(1 1/6)(-5/-7)

Answer 1

To compute \((1 \frac{1}{6}) \times \left(-\frac{5}{-7}\right)\), we first convert the mixed number into an improper fraction.

1. Convert \(1 \frac{1}{6}\) to an improper fraction: \[ 1 \frac{1}{6} = \frac{6 \cdot 1 + 1}{6} = \frac{7}{6} \]

2. Simplify \(-\frac{5}{-7}\): \[ -\frac{5}{-7} = \frac{5}{7} \]

Now we multiply the two fractions: \[ \frac{7}{6} \times \frac{5}{7} \]

3. Multiply the numerators and the denominators: \[ \frac{7 \times 5}{6 \times 7} = \frac{35}{42} \]

4. Simplify \(\frac{35}{42}\):

   • Find the greatest common divisor (GCD) of 35 and 42, which is 7. \[ \frac{35 \div 7}{42 \div 7} = \frac{5}{6} \]

Therefore, the final result is: \[ \frac{5}{6} \]