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Let's analyze each statement to determine which ones are true about rational and irrational numbers:

1. **Since it is a ratio of two integers, \( \frac{15}{6} \) is irrational.**  
   **Analysis**: A rational number is defined as a number that can be expressed as a ratio of two integers. Here, \( \frac{15}{6} \) is a ratio of two integers, which simplifies to \( \frac{5}{2} \). Since this is a fraction of two integers, it is **rational**, not irrational.  
   **Conclusion**: This statement is **false**.

2. **Since 7 is not a perfect square, \( \sqrt{7} \) is irrational.**  
   **Analysis**: If a number is not a perfect square, then its square root is not a rational number. Since 7 is not a perfect square, \( \sqrt{7} \) is indeed irrational.  
   **Conclusion**: This statement is **true**.

3. **Since it is a terminating decimal, 8.4 is rational.**  
   **Analysis**: A terminating decimal can be written as a fraction of two integers (in this case, \( \frac{84}{10} \) which simplifies to \( \frac{42}{5} \)). Therefore, it is a rational number.  
   **Conclusion**: This statement is **true**.

4. **Since it is a repeating decimal, \( 16.\overline{43} \) is irrational.**  
   **Analysis**: A repeating decimal is always a rational number because it can be represented as a fraction. \( 16.\overline{43} \) can be expressed as a fraction of two integers, making it rational.  
   **Conclusion**: This statement is **false**.

5. **Since it is an integer, \( -15 \) is rational.**  
   **Analysis**: Any integer can be expressed as a fraction (e.g., \( -15 = \frac{-15}{1} \)). Therefore, \( -15 \) is a rational number.  
   **Conclusion**: This statement is **true**.

6. **None of the above statements are true.**  
   **Analysis**: We found that statements 2, 3, and 5 are true, so this statement is not correct.  
   **Conclusion**: This statement is **false**.

### True Statements:
- **Statement 2**: \( \sqrt{7} \) is irrational.
- **Statement 3**: 8.4 is rational.
- **Statement 5**: \( -15 \) is rational.

Would you like further details or explanations on any part of this? 

### Related Questions:

1. What makes a number rational or irrational?
2. How can you convert repeating decimals to fractions?
3. Why are square roots of non-perfect squares irrational?
4. How can you simplify a fraction like \( \frac{15}{6} \)?
5. What is the difference between terminating and repeating decimals?

**Tip:** When determining if a number is rational or irrational, remember that rational numbers can always be expressed as a fraction of two integers.

Identifying true statements about rational and irrational numbers.

Explore the distinctions between rational and irrational numbers through examples including square roots, terminating decimals, and repeating decimals. Suitable for students in grades 6 to 9, this page clarifies concepts with detailed analyses of common confusions in mathematics.

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