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

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To divide $$ 8 \frac{6}{7} $$ by $$ 1 \frac{1}{6} $$ and express the result as a simplified mixed number, follow these steps:

1. **Convert Mixed Numbers to Improper Fractions:**

- $$ 8 \frac{6}{7} = \frac{8 \times 7 + 6}{7} = \frac{56 + 6}{7} = \frac{62}{7} $$
   - $$ 1 \frac{1}{6} = \frac{1 \times 6 + 1}{6} = \frac{6 + 1}{6} = \frac{7}{6} $$

2. **Divide the Fractions:**

Dividing by a fraction is the same as multiplying by its reciprocal.
   
   $$
   \frac{62}{7} \div \frac{7}{6} = \frac{62}{7} \times \frac{6}{7} = \frac{62 \times 6}{7 \times 7} = \frac{372}{49}
   $$

3. **Convert the Improper Fraction to a Mixed Number:**

- Divide 372 by 49:
     $$
     372 \div 49 = 7 \text{ with a remainder of } 29
     $$
     
   - So, $$ \frac{372}{49} = 7 \frac{29}{49} $$

4. **Simplify the Fraction (if possible):**

The fraction $$ \frac{29}{49} $$ cannot be simplified further since 29 is a prime number and does not divide evenly into 49.

**Final Answer:**
$$
7 \frac{29}{49}
$$
The result of dividing $$ 8 \frac{6}{7} $$ by $$ 1 \frac{1}{6} $$ is $$ 7 \frac{29}{49} $$.

Divide by . Simplify the answer and write as a mixed number.
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Divide by . Simplify the answer and write as a mixed number. Question Help: Video Message instructor D Post to forum Submit Question