Use the properties of operations and rules for multiplying and dividing to solve: (−3) ÷ (34) × (27) × (−516) ÷ (57)

Answer 1

To solve the expression \((−3) ÷ (34) × (27) × (−516) ÷ (57)\), we can follow the order of operations and simplify step by step.

1. Start with the expression: \[ \frac{-3}{34} \times 27 \times \frac{-516}{57} \]

2. Calculate \(\frac{-3}{34} \times 27\): \[ -3 \times 27 = -81 \] \[ \frac{-81}{34} \]

3. Now take \(\frac{-81}{34} \times \frac{-516}{57}\): \[ \frac{(-81) \times (-516)}{34 \times 57} \]

4. Compute the numerator: \[ 81 \times 516 = 41796 \]

5. Compute the denominator: \[ 34 \times 57 = 1938 \]

6. Now assemble the fraction: \[ \frac{41796}{1938} \]

7. Simplify \(\frac{41796}{1938}\). We can do this by dividing both the numerator and the denominator by their greatest common divisor (GCD). Using a calculator or through long division, we find that \(41796 \div 66 = 633\) and \(1938 \div 66 = 29\).

8. Thus: \[ \frac{41796}{1938} = \frac{633}{29} \]

Finally, the simplified value of the original expression is: \[ \frac{633}{29} \approx 21.81 \text{ or you can leave it as a proper fraction.} \]