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Let's solve this problem step by step.

### Problem Breakdown:
- **Fraction of red fruits**: \( \frac{1}{5} \) of all the fruits are red.
- **Fraction of red fruits that are apples**: \( \frac{2}{3} \) of the red fruits are apples.

### Steps to Solve:
1. **Determine the fraction of fruits that are red apples**:
   \[
   \text{Fraction of red apples} = \frac{1}{5} \times \frac{2}{3} = \frac{2}{15}
   \]
   
2. **Determine the fraction of fruits that are *not* red apples**:
   Since the total fraction of all fruits is 1, the fraction of fruits that are not red apples is:
   \[
   \text{Fraction of non-red apples} = 1 - \frac{2}{15} = \frac{15}{15} - \frac{2}{15} = \frac{13}{15}
   \]

### Conclusion:
The correct answer is **13/15**, which matches the option you've highlighted in yellow.

Would you like more details or have any further questions? Here are some related questions that might interest you:

1. How do you calculate the fraction of one part of a whole when given the proportions of the parts?
2. What is the general method for finding the fraction of a whole when given multiple steps?
3. How does multiplying fractions work in practical examples?
4. How can we express the remaining part of a whole after a fraction is taken out?
5. Can you find a similar problem involving different fractions and percentages?

**Tip:** Always double-check the fractions by simplifying or converting them to a common denominator to avoid mistakes.

One-fifth of all the fruits on a certain basket are red, and two-thirds of all the red fruits are apples. What fraction of all the fruits are not red apples?

Solve a fraction-based problem involving fruits where one-fifth are red and two-thirds of those red fruits are apples. Learn how to calculate what fraction of all the fruits are not red apples with this detailed step-by-step solution. Suitable for Grades 5-7.

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