Sudha planted tomatoes in 1/2 portion of her kitchen garden. She planted spinach in one-fourth of the remaining portion. What fraction of the garden has spinach?

Options

A. `1/2`
B. `1/3`
C. `1/8`
D. `1/5`

Answer

To solve the problem step by step, we will follow these calculations:

1. **Identify the total portion of the garden**: The total portion of the garden is represented by 1 (which means 100% of the garden).

2. **Determine the portion of the garden where tomatoes are planted**: Sudha planted tomatoes in half of her garden. This can be expressed as:
\[ \text{Portion for tomatoes} = \frac{1}{2} \]

3. **Calculate the remaining portion of the garden**: To find the remaining portion of the garden after planting tomatoes, we subtract the portion used for tomatoes from the total garden:
\[ \text{Remaining portion} = 1 - \frac{1}{2} = \frac{1}{2} \]

4. **Determine the portion of the remaining garden where spinach is planted**: Sudha planted spinach in one-fourth of the remaining portion. We need to calculate one-fourth of the remaining portion:
\[ \text{Portion for spinach} = \frac{1}{4} \times \text{Remaining portion} = \frac{1}{4} \times \frac{1}{2} \]

5. **Perform the multiplication**: To multiply the fractions, we multiply the numerators and the denominators:
\[ \text{Portion for spinach} = \frac{1 \times 1}{4 \times 2} = \frac{1}{8} \]

6. **Conclusion**: Therefore, the fraction of the garden that has spinach is:
\[ \text{Fraction of garden with spinach} = \frac{1}{8} \]

### Final Answer:
The fraction of the garden that has spinach is \(\frac{1}{8}\).