Find the product.

Question

(116)(−57)\left(1\frac{1}{6}\right)\left(-\frac{5}{7}\right)(1
6
1
​
)(−
7
5
​
)

Answer 1

To find the product of the numbers \((116)(-57)\left(1\frac{1}{6}\right)\left(-\frac{5}{7}\right)\), we can perform the multiplication step-by-step.

1. Convert mixed number to improper fraction: \[ 1\frac{1}{6} = 1 + \frac{1}{6} = \frac{6}{6} + \frac{1}{6} = \frac{7}{6} \]

2. Rewrite the product: \[ (116)(-57)\left(\frac{7}{6}\right)\left(-\frac{5}{7}\right) \]

3. Combine the fractions: \[ \frac{7}{6} \cdot -\frac{5}{7} = \frac{7 \cdot (-5)}{6 \cdot 7} = \frac{-35}{6} \] (The \(7\) cancels out)

4. Now we need to compute: \[ (116)(-57)\left(\frac{-35}{6}\right) \]

5. Calculate \(116 \cdot (-57)\): \[ 116 \cdot -57 = -6612 \]

6. Now multiply by \(-\frac{35}{6}\): \[ -6612 \cdot -\frac{35}{6} = \frac{6612 \cdot 35}{6} \]

7. Calculate \(6612 \cdot 35\): \[ 6612 \cdot 35 = 231420 \]

8. Now divide by \(6\): \[ \frac{231420}{6} = 38735 \]

The final result is: \[ \boxed{38735} \]