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The question asks whether Arjun's statement is correct regarding fractions with a denominator of 12 always producing repeating decimals. He claims that since \( \frac{1}{12} \) and \( \frac{2}{12} \) produce repeating decimal values, all fractions with denominator 12 will do so.

Let's analyze the situation:

- \( \frac{1}{12} = 0.08333\ldots \) (a repeating decimal).
- \( \frac{2}{12} = 0.16666\ldots \) (also a repeating decimal).

Arjun assumes that this pattern applies to any fraction with a denominator of 12.

However, not all fractions produce repeating decimals. For instance:
- \( \frac{3}{12} = 0.25 \), which is a terminating decimal.

Therefore, Arjun's claim is incorrect. While many fractions with a denominator of 12 do produce repeating decimals, not all of them do, as demonstrated by \( \frac{3}{12} \), which results in a terminating decimal.

The correct answer is **No**.

Would you like further details on how repeating and terminating decimals work?

Here are five related questions to expand your knowledge:
1. What types of fractions result in repeating decimals?
2. How can you determine whether a fraction will produce a repeating or terminating decimal?
3. Are there other common denominators like 12 that produce both repeating and terminating decimals?
4. What is the relationship between prime factors of a denominator and repeating decimals?
5. How do you convert a repeating decimal back into a fraction?

**Tip:** A fraction produces a terminating decimal if its denominator has only the prime factors 2 and 5 after simplification. Otherwise, it will result in a repeating decimal.

Arjun says that because 1/12 and 2/12 produce repeating decimal values, any fraction with a denominator of 12 will also produce a repeating decimal. Is Arjun correct?

Explore whether all fractions with denominator 12 produce repeating decimals. Learn the difference between repeating and terminating decimals through examples like 1/12, 2/12, and 3/12. Ideal for students in Grades 5-7.

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