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.