Compare fractions to find the smallest value: Among 11/13, 9/11, 3/4, and 5/7, determine which fraction is the smallest.
Aptitude
Decimal Fraction
Difficulty: Easy
Choose an option
-
A11/13
-
B9/11
-
C3/4
-
D5/7
Answer
Correct Answer: 5/7
Explanation
Introduction / Context:Comparing fractions appears frequently in aptitude tests. Efficient techniques include converting to decimals mentally, using cross-multiplication for pairs, or bringing them to a common denominator. Here we identify the smallest among four familiar ratios.
Given Data / Assumptions:
- Candidates: 11/13, 9/11, 3/4, 5/7
- All are proper fractions between 0 and 1.
Concept / Approach:Two quick approaches: approximate decimal values or cross-multiply pairwise against a benchmark. Noting that denominators near numerators give fractions close to 1; larger gaps yield smaller values. Compute or estimate to rank them reliably.
Step-by-Step Solution:
11/13 ≈ 0.84629/11 ≈ 0.81823/4 = 0.755/7 ≈ 0.7143Smallest ≈ 0.7143 ⇒ 5/7Verification / Alternative check:
Cross-compare 5/7 vs 3/4: 5*4 = 20; 3*7 = 21 ⇒ 20 < 21 so 5/7 < 3/4. Similarly check against 9/11 and 11/13 to confirm.Why Other Options Are Wrong:
- 11/13, 9/11, 3/4: Each has a value greater than 5/7 when compared by cross-multiplication or decimal conversion.
Common Pitfalls:
- Assuming larger denominators always imply smaller values without considering numerators.
- Rounding errors when estimating decimals too coarsely.
Final Answer:
5/7