In this fraction analogy, -3/7 is related to 7/3 by a clear numeric rule; using the same rule, determine the fraction related to 9/2: -3/7 : 7/3 :: 9/2 : ?

Introduction / Context:
This question is a fraction analogy that tests your understanding of reciprocals and sign changes. The given pair -3/7 : 7/3 shows how one fraction is transformed into another. You are required to apply exactly the same transformation to 9/2 and select the correct resulting fraction from the options. Such questions reinforce concepts like reciprocal, absolute value and negative sign handling in arithmetic.

Given Data / Assumptions:

• The first fraction in the example pair is -3/7.
• The second fraction in the example pair is 7/3.
• The first fraction in the target pair is 9/2, a positive fraction.
• We assume basic familiarity with how reciprocals of fractions are computed.

Concept / Approach:
We start by examining how -3/7 becomes 7/3. The reciprocal of a fraction a/b is b/a. The reciprocal of -3/7 is -7/3, but the given result is 7/3, which is the positive reciprocal. Therefore, the transformation appears to be "take the reciprocal and drop the negative sign, that is, use the absolute value of the reciprocal." Once we confirm this rule, we apply it step by step to 9/2.

Step-by-Step Solution:
Step 1: Write the given fraction -3/7.Step 2: Compute its reciprocal. Reciprocal of -3/7 is -7/3.Step 3: Compare this with the given image fraction 7/3. The difference is that the sign has been made positive.Step 4: Conclude that the transformation from -3/7 to 7/3 is "take the reciprocal and then take the absolute value," meaning we remove the negative sign.Step 5: Apply the same rule to 9/2. First, compute the reciprocal: reciprocal of 9/2 is 2/9.Step 6: Since 9/2 is already positive, the reciprocal 2/9 is also positive, and taking absolute value does not change it.Step 7: Therefore, the fraction corresponding to 9/2 under this rule is 2/9.

Verification / Alternative check:
We can verify by checking each option against the discovered rule. The reciprocal of 9/2 is 2/9. Any answer that is not 2/9 or that introduces an unnecessary negative sign would break the pattern. Option A is 2/9 and matches the positive reciprocal exactly. Options B and D both involve negative signs, which are inconsistent with the loss of negativity in the first pair, while option C, 7/2, is unrelated to reciprocals of 9/2. This confirms 2/9 as the correct answer.

Why Other Options Are Wrong:
Option B, -9/2, simply reproduces the original fraction with a negative sign and does not involve any reciprocal. Option C, 7/2, neither matches the reciprocal nor reflects any simple relation to 9/2. Option D, -2/9, is the negative reciprocal, but the example pair shows that the mapping removes the negative sign in the result. Therefore, these three options do not obey the same transformation used between -3/7 and 7/3.

Common Pitfalls:
A common mistake is to think the rule is "just take the reciprocal" and then incorrectly choose -2/9 because of confusion about the sign. Another pitfall is to focus only on the numeric values and ignore the sign change between -3/7 and 7/3. To avoid this, always check both the magnitude and the sign of the numbers when you deduce the transformation from the first pair.

Final Answer:
Applying the same rule to 9/2 gives the positive reciprocal 2/9, so option A is correct.