Divide \( 8 \frac{6}{7} \) by \( 1 \frac{1}{6} \). Simplify the answer and write as a mixed number. Question Help: Video Message instructor D Post to forum Submit Question

To divide \( 8 \frac{6}{7} \) by \( 1 \frac{1}{6} \), first convert both mixed numbers into improper fractions. For \( 8 \frac{6}{7} \): - Multiply the whole number part (8) by the denominator (7): \( 8 \times 7 = 56 \) - Add the numerator (6): \( 56 + 6 = 62 \) So, \( 8 \frac{6}{7} = \frac{62}{7} \). For \( 1 \frac{1}{6} \): - Multiply the whole number part (1) by the denominator (6): \( 1 \times 6 = 6 \) - Add the numerator (1): \( 6 + 1 = 7 \) So, \( 1 \frac{1}{6} = \frac{7}{6} \). Now, to perform the division: \[ \frac{62}{7} \div \frac{7}{6} = \frac{62}{7} \times \frac{6}{7} = \frac{62 \times 6}{7 \times 7} = \frac{372}{49} \] Next, convert \( \frac{372}{49} \) back to a mixed number. Divide 372 by 49: - \( 372 \div 49 \approx 7 \) (since \( 49 \times 7 = 343 \)) - The remainder is \( 372 - 343 = 29 \). So, \( \frac{372}{49} = 7 \frac{29}{49} \). Thus, the final answer is: \[ 7 \frac{29}{49} \]