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To classify the fractions into their respective categories, let's evaluate each fraction compared to \( \frac{1}{2} \) and 1.

1. **\(\frac{2}{3}\)**: 
   - \( \frac{2}{3} \approx 0.6667 \), which is greater than \( \frac{1}{2} \) but less than 1.
   
2. **\(\frac{6}{8}\)**: 
   - Simplifies to \( \frac{3}{4} \), which is also greater than \( \frac{1}{2} \) but less than 1.
   
3. **\(\frac{5}{10}\)**: 
   - Simplifies to \( \frac{1}{2} \), so this is equivalent to \( \frac{1}{2} \).
   
4. **\(\frac{1}{5}\)**: 
   - \( \frac{1}{5} = 0.2 \), which is less than \( \frac{1}{2} \).
   
5. **\(\frac{2}{7}\)**: 
   - \( \frac{2}{7} \approx 0.2857 \), which is also less than \( \frac{1}{2} \).
   
6. **\(\frac{3}{2}\)**: 
   - \( \frac{3}{2} = 1.5 \), which is greater than 1.
   
7. **\(\frac{12}{4}\)**: 
   - Simplifies to 3, which is greater than 1.

### Correct categories:

- **Less than \( \frac{1}{2} \)**: \( \frac{1}{5}, \frac{2}{7} \)
- **Equivalent to \( \frac{1}{2} \)**: \( \frac{5}{10} \)
- **Greater than \( \frac{1}{2} \) but less than 1**: \( \frac{2}{3}, \frac{6}{8} \)
- **Greater than 1**: \( \frac{3}{2}, \frac{12}{4} \)

Would you like further details on any of these calculations?

Here are some follow-up questions:
1. Can you explain how to compare fractions like \( \frac{2}{7} \) to \( \frac{1}{2} \)?
2. How do you simplify fractions like \( \frac{6}{8} \)?
3. What happens when a fraction's numerator is larger than its denominator, such as \( \frac{3}{2} \)?
4. How do you convert improper fractions like \( \frac{12}{4} \) into whole numbers?
5. Why is \( \frac{5}{10} \) equivalent to \( \frac{1}{2} \)?

**Tip**: When comparing fractions, converting them to decimals or using cross-multiplication can help simplify the process.

Drag and drop each fraction into the correct category: less than 1/2, equivalent to 1/2, greater than 1/2 but less than 1, greater than 1. Fractions provided: 2/3, 6/8, 5/10, 1/5, 2/7, 3/2, 12/4.

Learn how to classify fractions based on their value compared to 1/2. This exercise involves comparing fractions like 2/3, 6/8, 5/10, 1/5, 2/7, 3/2, and 12/4. Suitable for students in Grades 4-6.

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