Divide
6`3/16 div 3 (1)/(7)`

Answer

To solve the problem \( 6 \frac{3}{16} \div 3 \frac{1}{7} \), 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 \( 6 \frac{3}{16} \):
\[ 6 \frac{3}{16} = \frac{(6 \times 16) + 3}{16} = \frac{96 + 3}{16} = \frac{99}{16} \]

For \( 3 \frac{1}{7} \):
\[ 3 \frac{1}{7} = \frac{(3 \times 7) + 1}{7} = \frac{21 + 1}{7} = \frac{22}{7} \]

### Step 2: Set Up the Division of Fractions
Now we can set up the division of these two improper fractions:
\[ \frac{99}{16} \div \frac{22}{7} \]

### Step 3: Change Division to Multiplication
To divide fractions, we multiply by the reciprocal of the second fraction:
\[ \frac{99}{16} \times \frac{7}{22} \]

### Step 4: Multiply the Numerators and Denominators
Now we multiply the numerators and the denominators:
\[ \frac{99 \times 7}{16 \times 22} \]

### Step 5: Simplify the Fractions
Before multiplying, we can simplify the fraction. We can divide \( 99 \) and \( 22 \) by \( 11 \):
\[ 99 \div 11 = 9 \quad \text{and} \quad 22 \div 11 = 2 \]
So now we have:
\[ \frac{9 \times 7}{16 \times 2} \]

### Step 6: Calculate the Final Multiplication
Now we can calculate:
\[ 9 \times 7 = 63 \quad \text{and} \quad 16 \times 2 = 32 \]
Thus, we have:
\[ \frac{63}{32} \]

### Final Answer
The final answer for \( 6 \frac{3}{16} \div 3 \frac{1}{7} \) is:
\[ \frac{63}{32} \]

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