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The question displayed in your image asks you to compare the values of the following fractions:

- \( \frac{9}{16} \)
- \( \frac{7}{12} \)
- \( \frac{1}{3} \)
- \( \frac{5}{12} \)

You are instructed to determine the fraction with the greatest value by using strategies such as:

- **Common denominator**
- **Common numerator**
- **Benchmark fractions**

You are also asked not to convert the fractions to decimals.

### Solution Strategy:
We can approach this using the **common denominator** method. Here's how:

1. The denominators are 16, 12, and 3. Find the **least common denominator (LCD)** of these numbers. The LCD of 16, 12, and 3 is **48**.
   
2. Now convert each fraction to have a denominator of 48:
   - \( \frac{9}{16} = \frac{9 \times 3}{16 \times 3} = \frac{27}{48} \)
   - \( \frac{7}{12} = \frac{7 \times 4}{12 \times 4} = \frac{28}{48} \)
   - \( \frac{1}{3} = \frac{1 \times 16}{3 \times 16} = \frac{16}{48} \)
   - \( \frac{5}{12} = \frac{5 \times 4}{12 \times 4} = \frac{20}{48} \)

3. Compare the numerators:
   - \( \frac{27}{48} \)
   - \( \frac{28}{48} \)
   - \( \frac{16}{48} \)
   - \( \frac{20}{48} \)

The largest numerator is 28, which corresponds to \( \frac{7}{12} \).

### Conclusion:
The fraction with the greatest value is **\( \frac{7}{12} \)**.

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Do you need more details or further explanation on any part of the solution?

Here are 5 related questions you might find helpful:
1. How can I quickly find the least common denominator of fractions?
2. How does using benchmark fractions help compare fractions?
3. What is the difference between using common denominators and common numerators in comparing fractions?
4. What role do visual models, like number lines or fraction bars, play in comparing fractions?
5. Can mixed numbers be compared in the same way as proper fractions?

**Tip:** When comparing fractions, using common denominators often simplifies the comparison, especially when the numerators are close in value.

Compare the values of the fractions: 9/16, 7/12, 1/3, and 5/12. Determine the greatest fraction using strategies such as common denominator, common numerator, or benchmark fractions.

Learn how to compare fractions like 9/16, 7/12, 1/3, and 5/12 using the common denominator and benchmark fraction strategies. This step-by-step guide simplifies the process of finding the greatest fraction. Ideal for students in Grades 5-7.

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