Reduce the fraction 2714/5074 to its lowest terms (that is, express it in simplest fractional form).

Introduction / Context:
Reducing fractions to lowest terms is a standard operation in arithmetic and is used repeatedly in algebra, ratio and proportion, and data interpretation. Here, we are given a relatively large fraction, 2714/5074, and we must simplify it by cancelling out common factors from the numerator and the denominator.

Given Data / Assumptions:

• Original fraction: 2714/5074.
• We need to find an equivalent fraction that has the smallest possible positive numerator and denominator.
• The answer must match one of the options provided.

Concept / Approach:
To reduce a fraction to lowest terms, we divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD can be found by prime factorization, using the Euclidean algorithm, or testing divisibility by likely factors. Once we divide numerator and denominator by the GCD, the resulting fraction is in simplest form and will be unique.

Step-by-Step Solution:
Step 1: Consider the fraction 2714/5074. Step 2: Look for common factors between 2714 and 5074. Both numbers are even, so they are divisible by 2. Step 3: 2714 ÷ 2 = 1357 and 5074 ÷ 2 = 2537. So we can rewrite the fraction as 1357/2537. Step 4: Now look for a common factor between 1357 and 2537. Through further factor checking, we find that 2714 and 5074 actually share a greater common divisor, 118. Step 5: Divide numerator and denominator by 118 directly: 2714 ÷ 118 = 23 and 5074 ÷ 118 = 43. Step 6: The fraction simplifies exactly to 23/43. Step 7: Check if 23 and 43 have any common factor other than 1. Both are prime and distinct, so 23/43 is in lowest terms.

Verification / Alternative Check:
We can verify by multiplying back: 23 * 118 = 2714 and 43 * 118 = 5074. Since both are exact, 118 is indeed a common factor and 23/43 is the reduced fraction. No smaller common factor exists for 23 and 43, so we have the correct simplest form.

Why Other Options Are Wrong:
17/23, 29/43 and 31/37 do not yield 2714/5074 when multiplied by any common integer factor. For example, 17/23 would correspond to 17k/23k, which cannot match 2714/5074 for an integer k. Hence those options are not equivalent to the given fraction.

Common Pitfalls:
Students may stop after dividing by a small factor like 2 and assume the result is in simplest form. However, it is important to check if a larger common factor exists. Using the GCD or the Euclidean algorithm helps avoid premature stopping and ensures the fraction is fully reduced.

Final Answer:
The fraction 2714/5074 in lowest terms is 23/43.