To solve the expression \((−35)×(516)×(712)÷(−316)×(−57)\), we can first rearrange the expression and apply the rules of multiplication and division.
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Combine the multiplication and division parts: \[ (−35) × (516) × (712) ÷ (−316) × (−57) = \frac{(−35) × (516) × (712)}{(−316) × (−57)} \]
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Determine the signs:
- The product of two negative numbers (−316 and −57) is positive.
- The numerator has one negative number (−35), so the overall numerator is negative.
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Simplify the sign to: \[ -\frac{(35) × (516) × (712)}{(316) × (57)} \]
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Perform the multiplications in the numerator and the denominator:
Numerator: \[ 35 × 516 × 712 \] Calculating step by step:
- \(35 × 516 = 18180\)
- \(18180 × 712 = 12920016\)
Denominator: \[ 316 × 57 \] Calculating step by step:
- \(316 × 57 = 18012\)
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Now we have: \[ -\frac{12920016}{18012} \]
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Perform the division: Calculating \(12920016 ÷ 18012\):
After performing the division, we find: \[ 12920016 ÷ 18012 \approx 716 \]
Thus, the complete expression evaluates to: \[ -716 \]
Therefore, the final answer is: \[ \boxed{-716} \]