Compare the fractions 29/6 and 43/12 and identify which of the given comparison statements is definitely true.

Introduction / Context:
This is a basic arithmetic problem that asks you to compare two fractions and select the correct relationship. Such questions test comfort with equivalent fractions and simple numerical comparisons without a calculator.

Given Data / Assumptions:

• Fractions involved: 29/6, 43/12 and 53/12.
• We must decide which comparison between 29/6 and the other fractions is definitely correct.
• No approximation or rounding is allowed; the relation must be exact.

Concept / Approach:
When comparing fractions with different denominators, it is safest to convert them to a common denominator. Here the denominators are 6 and 12, so the least common denominator is 12. Once the denominators are the same, we only need to compare the numerators to determine whether one fraction is greater than, less than or equal to the other.

Step-by-Step Solution:
Step 1: Convert 29/6 to an equivalent fraction with denominator 12. Multiply top and bottom by 2. Step 2: 29/6 becomes (29 × 2) / (6 × 2) = 58/12. Step 3: Compare 58/12 with 43/12. Since both have denominator 12, compare numerators: 58 is greater than 43. Step 4: Therefore 29/6 > 43/12. This matches option B. Step 5: Briefly check other options. 29/6 = 43/12 would require 58 = 43, which is false. 29/6 = 53/12 would require 58 = 53, also false. 29/6 < 43/12 contradicts 58 > 43. 29/6 < 53/12 contradicts 58 > 53.

Verification / Alternative check:
As a quick mental check, convert to decimals. 29/6 is approximately 4.83, while 43/12 is approximately 3.58 and 53/12 is approximately 4.42. Clearly 4.83 is greater than both 3.58 and 4.42, so 29/6 is the largest of the three fractions, which is consistent with the exact comparison above.

Why Other Options Are Wrong:
Options A and D assert equalities, but equalities require identical numerators once denominators match. This is not the case here. Option C reverses the correct inequality sign, and option E also gives the wrong direction of comparison with 53/12. Only option B expresses the true relationship based on exact arithmetic.

Common Pitfalls:
Candidates sometimes compare fractions by looking only at denominators or only at numerators, which can be misleading. Another pitfall is relying on rough guesses instead of computing equivalent fractions or simple decimal values. Using a common denominator is a reliable and fast method for such questions.

Final Answer:
The definitely true statement is 29/6 > 43/12.