Divide
8 `1/21 div1(6)/(7)`

Answer

To solve the problem of dividing \( 8 \frac{1}{21} \) by \( 1 \frac{6}{7} \), we will follow these steps:

### Step 1: Convert Mixed Numbers to Improper Fractions
First, we need to convert the mixed numbers into improper fractions.

For \( 8 \frac{1}{21} \):
\[ 8 \frac{1}{21} = \frac{(8 \times 21) + 1}{21} = \frac{168 + 1}{21} = \frac{169}{21} \]

For \( 1 \frac{6}{7} \):
\[ 1 \frac{6}{7} = \frac{(1 \times 7) + 6}{7} = \frac{7 + 6}{7} = \frac{13}{7} \]

### Step 2: Set Up the Division
Now we can set up the division:
\[ \frac{169}{21} \div \frac{13}{7} \]

### Step 3: Change Division to Multiplication
To divide by a fraction, we multiply by its reciprocal:
\[ \frac{169}{21} \times \frac{7}{13} \]

### Step 4: Multiply the Fractions
Now we multiply the fractions:
\[ \frac{169 \times 7}{21 \times 13} \]

### Step 5: Simplify the Fractions
Before multiplying, we can simplify:
- \( 21 = 7 \times 3 \), so we can cancel \( 7 \) in the numerator and denominator:
\[ \frac{169 \times 1}{3 \times 13} = \frac{169}{39} \]

### Step 6: Simplify Further
Now, we can simplify \( \frac{169}{39} \):
- \( 169 = 13 \times 13 \) and \( 39 = 3 \times 13 \), so we can cancel \( 13 \):
\[ \frac{13}{3} \]

### Final Answer
Thus, the final answer is:
\[ \frac{13}{3} \]

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