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To determine which fractions correspond to terminating decimals and which correspond to repeating decimals, we need to examine their denominators after reducing them to their lowest terms.

### Key Rule:
A fraction will result in a **terminating decimal** if its denominator (after simplification) only contains the prime factors **2** and/or **5**. If the denominator contains any prime factors other than 2 or 5, the decimal will be **repeating**.

Let's go through each fraction:

1. **7/25**: The denominator is 25, which is \( 5^2 \). Since 25 is made up of only the prime factor 5, this fraction has a terminating decimal.

2. **7/11**: The denominator is 11, which is a prime number other than 2 or 5. Hence, this fraction has a repeating decimal.

3. **4/5**: The denominator is 5, which is a prime factor. Therefore, this fraction has a terminating decimal.

4. **5/6**: The denominator is 6, which factors into \( 2 \times 3 \). Since 3 is a prime number other than 2 or 5, this fraction has a repeating decimal.

5. **8/15**: The denominator is 15, which factors into \( 3 \times 5 \). Since 3 is present, this fraction has a repeating decimal.

### Classification:

- **Terminating Decimal**: 7/25, 4/5
- **Repeating Decimal**: 7/11, 5/6, 8/15

Let me know if you would like further clarification or additional details!

Here are 5 relative questions to expand this topic:
1. Why do prime factors 2 and 5 result in terminating decimals?
2. Can you simplify fractions to check if they will have a terminating decimal?
3. What is the difference between a repeating decimal and a terminating decimal?
4. How can you convert a repeating decimal into a fraction?
5. Can all fractions be converted into either a terminating or repeating decimal?

**Tip:** Always check the prime factorization of a fraction's denominator to determine whether it will terminate or repeat!

Which of the fractions would be written as a terminating decimal and which would be written as a repeating decimal? Classify fractions: 7/25, 7/11, 4/5, 5/6, 8/15.

Learn how to classify fractions as either terminating or repeating decimals. This problem involves identifying the prime factorization of the denominator to determine the type of decimal. Explore examples such as 7/25, 7/11, 4/5, and more, with clear explanations. Suitable for Grades 5-7.

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