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!