`832/24xx84/26div252/72=?`

Options

A. 64
B. 16
C. 32
D. 128

Answer

To solve the expression \( \frac{832}{24} \times \frac{84}{26} \div \frac{252}{72} \), we will follow the order of operations and simplify step by step.

### Step 1: Rewrite the expression
First, we rewrite the division as multiplication by the reciprocal:
\[ \frac{832}{24} \times \frac{84}{26} \times \frac{72}{252} \]

### Step 2: Simplify each fraction
Now, we can simplify the fractions where possible.

1. **Simplifying \( \frac{832}{24} \)**:
- Divide both the numerator and the denominator by 8:
\[ \frac{832 \div 8}{24 \div 8} = \frac{104}{3} \]

2. **Simplifying \( \frac{84}{26} \)**:
- Divide both the numerator and the denominator by 2:
\[ \frac{84 \div 2}{26 \div 2} = \frac{42}{13} \]

3. **Simplifying \( \frac{72}{252} \)**:
- Divide both the numerator and the denominator by 36:
\[ \frac{72 \div 36}{252 \div 36} = \frac{2}{7} \]

### Step 3: Substitute the simplified fractions back into the expression
Now we substitute the simplified fractions back into the expression:
\[ \frac{104}{3} \times \frac{42}{13} \times \frac{2}{7} \]

### Step 4: Multiply the fractions
Now we multiply the numerators and the denominators:
\[ \text{Numerator: } 104 \times 42 \times 2 \]
\[ \text{Denominator: } 3 \times 13 \times 7 \]

Calculating the numerator:
\[ 104 \times 42 = 4368 \]
\[ 4368 \times 2 = 8736 \]

Calculating the denominator:
\[ 3 \times 13 = 39 \]
\[ 39 \times 7 = 273 \]

### Step 5: Final fraction
Now we have:
\[ \frac{8736}{273} \]

### Step 6: Simplify the final fraction
To simplify \( \frac{8736}{273} \), we can divide both the numerator and the denominator by their greatest common divisor (GCD). After calculating, we find:
\[ \frac{8736 \div 273}{273 \div 273} = \frac{32}{1} = 32 \]

### Final Answer
Thus, the final answer is:
\[ \boxed{32} \]

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