`a% ` of b `+ b %` of a =__________

Options

A. `2a%` of b
B. `2a%` of 2b
C. `2a%` of 2a
D. `2b%` of 2b

Answer

To solve the problem \( a\% \text{ of } b + b\% \text{ of } a \), we can break it down step by step.

### Step-by-Step Solution:

1. **Understand the percentage notation**:
- \( a\% \) means \( \frac{a}{100} \).
- \( b\% \) means \( \frac{b}{100} \).

2. **Calculate \( a\% \text{ of } b \)**:
- This can be expressed as:
\[ a\% \text{ of } b = \frac{a}{100} \times b = \frac{ab}{100} \]

3. **Calculate \( b\% \text{ of } a \)**:
- This can be expressed as:
\[ b\% \text{ of } a = \frac{b}{100} \times a = \frac{ba}{100} = \frac{ab}{100} \]

4. **Add the two results together**:
- Now we combine both results:
\[ a\% \text{ of } b + b\% \text{ of } a = \frac{ab}{100} + \frac{ab}{100} \]
- This simplifies to:
\[ = \frac{ab + ab}{100} = \frac{2ab}{100} \]

5. **Simplify the expression**:
- We can further simplify:
\[ = \frac{2ab}{100} = \frac{2}{100} \times ab = \frac{1}{50} \times ab \]

6. **Final Result**:
- Therefore, the final answer is:
\[ a\% \text{ of } b + b\% \text{ of } a = \frac{2ab}{100} \]