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The question asks you to compare four fractions: \( \frac{23}{24}, \frac{23}{27}, \frac{24}{23}, \frac{27}{23} \), using strategies like common denominators, common numerators, or benchmark fractions, without converting them to decimals.

### Let's evaluate:

1. **Use of Common Numerators:**
   - Fractions with the same numerator (23 in this case) can be compared by their denominators. The smaller the denominator, the larger the fraction. 
   - So, \( \frac{23}{24} \) vs. \( \frac{23}{27} \): Since 24 < 27, \( \frac{23}{24} \) is greater than \( \frac{23}{27} \).

2. **Comparing Other Fractions:**
   - Now, look at \( \frac{24}{23} \) and \( \frac{27}{23} \): Both have the same denominator, so the larger numerator will give the larger fraction.
   - Since 27 > 24, \( \frac{27}{23} \) is greater than \( \frac{24}{23} \).

3. **Overall Comparison:**
   - Comparing \( \frac{23}{24} \) (just less than 1) with \( \frac{24}{23} \) (greater than 1) and \( \frac{27}{23} \) (also greater than 1), it's clear that both \( \frac{24}{23} \) and \( \frac{27}{23} \) are larger than \( \frac{23}{24} \).
   - Between \( \frac{23}{24} \) and \( \frac{23}{27} \), we've established \( \frac{23}{24} \) is greater.
   - So, \( \frac{27}{23} \) is the greatest fraction.

### Conclusion:
The fraction with the greatest value is \( \frac{27}{23} \).

Let me know if you'd like more detailed steps!

### Relative Questions:
1. How can you visually represent fractions like \( \frac{23}{24} \) vs. \( \frac{23}{27} \)?
2. Why does having a smaller denominator make a fraction larger when the numerator is constant?
3. What method can you use to convert improper fractions to mixed numbers, and does it help in comparison?
4. What are benchmark fractions, and how can they simplify comparisons?
5. Why are improper fractions always larger than 1 when the numerator exceeds the denominator?

### Tip:
When comparing fractions, keeping the numerator constant and varying the denominator is a quick way to determine relative sizes—smaller denominators result in larger values!

Compare the values of the fractions 23/24, 23/27, 24/23, 27/23 using strategies like common denominators, numerators, or benchmark fractions.

Learn how to compare fractions like 23/24, 23/27, 24/23, and 27/23 by using strategies such as common numerators, common denominators, and benchmark fractions. Suitable for Grades 5-7, this solution focuses on visualizing and understanding improper fractions.

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