In this fraction based number analogy, “3/7 is to 7/3 as 9/2 is to ______”. Select the fraction that completes the analogy by following the same reciprocal pattern where the numerator and denominator are interchanged.

Introduction / Context:
This question is a simple fraction analogy from quantitative aptitude. The pair 3/7 : 7/3 shows a clear numerical relationship between two fractions. The task is to apply the same relationship to the second fraction 9/2 and select the correct related fraction from the given options. Questions of this type test the candidate's understanding of basic fraction operations and pattern recognition rather than heavy calculation.

Given Data / Assumptions:

• First pair of fractions: 3/7 and 7/3. • Second fraction: 9/2 with an unknown partner. • Options: 2/9, -9/2, 7/2, -2/9. • All fractions are assumed to be ordinary rational numbers with non zero denominators.

Concept / Approach:
Look at how 3/7 is transformed into 7/3. Here, the numerator and denominator simply interchange their positions. This operation produces what is known as the reciprocal of a fraction. The reciprocal of a fraction a/b is b/a. Therefore, 3/7 becomes 7/3. If the analogy is based on taking reciprocals, then 9/2 must be mapped to its reciprocal as well. We then check which option represents that reciprocal.

Step-by-Step Solution:
Step 1: Identify the pattern in the first pair. 3/7 becomes 7/3 by swapping numerator and denominator. Step 2: Express this in general terms. If the first fraction is a/b, the second is b/a. This is the reciprocal pattern. Step 3: Apply the pattern to 9/2. For 9/2, a = 9 and b = 2. The reciprocal is 2/9. Step 4: Match with the options. Among the given options, 2/9 is present and matches the required reciprocal.

Verification / Alternative check:
To confirm, take the reciprocal of 2/9 and see if it returns 9/2, which it does. Also check that no sign change or extra multiplication is involved in the first pair. 3/7 is positive and 7/3 is also positive. Hence, introducing a negative sign for 9/2 would break the pattern. The most natural and consistent rule is simple reciprocation without any additional operations or sign changes.

Why Other Options Are Wrong:
• -9/2: This keeps the original fraction but introduces a negative sign; no such sign change appears in the example pair. • 7/2: This does not arise from any direct reciprocal relation with 9/2. • -2/9: This is the negative reciprocal, which again is not suggested by the first pair.

Common Pitfalls:
A common mistake is to focus on the numerical values and attempt operations such as addition or subtraction instead of noticing the simple interchange of numerator and denominator. Another error is to assume that a sign change is involved without any evidence in the given pair. In fraction analogies, always check for reciprocal and inversion patterns first, as they are very frequently used.

Final Answer:
The fraction that correctly completes the analogy is 2/9.