What percent of `(2)/(7)` is `(1)/(35)` ?

Options

A. `2.5%`
B. `10%`
C. `20%`
D. `25%`

Answer

To find what percent of \( \frac{2}{7} \) is \( \frac{1}{35} \), we can set up the equation as follows:

1. **Set up the equation**: Let \( x \) be the percentage we are trying to find. We can express the relationship as:
\[ x\% \text{ of } \frac{2}{7} = \frac{1}{35} \]
This can be rewritten in equation form:
\[ \frac{x}{100} \cdot \frac{2}{7} = \frac{1}{35} \]

2. **Multiply both sides by 100**: To eliminate the fraction on the left side, multiply both sides of the equation by 100:
\[ x \cdot \frac{2}{7} = \frac{100}{35} \]

3. **Simplify \( \frac{100}{35} \)**: We can simplify \( \frac{100}{35} \):
\[ \frac{100}{35} = \frac{20}{7} \]

4. **Substitute back into the equation**: Now we have:
\[ x \cdot \frac{2}{7} = \frac{20}{7} \]

5. **Divide both sides by \( \frac{2}{7} \)**: To isolate \( x \), divide both sides by \( \frac{2}{7} \):
\[ x = \frac{20}{7} \div \frac{2}{7} \]

6. **Perform the division**: Dividing by a fraction is the same as multiplying by its reciprocal:
\[ x = \frac{20}{7} \cdot \frac{7}{2} = \frac{20 \cdot 7}{7 \cdot 2} = \frac{20}{2} = 10 \]

7. **Conclusion**: Therefore, \( x = 10 \). This means that \( \frac{1}{35} \) is \( 10\% \) of \( \frac{2}{7} \).

### Final Answer:
\[ \text{The answer is } 10\%. \]