Difficulty: Easy
Correct Answer: 1/6
Explanation:
Introduction:
This question tests your understanding of comparing fractions and finding the numerical difference between them. Being able to order fractions and compute differences is important for solving ratio, proportion, and percentage problems in aptitude tests.
Given Data / Assumptions:
Concept / Approach:
There are two practical methods: convert each fraction to a decimal or bring them to a common denominator. For quick comparisons, approximate decimals are often easiest. Once we know which is smallest and which is largest, we subtract them using fraction arithmetic to obtain the exact difference.
Step-by-Step Solution:
Step 1: Convert each fraction to decimal for comparison.2/3 ≈ 0.6667.3/4 = 0.75.4/5 = 0.8.5/6 ≈ 0.8333.Step 2: Identify smallest and largest.The smallest value is 2/3 (≈ 0.6667).The largest value is 5/6 (≈ 0.8333).Step 3: Compute the difference: 5/6 − 2/3.Step 4: Express 2/3 with denominator 6: 2/3 = 4/6.Step 5: Now subtract: 5/6 − 4/6 = (5 − 4)/6 = 1/6.So the difference is 1/6.
Verification / Alternative check:
Using decimals, approximate difference is 0.8333 − 0.6667 ≈ 0.1666. The fraction 1/6 is equal to approximately 0.1666, which confirms that the exact fractional difference is 1/6.
Why Other Options Are Wrong:
1/12 is about 0.0833, which is only half the actual difference. 1/20 is 0.05 and 1/30 is about 0.0333, both too small. 1/15 is about 0.0667, also too small. Only 1/6 matches the calculated difference between 5/6 and 2/3.
Common Pitfalls:
Some learners may incorrectly assume that 2/3 is larger than 5/6 or compare only numerators without considering denominators. Others may make errors in converting to decimals or subtracting fractions with unlike denominators. Always use a consistent method, such as converting to a common denominator or accurately using decimal approximations.
Final Answer:
The difference between the largest and smallest fractions is 1/6.
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