What is the value of `(5div1/5" of "25/4+20/3 div 100/9)`?

Options

A. `23/5`
B. `5/27`
C. `5/23`
D. `5/18`

Answer

To solve the expression \( 5 \div \frac{1}{5} \text{ of } \frac{25}{4} + \frac{20}{3} \div \frac{100}{9} \), we will follow the BODMAS rule (Brackets, Orders, Division and Multiplication, Addition and Subtraction).

### Step-by-Step Solution:

1. **Rewrite the expression**:
\[ 5 \div \frac{1}{5} \times \frac{25}{4} + \frac{20}{3} \div \frac{100}{9} \]

2. **Calculate \( 5 \div \frac{1}{5} \)**:
Dividing by a fraction is the same as multiplying by its reciprocal:
\[ 5 \div \frac{1}{5} = 5 \times 5 = 25 \]

3. **Multiply by \( \frac{25}{4} \)**:
Now we multiply the result by \( \frac{25}{4} \):
\[ 25 \times \frac{25}{4} = \frac{625}{4} \]

4. **Calculate \( \frac{20}{3} \div \frac{100}{9} \)**:
Again, dividing by a fraction means multiplying by its reciprocal:
\[ \frac{20}{3} \div \frac{100}{9} = \frac{20}{3} \times \frac{9}{100} = \frac{20 \times 9}{3 \times 100} = \frac{180}{300} \]
Simplifying \( \frac{180}{300} \):
\[ \frac{180 \div 60}{300 \div 60} = \frac{3}{5} \]

5. **Add the two results**:
Now we add \( \frac{625}{4} \) and \( \frac{3}{5} \). To do this, we need a common denominator:
The least common multiple of 4 and 5 is 20.
\[ \frac{625}{4} = \frac{625 \times 5}{4 \times 5} = \frac{3125}{20} \]
\[ \frac{3}{5} = \frac{3 \times 4}{5 \times 4} = \frac{12}{20} \]
Now add:
\[ \frac{3125}{20} + \frac{12}{20} = \frac{3125 + 12}{20} = \frac{3137}{20} \]

### Final Answer:
The value of the expression is:
\[ \frac{3137}{20} \]