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Let's examine the answers you provided to determine which fractions are equivalent.

1. **\( \frac{1}{2} \) and \( \frac{1}{3} \)**  
   - **Not equivalent**: Correct. These fractions are not the same, as they don’t simplify to the same fraction.

2. **\( \frac{2}{14} \) and \( \frac{3}{21} \)**  
   - **Equivalent**: Correct. Simplifying both fractions:
     - \( \frac{2}{14} = \frac{1}{7} \)
     - \( \frac{3}{21} = \frac{1}{7} \)
   - Both simplify to \( \frac{1}{7} \).

3. **\( \frac{5}{6} \) and \( \frac{15}{18} \)**  
   - **Equivalent**: Correct. Simplifying both fractions:
     - \( \frac{5}{6} \) is already in its simplest form.
     - \( \frac{15}{18} = \frac{5}{6} \)
   - Both are equivalent as they reduce to \( \frac{5}{6} \).

4. **\( \frac{8}{24} \) and \( \frac{20}{60} \)**  
   - **Equivalent**: Correct. Simplifying both fractions:
     - \( \frac{8}{24} = \frac{1}{3} \)
     - \( \frac{20}{60} = \frac{1}{3} \)
   - Both simplify to \( \frac{1}{3} \).

5. **\( \frac{15}{20} \) and \( \frac{20}{25} \)**  
   - **Equivalent**: Correct. Simplifying both fractions:
     - \( \frac{15}{20} = \frac{3}{4} \)
     - \( \frac{20}{25} = \frac{4}{5} \)
   - This one appears to be incorrect, as \( \frac{3}{4} \neq \frac{4}{5} \).

Your answers are mostly correct, except for the last one. Let me know if you'd like more details!

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Here are some questions related to equivalent fractions for further exploration:

1. How do you determine if two fractions are equivalent?
2. What are the steps to simplify a fraction?
3. Can two fractions with different numerators and denominators ever be equivalent?
4. Why is it important to express fractions in their simplest form?
5. How can you use cross-multiplication to check for equivalent fractions?

**Tip:** Always simplify fractions to their lowest terms when checking for equivalency—it makes comparisons clearer!

Explore how to identify equivalent fractions by simplifying them to their lowest terms. This exercise includes various fraction pairs, providing a step-by-step solution to determine if they are equivalent. Suitable for students in Grades 5-6.

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