Among the fractions 12/49, 7/30, 13/56 and 11/46, which one has the greatest value?

Introduction / Context:
This question checks your understanding of how to compare fractions without converting all of them into long decimals. Being able to decide which fraction is largest is a common aptitude skill used in data interpretation, number comparisons and exams where speed matters.

Given Data / Assumptions:

• We have four fractions: 12/49, 7/30, 13/56 and 11/46.
• All denominators are positive, so normal comparison rules apply.
• We must identify the fraction with the greatest numerical value.

Concept / Approach:
To compare fractions, two standard methods are common: converting them to decimals or converting them to a common denominator using cross multiplication. Cross multiplication is efficient and avoids actual division. If a/b and c/d are positive, then a/b > c/d if and only if a * d > c * b.

Step-by-Step Solution:
Step 1: Compare 12/49 and 7/30. Compute cross products: 12 * 30 = 360 and 7 * 49 = 343. Since 360 > 343, 12/49 > 7/30.Step 2: Compare 12/49 and 13/56. Compute: 12 * 56 = 672 and 13 * 49 = 637. Since 672 > 637, 12/49 > 13/56.Step 3: Compare 12/49 and 11/46. Compute: 12 * 46 = 552 and 11 * 49 = 539. Since 552 > 539, 12/49 > 11/46.Step 4: Since 12/49 is larger than each of the other three fractions individually, it is the greatest among the four options.

Verification / Alternative check:
You can convert each fraction to an approximate decimal: 12/49 ≈ 0.245, 7/30 ≈ 0.233, 13/56 ≈ 0.232, and 11/46 ≈ 0.239. The approximate decimal values confirm that 12/49 is the largest.Both methods, cross multiplication and decimal approximation, lead to the same conclusion, which verifies our answer.

Why Other Options Are Wrong:
7/30 is smaller than 12/49 because its cross product with 12/49 is lower.13/56 is also smaller, as its cross product comparison gives a lower product than 12/49.11/46 is close in value but still slightly smaller than 12/49 when compared using cross multiplication.

Common Pitfalls:
Many learners try to compare by looking only at numerators or denominators separately, which does not work for general fractions.Rounding too early or approximating very roughly can lead to mistakes when fractions are close in value.Some candidates may incorrectly assume that the fraction with the largest numerator or smallest denominator is always the greatest, which is not necessarily true.

Final Answer:
The largest fraction is 12/49.