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To solve this task, we need to match pairs of equivalent fractions among the given options. Let's analyze each fraction to see which ones can be simplified or converted to match others.

The fractions provided are:
1. \( \frac{3}{4} \)
2. \( \frac{6}{10} \)
3. \( \frac{2}{5} \)
4. \( \frac{3}{5} \)
5. \( \frac{4}{10} \)
6. \( \frac{9}{12} \)

### Steps to Find Equivalent Fractions

1. **Simplify each fraction (if possible) and compare them**:

   - \( \frac{3}{4} \) cannot be simplified further.
   - \( \frac{6}{10} \) simplifies to \( \frac{3}{5} \) (dividing both the numerator and the denominator by 2).
   - \( \frac{2}{5} \) cannot be simplified further.
   - \( \frac{3}{5} \) cannot be simplified further.
   - \( \frac{4}{10} \) simplifies to \( \frac{2}{5} \) (dividing both the numerator and the denominator by 2).
   - \( \frac{9}{12} \) simplifies to \( \frac{3}{4} \) (dividing both the numerator and the denominator by 3).

2. **Pair the equivalent fractions**:

   - \( \frac{3}{4} \) is equivalent to \( \frac{9}{12} \).
   - \( \frac{6}{10} \) is equivalent to \( \frac{3}{5} \).
   - \( \frac{2}{5} \) is equivalent to \( \frac{4}{10} \).

### Solution

The matching pairs are:
- \( \frac{3}{4} \) and \( \frac{9}{12} \)
- \( \frac{6}{10} \) and \( \frac{3}{5} \)
- \( \frac{2}{5} \) and \( \frac{4}{10} \)

Would you like further details on this? 

### Additional Questions to Expand Understanding

1. How do we determine if two fractions are equivalent?
2. What other methods can be used to check fraction equivalency?
3. Can you find equivalent fractions by cross-multiplication?
4. What does simplifying a fraction mean, and why is it useful?
5. Are there other equivalent fractions for \( \frac{3}{4} \)?

### Tip
When simplifying fractions, always divide by the greatest common divisor (GCD) of the numerator and the denominator to make the fraction fully simplified.

Match pairs of equivalent fractions among the given options.

Understand how to match pairs of equivalent fractions with this example. Learn key concepts of simplifying fractions, cross-multiplying, and finding equivalent pairs, ideal for students in Grades 4-6.

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