`(237)2/23xx(2)4/21 div2/3 of 3.001=?`

Options

A. 270
B. 260
C. 250
D. 280

Answer

To solve the expression `(237)2/23xx(2)4/21 div2/3 of 3.001`, we will follow a step-by-step approach.

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

1. **Convert \(237 \frac{2}{23}\)**:
\[ 237 \frac{2}{23} = \frac{(237 \times 23) + 2}{23} = \frac{5451 + 2}{23} = \frac{5453}{23} \]

2. **Convert \(2 \frac{4}{21}\)**:
\[ 2 \frac{4}{21} = \frac{(2 \times 21) + 4}{21} = \frac{42 + 4}{21} = \frac{46}{21} \]

So, we rewrite the expression as:
\[ \frac{5453}{23} \times \frac{46}{21} \]

### Step 2: Solve the "of" part
Next, we need to calculate the "of" part, which is \( \frac{2}{3} \) of \( 3.001 \).

\[ \frac{2}{3} \times 3.001 = \frac{2 \times 3.001}{3} = \frac{6.002}{3} = 2.0006667 \approx 2 \]

### Step 3: Rewrite the Expression
Now we can rewrite the expression as:
\[ \frac{5453}{23} \times \frac{46}{21} \div 2 \]

### Step 4: Perform the Division
To divide by 2, we can multiply by \( \frac{1}{2} \):
\[ \frac{5453}{23} \times \frac{46}{21} \times \frac{1}{2} \]

### Step 5: Multiply the Fractions
Now we multiply the fractions:
\[ = \frac{5453 \times 46}{23 \times 21 \times 2} \]

### Step 6: Calculate the Numerator and Denominator
1. **Calculate the numerator**:
\[ 5453 \times 46 = 250878 \]

2. **Calculate the denominator**:
\[ 23 \times 21 \times 2 = 966 \]

### Step 7: Final Calculation
Now we have:
\[ \frac{250878}{966} \]

### Step 8: Simplify the Fraction
Now we simplify \( \frac{250878}{966} \):
\[ 250878 \div 966 = 259 \]

Thus, the final answer is:
\[ \boxed{259} \]