note: The product is positive because we multiplied two negative numbers.
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Now multiply this result with \(\frac{7}{5}\): \[ 3 \times \frac{7}{5} = \frac{3 \times 7}{1 \times 5} = \frac{21}{5} \]
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Now divide this result by \(\frac{7}{15}\): To divide by a fraction, we multiply by its reciprocal: \[ \frac{21}{5} \div \frac{7}{15} = \frac{21}{5} \times \frac{15}{7} \]
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Multiply the fractions: \[ \frac{21 \times 15}{5 \times 7} \] Simplifying:
- \(21\) and \(7\) can be simplified: \(21 ÷ 7 = 3\)
- \(15\) and \(5\) can be simplified: \(15 ÷ 5 = 3\)
So we have: \[ \frac{3 \times 3}{1 \times 1} = 9 \]
Thus, the final result of \((−4)×(7/5)×(−3/4)÷(7/15)\) is:
9