7. Which of the following is the largest? (1m)
(a) 1001/100
(b) 1001/101
(c) 101/51
(d) 101/52
Which is the Largest: 1001/100, 1001/101, 101/51, or 101/52?
1001/100 is the largest value among the options.
Option Analysis
Direct division shows the approximate values: 1001/100 equals 10.01, 1001/101 equals about 9.91, 101/51 equals about 1.98, and 101/52 equals about 1.94. Option (a) exceeds 10, while (b) falls below it since the larger denominator reduces the quotient for the same numerator. Options (c) and (d) remain under 2, as 101 divided by numbers over 50 yields less than 2.
Comparison Methods
Cross-multiplication confirms without decimals: for (a) and (b), 1001 × 101 = 101101 exceeds 100 × 1001 = 100100, so 1001/100 > 1001/101. Comparing (c) and (d), 101 × 52 = 5252 surpasses 51 × 101 = 5151, so 101/51 > 101/52. All pairs show (a) dwarfs the rest, as 1001/100 × 51 > 101 confirms dominance over (c).
Why 1001/100 Wins
The numerator 1001 pairs best with the smallest denominator 100 among viable options, maximizing the result. Smaller numerators like 101 with larger denominators (51 or 52) produce minimal values near 2. This pattern holds in competitive math exams testing fraction comparisons.
In competitive exams like CSIR NET or math olympiads, questions like “which is the largest fraction among 1001/100, 1001/101, 101/51, 101/52” test quick fraction comparison skills. The largest fraction here is 1001/100 at 10.01, outpacing others due to its high numerator-to-denominator ratio. This guide breaks down every option with precise calculations and SEO-optimized tips for mastering largest fraction comparisons.
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1001/100 = 10.01: Highest value; smallest denominator boosts it over similar pairs.
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1001/101 ≈ 9.91: Slightly smaller as 101 > 100 reduces quotient.
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101/51 ≈ 1.98: Moderate but far below 10 due to tiny numerator.
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101/52 ≈ 1.94: Smallest; largest denominator minimizes it.
Cross-multiplication avoids decimals: 1001/100 > 1001/101 since 1001×101 > 100×1001. Similarly, 101/51 > 101/52 as 101×52 > 51×101. Practice these for fastest solves in exams targeting largest fraction 1001/100 1001/101 101/51 101/52 queries.
