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To find fractions equivalent to \( \frac{4}{10} \), we need fractions that simplify to the same value as \( \frac{4}{10} \) or have a proportional numerator and denominator.

### Step 1: Simplify \( \frac{4}{10} \)
The fraction \( \frac{4}{10} \) simplifies to \( \frac{2}{5} \) by dividing both the numerator and denominator by 2.

### Step 2: Check Each Option
1. **\( \frac{2}{8} \)**: Simplifies to \( \frac{1}{4} \), so it is *not* equivalent.
2. **\( \frac{1}{6} \)**: Cannot be simplified further, and is not equivalent to \( \frac{2}{5} \).
3. **\( \frac{2}{5} \)**: Already matches the simplified form of \( \frac{4}{10} \), so this is correct.
4. **\( \frac{8}{10} \)**: Simplifies to \( \frac{4}{5} \), so it is *not* equivalent.
5. **\( \frac{40}{100} \)**: Simplifies to \( \frac{2}{5} \), which matches, so this is also correct.

### Conclusion
The equivalent fractions to \( \frac{4}{10} \) are:
- \( \frac{2}{5} \)
- \( \frac{40}{100} \)

Would you like more details on how I simplified each fraction? 

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Here are five related questions:
1. How do you find equivalent fractions for a given fraction?
2. What are some other fractions equivalent to \( \frac{2}{5} \)?
3. How can you verify if two fractions are equivalent?
4. How does simplifying fractions help in finding equivalents?
5. Why is finding equivalent fractions useful in real-life math problems?

**Tip:** Always try dividing both the numerator and denominator by their greatest common factor (GCF) to simplify a fraction quickly!

Which fractions are equivalent to 4/10? Choose all the correct answers from the options: 2/8, 1/6, 2/5, 8/10, and 40/100.

Explore how to find equivalent fractions for 4/10 with a detailed step-by-step solution. Learn to simplify fractions and identify equivalent values like 2/5 and 40/100. Perfect for students in Grades 4-6.

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