Divide
32 `1/2 div8(3)/(4)`

Answer

To solve the problem \( 32 \frac{1}{2} \div 8 \frac{3}{4} \), 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 \( 32 \frac{1}{2} \):
\[ 32 \frac{1}{2} = \frac{32 \times 2 + 1}{2} = \frac{64 + 1}{2} = \frac{65}{2} \]

- For \( 8 \frac{3}{4} \):
\[ 8 \frac{3}{4} = \frac{8 \times 4 + 3}{4} = \frac{32 + 3}{4} = \frac{35}{4} \]

### Step 2: Set Up the Division of Fractions
Now we can set up the division:
\[ \frac{65}{2} \div \frac{35}{4} \]

### Step 3: Change Division to Multiplication
To divide by a fraction, we multiply by its reciprocal:
\[ \frac{65}{2} \times \frac{4}{35} \]

### Step 4: Multiply the Fractions
Now, we multiply the numerators and the denominators:
\[ \frac{65 \times 4}{2 \times 35} = \frac{260}{70} \]

### Step 5: Simplify the Fraction
Next, we simplify \( \frac{260}{70} \):
- Find the greatest common divisor (GCD) of 260 and 70, which is 10.
- Divide both the numerator and the denominator by 10:
\[ \frac{260 \div 10}{70 \div 10} = \frac{26}{7} \]

### Final Answer
Thus, the result of \( 32 \frac{1}{2} \div 8 \frac{3}{4} \) is:
\[ \frac{26}{7} \]

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