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To solve this problem, we need to identify which two fractions from the given options can be rewritten with a denominator of 24.

We will check if the given denominators can be multiplied by an integer to reach 24:

1. **Option A: \( \frac{1}{6} \)**  
   - Can 6 be multiplied to become 24?  
   Yes, \( 6 \times 4 = 24 \). So, this fraction can be rewritten with a denominator of 24.  
   \( \frac{1}{6} = \frac{1 \times 4}{6 \times 4} = \frac{4}{24} \).

2. **Option B: \( \frac{1}{5} \)**  
   - Can 5 be multiplied to become 24?  
   No, there is no integer that makes \( 5 \times \text{integer} = 24 \).

3. **Option C: \( \frac{5}{7} \)**  
   - Can 7 be multiplied to become 24?  
   No, 7 cannot be multiplied by an integer to equal 24.

4. **Option D: \( \frac{9}{10} \)**  
   - Can 10 be multiplied to become 24?  
   No, 10 cannot be multiplied by an integer to equal 24.

5. **Option E: \( \frac{1}{9} \)**  
   - Can 9 be multiplied to become 24?  
   No, 9 cannot be multiplied by an integer to equal 24.

6. **Option F: \( \frac{7}{8} \)**  
   - Can 8 be multiplied to become 24?  
   Yes, \( 8 \times 3 = 24 \). So, this fraction can be rewritten with a denominator of 24.  
   \( \frac{7}{8} = \frac{7 \times 3}{8 \times 3} = \frac{21}{24} \).

### Conclusion:  
The two fractions that can be rewritten with a denominator of 24 are:  
- **A ( \( \frac{1}{6} \) )**  
- **F ( \( \frac{7}{8} \) )**

Would you like further details on the process or any other questions?

### Follow-up Questions:
1. How do you simplify fractions to their lowest terms?
2. Can any fraction be rewritten with any denominator?
3. What is the general method for converting fractions to a common denominator?
4. How can you determine if two fractions are equivalent?
5. How do improper fractions relate to mixed numbers?

**Tip:** Always ensure the denominator is a multiple of the target number when converting fractions to have a common denominator.

Select two fractions that can be rewritten with a denominator of 24.

Learn how to determine which fractions can be rewritten with a denominator of 24. This problem involves finding common denominators and applying the concept of multiplying fractions to achieve the same denominator. The fractions selected are from a list including 1/6, 1/5, 5/7, 9/10, 1/9, and 7/8. Suitable for students in Grades 5-7.

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