What is the value of `[4+200-:50+3/2" of "(1/5-1/4)]`?

Options

A. `(317)/(40)`
B. `(323)/(40)`
C. `(337)/(40)`
D. `(320)/(40)`

Answer

To solve the expression \([4 + 200 \div 50 + \frac{3}{2} \text{ of } ( \frac{1}{5} - \frac{1}{4} )]\), we will follow the order of operations (BODMAS/BIDMAS).

### Step-by-Step Solution:

1. **Evaluate the expression inside the parentheses**:
\[ \frac{1}{5} - \frac{1}{4} \]
To subtract these fractions, we need a common denominator. The least common multiple of 5 and 4 is 20.
\[ \frac{1}{5} = \frac{4}{20}, \quad \frac{1}{4} = \frac{5}{20} \]
Thus,
\[ \frac{1}{5} - \frac{1}{4} = \frac{4}{20} - \frac{5}{20} = \frac{-1}{20} \]

2. **Substitute back into the expression**:
\[ [4 + 200 \div 50 + \frac{3}{2} \text{ of } \left( \frac{-1}{20} \right)] \]

3. **Calculate \(\frac{3}{2} \text{ of } \left( \frac{-1}{20} \right)\)**:
\[ \frac{3}{2} \times \frac{-1}{20} = \frac{-3}{40} \]

4. **Now substitute this value back into the expression**:
\[ [4 + 200 \div 50 - \frac{3}{40}] \]

5. **Perform the division \(200 \div 50\)**:
\[ 200 \div 50 = 4 \]

6. **Now substitute this value back into the expression**:
\[ [4 + 4 - \frac{3}{40}] \]

7. **Combine the whole numbers**:
\[ 4 + 4 = 8 \]
So now we have:
\[ [8 - \frac{3}{40}] \]

8. **Convert 8 into a fraction with a denominator of 40**:
\[ 8 = \frac{320}{40} \]

9. **Now perform the subtraction**:
\[ \frac{320}{40} - \frac{3}{40} = \frac{320 - 3}{40} = \frac{317}{40} \]

### Final Answer:
The value of the expression is \(\frac{317}{40}\).

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