What is the value of `(2000-:(1/2)"of"(25/2)xx(5/2)"of"(4/25)-5)`?

Options

A. 121
B. 123
C. 122
D. 126

Answer

To solve the expression \( (2000 - \frac{1}{2} \text{ of } \frac{25}{2} \times \frac{5}{2} \text{ of } \frac{4}{25} - 5) \), we will follow the order of operations: first calculate the "of" (multiplication), then division, and finally subtraction.

### Step-by-step Solution:

1. **Calculate \( \frac{1}{2} \text{ of } \frac{25}{2} \)**:
\[ \frac{1}{2} \text{ of } \frac{25}{2} = \frac{1}{2} \times \frac{25}{2} = \frac{25}{4} \]

**Hint**: "Of" means multiplication; multiply the fractions directly.

2. **Calculate \( \frac{5}{2} \text{ of } \frac{4}{25} \)**:
\[ \frac{5}{2} \text{ of } \frac{4}{25} = \frac{5}{2} \times \frac{4}{25} = \frac{20}{50} = \frac{2}{5} \]

**Hint**: Again, "of" means to multiply the two fractions.

3. **Combine the results**:
Now we need to multiply the results from steps 1 and 2:
\[ \frac{25}{4} \times \frac{2}{5} = \frac{25 \times 2}{4 \times 5} = \frac{50}{20} = \frac{5}{2} \]

**Hint**: Multiply the numerators and denominators separately.

4. **Divide 2000 by the result from step 3**:
\[ 2000 \div \frac{5}{2} = 2000 \times \frac{2}{5} = \frac{4000}{5} = 800 \]

**Hint**: Dividing by a fraction is the same as multiplying by its reciprocal.

5. **Subtract 5 from the result**:
\[ 800 - 5 = 795 \]

**Hint**: Perform the final subtraction to get the answer.

### Final Result:
The value of the expression \( (2000 - \frac{1}{2} \text{ of } \frac{25}{2} \times \frac{5}{2} \text{ of } \frac{4}{25} - 5) \) is **795**.